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JP3286372B2 - Pressure wave dispersion device in tubular passage for high-speed train - Google Patents
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JP3286372B2 - Pressure wave dispersion device in tubular passage for high-speed train - Google Patents

Pressure wave dispersion device in tubular passage for high-speed train

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Publication number
JP3286372B2
JP3286372B2 JP02875193A JP2875193A JP3286372B2 JP 3286372 B2 JP3286372 B2 JP 3286372B2 JP 02875193 A JP02875193 A JP 02875193A JP 2875193 A JP2875193 A JP 2875193A JP 3286372 B2 JP3286372 B2 JP 3286372B2
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JP
Japan
Prior art keywords
wave
tunnel
pressure
frequency
container
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Lifetime
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JP02875193A
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Japanese (ja)
Other versions
JPH074200A (en
Inventor
信正 杉本
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Individual
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Individual
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Description

【発明の詳細な説明】DETAILED DESCRIPTION OF THE INVENTION

【0001】[0001]

【産業上の利用分野】本発明は,高速列車用管状通路内
の圧力波分散装置等として構成する管状通路構造に関す
るものである。将来の高速大量輸送手段としてリニア新
幹線の早期実現が望まれているが,環境騒音をいかに低
減させるかが大きな問題である。そこで,列車を山間部
の,しかもトンネル内を走行させることによって,騒音
問題を極力回避することが考えられる。しかし,人口密
集地域ではそうもいかず,列車の通行路を管状にして防
音をはかる必要が生じる。これが実現すれば,列車は今
までにない長い管状通路(以下単にトンネルという)内
を,しかも高速で走行することになる。
BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a tubular passage structure constructed as a pressure wave dispersion device in a tubular passage for a high-speed train. The early realization of the linear Shinkansen as a future high-speed mass transportation is desired, but how to reduce environmental noise is a major problem. Therefore, it is conceivable to avoid the noise problem as much as possible by running the train in mountainous areas and in tunnels. However, in densely populated areas, this is not the case, and it is necessary to make the train passages tubular to provide soundproofing. If this were realized, the train would travel in an ever-longer tubular path (hereinafter simply referred to as a tunnel) and at a higher speed.

【0002】列車が走行することによって引き起こされ
る圧力変動は,トンネル内を音波として伝播する。その
とき,トンネルが一種の導波管の役割を果たすため,特
に低周波の圧力波は空間の3次元的な広がりによる減衰
をうけることなく,遠方まで伝播することになる。走行
速度の上昇に伴い圧力変動が大きくなると,圧力波が伝
播するうちに,いわゆる非線形(有限振幅)効果によっ
て波形変形を起こし,列車の遙か遠方の予想もしない場
所で衝撃波が発生する。本発明は,高速列車がトンネル
内を走行することによって発生する圧力波を分散させる
ことによって,前述の衝撃波の発生を防止し,騒音を低
減させるものである。
[0002] Pressure fluctuations caused by running a train propagate as sound waves in a tunnel. At that time, since the tunnel plays a role of a kind of waveguide, the low-frequency pressure wave propagates to a distant place without being attenuated by the three-dimensional expansion of the space. When the pressure fluctuation increases with the increase in traveling speed, the waveform is deformed by the so-called nonlinear (finite amplitude) effect while the pressure wave propagates, and a shock wave is generated at an unexpected place far away from the train. The present invention is to prevent the above-mentioned shock wave from being generated and reduce noise by dispersing pressure waves generated by a high-speed train traveling in a tunnel.

【0003】[0003]

【従来の技術】山陽新幹線が建設された当初,列車がト
ンネルに進入する際に,トンネル出口側で大きな破裂音
を伴う騒音問題が発生した。これは微気圧波問題として
知られている。現在,この問題は,トンネル出入口にフ
ードを設け,列車がトンネルに持ち込む空気の量を少し
でも少なくする対策によりある程度軽減されている。し
かし,リニア新幹線のような超高速になれば,フードだ
けの対策では不十分であることは既に指摘されており,
新しい抜本的な方法が待望されている。そこで本出願人
は,抜本策の一つとして,トンネルの周辺に多数のしか
も種類の異なった幾つかのヘルムホルツ共鳴器列(以下
単に共鳴器列という)を取り付け,その固有(共鳴)周
波数を圧力波の周波数にあわせて設定することにより,
圧力波を減衰させ,衝撃波を防止することを,特開平4
−353193号公報として既に提案した。
2. Description of the Related Art When the Sanyo Shinkansen was constructed, when a train entered a tunnel, a noise problem accompanied by a loud popping sound occurred at the exit of the tunnel. This is known as the micro-pressure wave problem. Currently, this problem has been alleviated to some extent by installing hoods at the entrances and exits of the tunnel and reducing the amount of air that the train brings into the tunnel. However, it has already been pointed out that at ultra-high speeds such as the linear Shinkansen, measures using only the hood are not sufficient.
There is a long-awaited need for new drastic methods. Accordingly, as one of the drastic measures, the applicant has installed a number of Helmholtz resonator rows (hereinafter simply referred to as resonator rows) around the tunnel and changed their natural (resonant) frequency to pressure. By setting according to the frequency of the wave,
Japanese Patent Application Laid-Open No. Hei 4
No. 353193.

【0004】[0004]

【発明が解決しようとする課題】衝撃波が発生するメカ
ニズムは,圧力波の大きさが大きくなると,その伝播速
度がもはや音速ではなく,それより速く,しかも圧力波
の大きさと共に増大する。従って,最初,如何に圧力波
の波形が,空間的にも時間的にも,滑らかであっても,
圧力の高いところの伝播速度が,低いところの伝播速度
より速いために,波形が伝播するうちに次第に‘つっ立
ち’現象を起こすようになる。これが更に進行すると,
圧力波形勾配が非常に大きくなり,あたかも不連続的に
変化する箇所が発生する。これがいわゆる衝撃波であ
る。衝撃波が出現すれば,圧力の急激な変化に伴う高周
波成分が発生し,それが破裂音として聞こえる。また,
衝撃波がトンネル出口から放射されると,出口から十分
離れた地点の音圧は,出口手前での圧力の時間に関する
微分,すなわち勾配に比例して大きくなる。このため,
波形勾配がいわば無限大になるような衝撃波が発生する
と,深刻な環境騒音問題を引き起こす。本発明は以上の
問題点を解消するものである。
The mechanism by which a shock wave is generated is such that as the size of a pressure wave increases, the speed of propagation of the shock wave is no longer the speed of sound, but it is faster and increases with the size of the pressure wave. Therefore, at first, no matter how smooth the waveform of the pressure wave is, spatially, temporally,
Since the propagation speed at a high pressure is higher than the propagation speed at a low pressure, a 'stick-out' phenomenon occurs gradually as the waveform propagates. As this progresses further,
The pressure waveform gradient becomes very large, and a portion occurs as if it changes discontinuously. This is a so-called shock wave. When a shock wave appears, a high-frequency component is generated due to a sudden change in pressure, which is heard as a plosive sound. Also,
When a shock wave is emitted from the tunnel exit, the sound pressure at a point sufficiently far from the exit increases in proportion to the time derivative of the pressure before the exit, that is, the gradient. For this reason,
The generation of a shock wave with a waveform gradient of infinity causes a serious environmental noise problem. The present invention solves the above problems.

【0005】[0005]

【課題を解決するための手段】本発明が解決しようとす
る課題は以上の如くであり,次に該課題を解決するため
の手段を説明する。即ち,トンネルの壁面に,ある体積
をもった閉鎖容器もしくは閉鎖空洞を,トンネルの横断
面の周方向に一つないし複数個埋め込み,しかも通路方
向にも多数設置し,さらに各容器または各空洞とトンネ
ルとを開口連結する。容器とは,設置以前に既に何らか
の形状をもつ空間であるのに対して,ここでいう空洞と
は,何らかの方法で(壁や蓋等を設けることによって)
壁面に作り上げた空間を指す。容器であれ,空洞であ
れ,ここで重要なのは,ある体積をもつ閉鎖空間が確保
されることである。そこで以後簡単のため,容器もしく
は空洞と呼ぶ代わりに,しばしば単に容器としか呼ばな
い場合がある。本発明の特徴は,既に提案した共鳴器で
なくても,どのような形の容器であってもよい。ただ,
それらは後に示す音響インピーダンスに関する条件を満
足しさえすればよい。
The problem to be solved by the present invention is as described above. Next, means for solving the problem will be described. That is, one or more closed vessels or closed cavities with a certain volume are embedded in the tunnel wall in the circumferential direction of the cross section of the tunnel, and a large number of them are installed in the direction of the passage. Open connection with tunnel. A container is a space that already has some shape before installation, whereas a cavity here is somehow (by providing a wall, lid, etc.)
Refers to the space created on the wall. What is important here, whether a container or a cavity, is that a closed space with a certain volume is ensured. Therefore, for the sake of simplicity, instead of being called a container or a cavity, it is often simply called a container. A feature of the present invention is not limited to the resonator already proposed, but may be any type of container. However,
They only need to satisfy the conditions regarding acoustic impedance described later.

【0006】容器の代表的な例は,既に提案した共鳴器
がある。しかし,本装置では容器による分散効果を目的
としているので,それを減衰装置として用いるときに比
べて小さくとれる。従って,図1に示すようにトンネル
壁面内に取り付けることが出来る。また,もう一つの簡
単な例として,図2に示すような空洞断面の形が奥行き
方向に一定である‘4分の1波長管’が考えられる。こ
の変形として,図3に示すような,奥行き方向に緩やか
な曲率をもった4分の1波長管を,トンネルの周方向に
設けたり,図4に示すようにトンネルの長さ方向に取り
付けてもよい。さらに,これらの併用したものも考えら
れる。いずれにしても,トンネル壁面にいくつかの容器
を埋め込む。このとき,個々の容器の大きさは異なって
もよいが,簡単のため,一種類の同じ大きさの容器をト
ンネルの長さ方向に等間隔dで取り付ける場合を考え
る。
A typical example of the container is a resonator already proposed. However, since the present device aims at the dispersion effect of the container, it can be made smaller than when it is used as an attenuation device. Therefore, it can be mounted inside the tunnel wall as shown in FIG. Another simple example is a 'quarter-wavelength tube' in which the shape of the cavity cross section is constant in the depth direction as shown in FIG. As a modification, a quarter-wave tube having a gentle curvature in the depth direction as shown in FIG. 3 is provided in the circumferential direction of the tunnel, or is attached in the length direction of the tunnel as shown in FIG. Is also good. Furthermore, a combination of these is also conceivable. In any case, bury some containers on the tunnel wall. At this time, the size of each container may be different, but for the sake of simplicity, a case where one kind of the same size container is attached at equal intervals d in the length direction of the tunnel is considered.

【0007】容器列の効果は,次の二つのパラメータを
通して現れる。一つは,容器の大きさと取り付け間隔を
表す‘結合係数’と呼ぶK(=V/2εAd;ε(<<
1))である。ここで,Vは後に定義する容器の‘実質
体積’,εは圧力波の変動圧力の最大値Δpと大気圧p
0 の比に係数[(γ+1)/2γ](ただし,γは空気
の比熱比で,1.4である)を掛けたもの。Aはトンネ
ルの断面積である。もし,トンネルの周方向に同じ容器
をm個(mは正の整数)取り付けたときには,Kをm倍
する(Vをm倍するか,dをd/mと置くことに相当す
る)。もう一つのパラメータは,容器の固有(共鳴)周
波数ω0 と音波の代表周波数ωとの比の自乗で定義され
る‘同調係数’Ω(=(ω0 /ω)2 )である。共鳴器
列の場合には,Vはスロート部を除く容器の体積に等
しく,共鳴周波数ω0は,公知のように(Ba0 2/L
V)1/2 で与えられる。ただし,Bはトンネルとの取り
付け部でのスロート3の断面積,Lは管端補正をしたス
ロート3の有効長さ,そしてa0 は音速である。また,
図2に示す4分の1波長管では,その断面積をB,管端
補正をした有効奥行きをLとすると,Vはこのときも容
器の体積BLに等しく,最も小さな固有周波数ω0 はπ
0 /2Lで与えられる。
[0007] The effect of the row of containers appears through the following two parameters. One is K (= V / 2εAd; ε (<<), which is called “coupling coefficient” that indicates the size of the container and the mounting interval.
1)). Here, V is the 'real volume' of the container defined later, ε is the maximum value Δp of the fluctuation pressure of the pressure wave and the atmospheric pressure p
The value obtained by multiplying the ratio of 0 by the coefficient [(γ + 1) / 2γ] (where γ is the specific heat ratio of air and is 1.4). A is the cross-sectional area of the tunnel. If m same containers (m is a positive integer) are mounted in the circumferential direction of the tunnel, K is multiplied by m (equivalent to multiplying V by m or setting d to d / m). Another parameter is the 'tuning coefficient' Ω (= (ω 0 / ω) 2 ) defined by the square of the ratio of the natural (resonant) frequency ω 0 of the container and the representative frequency ω of the sound wave. In the case of a resonator row, V is equal to the volume of the container except for the three parts of the throat, and the resonance frequency ω 0 is known (Ba 0 2 / L
V) given by 1/2 . However, B is the effective length of the throat 3 the cross-sectional area of the throat 3 in the mounting portion of the tunnel, L is where the tube end correction, and a 0 is the speed of sound. Also,
In the quarter wavelength tube shown in FIG. 2, assuming that the cross-sectional area is B and the effective depth after tube end correction is L, V is still equal to the volume BL of the container, and the smallest natural frequency ω 0 is π
given by a 0 / 2L.

【0008】[0008]

【作用】衝撃波の発生を防ぐには,一つにはそれが発生
するまでに圧力波を速やかに減衰させることであり,圧
力減衰装置の作用として既に提案した。もう一つは,本
出願のように,衝撃波形成に至るつっ立ちを‘分散によ
り’抑え込むことである。圧力波の強さが大きくなる
と,単なる減衰作用だけで抑制することは不十分であ
る。これに対し,分散によってつっ立ちを抑えること
は,本質的な衝撃波防止法になる。分散とは,圧力波を
構成する各周波数の波の伝播速度が,周波数によって異
なることであり,もちろん,普通のトンネル内を伝わる
音波ではこの分散はない。
[Action] One way to prevent the generation of shock waves is to rapidly attenuate the pressure waves before they occur, which has already been proposed as an action of the pressure damping device. The other is, as in the present application, to suppress the occurrence of shock waves by 'dispersion'. When the intensity of the pressure wave increases, it is not sufficient to suppress the pressure wave by a mere damping effect. On the other hand, suppressing swelling by dispersion is an essential shock wave prevention method. The term “dispersion” means that the propagation speed of each of the frequencies constituting the pressure wave differs depending on the frequency. Of course, there is no such dispersion in a sound wave transmitted through a normal tunnel.

【0009】ところで,空間的な周期構造をもつ波動系
では,ブロッホ(Bloch)波と呼ばれるモードの波
が新しく出現することが量子力学において知られてい
る。その大きな特徴は,波が周期構造に依存する分散性
を示す点である。いま考えているような容器列を周期的
に取り付けたトンネル内を伝播する音波の場合も同様
で,容器を取り付けることにより,音波が反射や透過を
繰り返すうちに分散性が発生する。分散性は,つっ立ち
により生じる多くの高周波成分の各々の伝播速度を異な
らせしめ,圧力波形勾配の急峻化を抑制し,衝撃波の発
生を防止する。ブロッホ波のもう一つの特徴として,あ
る周波数帯では,波が伝播出来ない,いわゆる‘ストッ
プバンド’が現れることである。そのバンドの周波数成
分は,壁面摩擦等の散逸とは異なったメカニズムの減衰
作用をうける。このストップバンドをうまく利用すると
分散と同時に減衰も期待でき,衝撃波の防止には非常に
好都合である。以下,容器列の効果を定量化するため
に,トンネル内の音波の伝播を定式化する。
It is known in quantum mechanics that a wave of a mode called a Bloch wave newly appears in a wave system having a spatial periodic structure. The major feature is that the waves show dispersibility that depends on the periodic structure. The same applies to the case of sound waves propagating in a tunnel in which a row of containers is periodically attached, as is now considered. By attaching a container, dispersibility occurs while the sound waves are repeatedly reflected and transmitted. The dispersibility makes the propagation speed of each of many high-frequency components generated by the rise different, suppresses the steepness of the pressure waveform gradient, and prevents the generation of shock waves. Another characteristic of Bloch waves is that in certain frequency bands, a so-called 'stop band', in which waves cannot propagate, appears. The frequency component of the band is subject to a damping effect of a mechanism different from dissipation such as wall friction. If this stop band is used well, attenuation can be expected at the same time as dispersion, which is very convenient for preventing shock waves. In the following, in order to quantify the effect of the row of vessels, the sound wave propagation in the tunnel is formulated.

【0010】(定式化) 1.トンネル内のブロッホ波の線形分散関係式 周期的に容器を取り付けたトンネル内の音波の伝播特性
を知るために,ブロッホ波の線形分散関係式を示す。無
限に長いトンネルに,ある大きさをもつ適当な形状の容
器を等間隔で取り付ける。その容器の特性は,以下に定
義される音響インピーダンスで特徴づけられるとする。
容器取り付け部での圧力をpとしたとき,そこでの変動
(超過)圧力p’(=p−p0 :p0 は大気圧)がPe
xp(−iωt)+c.c.のように角周波数ωで変化
しているものとする。ただし,Pは複素振幅,iは虚数
単位で,tは時間である。また,c.c.はその前の項
の複素共役を表す。この圧力変動に応じて,容器へ流入
する空気の体積流量BvもQexp(−iωt)と変化
するものとする。ただし,Bは容器のトンネル取り付け
部での断面積,vは容器へ流入する空気の流速で,Qは
複素振幅である。それら複素振幅の比P/Qが,音響イ
ンピーダンスZを与える。一般に,音響インピーダンス
はiωの関数で,複素数である。その具体的な形は,共
鳴器の場合,
(Formulation) Linear dispersion relation of Bloch wave in tunnel The linear dispersion relation of Bloch wave is shown in order to know the propagation characteristics of sound wave in a tunnel with a periodically attached vessel. An infinitely long tunnel is fitted with equally sized containers of equal size at equal intervals. The characteristics of the container shall be characterized by the acoustic impedance defined below.
When the pressure at the container mounting portion is p, the fluctuating (excess) pressure p ′ (= p−p 0 : p 0 is atmospheric pressure) is Pe.
xp (−iωt) + c. c. Is changed at the angular frequency ω. Here, P is a complex amplitude, i is an imaginary unit, and t is time. Also, c. c. Represents the complex conjugate of the preceding term. It is assumed that the volume flow rate Bv of the air flowing into the container also changes to Qexp (−iωt) according to the pressure fluctuation. Here, B is the cross-sectional area of the container at the tunnel mounting portion, v is the flow velocity of the air flowing into the container, and Q is the complex amplitude. The ratio P / Q of the complex amplitudes gives the acoustic impedance Z. Generally, the acoustic impedance is a function of iω and is a complex number. The specific shape is, in the case of a resonator,

【数1】 で与えられる。ただし,ρ0 は静止平衡状態での空気の
密度である。また,4分の1波長管では,Zは
(Equation 1) Given by Here, ρ 0 is the density of air in the static equilibrium state. In a quarter-wave tube, Z is

【数2】 となる。(Equation 2) Becomes

【0011】二つの隣合う容器の間にはさまれたトンネ
ルにそれぞれ番号n(nは整数で,n=...−2,−
1,0,1,2...)を付け,n番目のトンネル内で
の変動圧力p’が,Φ(x)exp[i(qx−ω
t)]+c.c.のように変化する素解が存在する。こ
こで,xはトンネルの長さ方向の座標で,Φ(x)は周
期dをもつ周期関数,そしてqは波数である。このΦ及
びqを,ブロッホ波の波動関数及び波数という。波数q
と周波数ωとは,次のブロッホ波の分散関係式で関係づ
けられる:
Each of the tunnels sandwiched between two adjacent containers has a number n (n is an integer, n = ...- 2,-).
1,0,1,2,. . . ), And the fluctuating pressure p ′ in the n-th tunnel is Φ (x) exp [i (qx−ω
t)] + c. c. There exists a solution that changes as follows. Here, x is a coordinate in the length direction of the tunnel, Φ (x) is a periodic function having a period d, and q is a wave number. These Φ and q are called the wave function and wave number of the Bloch wave. Wave number q
And the frequency ω are related by the following Bloch dispersion relation:

【数3】 ここで,RはZとトンネルの音響インピーダンスρ0
0 /Aとの比である:
(Equation 3) Here, R is the acoustic impedance ρ 0 a of the tunnel and Z
It is the ratio to 0 / A:

【数4】 いま,Zがトンネルの音響インピーダンスに比べて十分
大きいときには,数式3から明らかなように,右辺第2
項が十分小さくなる。いま,R→∞とすると,qはω/
0 となり,分散性のない普通の音波の分散関係式に帰
着する。これは,高周波の音波,換言すれば取り付け間
隔dが音波の波長に比べて長過ぎる場合には,分散性が
発生しないことを示している。しかし,Rが小さくなる
と,qはω/a0 からずれ,その差が周波数に依存す
る,すなわち分散性を示すようになる。qは一般には実
数であるが,しかし周波数に応じて複素数にもなりう
る。これは,音波の拡散効果や壁面での摩擦を全く無視
しても発生することに注意したい。このとき,qの実部
はπ/dの整数倍になり,qが複素数といってもその定
義からも分かるように,実質的には純虚数の場合に相当
する。qの虚数部は波の空間的な減衰を表すので,波は
伝播出来ずに,減衰をうけるだけである。具体的なブロ
ッホ波の分散関係式のグラフを,図1の共鳴器列の場
合,図2の4分の1波長管の場合,それぞれ図5,図6
に示す。ここで用いた数値は,後に示す実施例1,実施
例2において与えたものである。
(Equation 4) Now, when Z is sufficiently larger than the acoustic impedance of the tunnel, as is apparent from Equation 3, the second on the right side
The term becomes sufficiently small. Now, if R → ∞, q is ω /
a 0 , which results in an ordinary sound wave dispersion relational expression having no dispersibility. This indicates that dispersibility does not occur when the high-frequency sound wave, in other words, the mounting interval d is too long compared to the wavelength of the sound wave. However, when R decreases, q deviates from ω / a 0 , and the difference depends on the frequency, that is, shows a dispersion. q is generally real, but can also be complex depending on frequency. Note that this occurs even if the sound diffusion effect and the friction on the wall are completely ignored. At this time, the real part of q becomes an integral multiple of π / d, and even if q is a complex number, as can be seen from the definition, it substantially corresponds to the case of a pure imaginary number. Since the imaginary part of q represents the spatial decay of the wave, the wave cannot propagate and is only attenuated. Specific graphs of the Bloch wave dispersion relations are shown in FIGS. 5 and 6 for the case of the resonator array of FIG. 1 and for the case of the quarter-wavelength tube of FIG.
Shown in The numerical values used here are given in Examples 1 and 2 described later.

【0012】物理的には,この減衰は, (i)音波の周波数が容器の固有振動数に近いときの共
鳴によるもの, (ii)容器取り付け間隔が音波の半波長πa0 /ωの整
数倍に近いときの,いわゆるブラッグ(Bragg)反
射による二つからなる。図5−(2),図6−(2)に
見られるように,qdの虚部がゼロでない周波数では,
波は伝播出来ないので,この周波数帯を既に述べたよう
にストップバンドと呼び,qが実数の場合のパスバンド
と区別する。従って,多くの周波数成分を含む圧力波で
は,減衰が周波数によって選択的に発生する。ストップ
バンドの幅は,Rの大きさによって決定され,かなり小
さなR以外はその幅は狭く,大半の周波数成分は通過し
てしまう。そこでRの値を小さくする,すなわちZを小
さくするには,数式3からも分かるように,Z=0にな
る共鳴周波数を音波の周波数と一致させるか(これは既
に提案した圧力波減衰装置の原理である),または容器
取り付け部の断面積Bを大きくすることである。しか
し,Bを大きくすることは,大きな容器が必要になり,
トンネル断面積を出来るだけ小さくしたいとする経済性
を考えると問題がある。このため,Z=0近傍以外では
Rを小さくはできない。そこで,Rを小さくする代わり
に,取り付け間隔をdを小さくすることによってその効
果高めることが考えれらる。
Physically, this attenuation is due to (i) resonance when the frequency of the sound wave is close to the natural frequency of the container, and (ii) the container mounting interval is an integral multiple of the half wavelength πa 0 / ω of the sound wave. , And two due to the so-called Bragg reflection. As can be seen in FIGS. 5- (2) and 6- (2), at frequencies where the imaginary part of qd is not zero,
Since a wave cannot propagate, this frequency band is called a stop band as described above, and is distinguished from a pass band when q is a real number. Therefore, in a pressure wave including many frequency components, attenuation occurs selectively depending on the frequency. The width of the stop band is determined by the size of R, and the width of the stop band is small except for R, which is quite small, so that most frequency components pass. Therefore, in order to reduce the value of R, that is, to reduce Z, as can be seen from Equation 3, the resonance frequency at which Z = 0 is matched with the frequency of the sound wave (this is the same as that of the already proposed pressure wave damping device). The principle is to increase the sectional area B of the container mounting portion. However, increasing B requires a large container,
There is a problem when considering the economics of making the tunnel cross-sectional area as small as possible. Therefore, R cannot be reduced except in the vicinity of Z = 0. Therefore, instead of reducing R, it is conceivable to increase the effect by reducing the mounting interval d.

【0013】2.低周波非線形音波の伝播 実際トンネル内を伝播する音波のち,衝撃波形成に直接
関係するのは低周波の音波である。その波長は十分長い
ため,取り付け間隔を小さくとることは容易に実現可能
である。このとき,容器があたかも連続的に分布してい
ると見なすことができる。この状況は,ブロッホ波の分
散関係式で,ω/ω0 (もしくはqd)が1に比べて十
分小さい場合に相当している。ブロッホ波の伝播特性
は,音波の振幅が十分小さい線形波の場合であり,衝撃
波が発生するような大きな振幅になると,それに非線形
性を考慮する必要が生じる。そのため,以下に低周波の
非線形音波の伝播を定式化する。
2. Propagation of low-frequency nonlinear sound waves Actually, low-frequency sound waves are directly related to shock wave formation after sound waves propagating in the tunnel. Since the wavelength is long enough, it is easy to realize a small mounting interval. At this time, it can be considered that the containers are distributed continuously. This situation corresponds to a case where ω / ω 0 (or qd) is sufficiently smaller than 1 in the Bloch wave dispersion relational expression. The propagation characteristic of a Bloch wave is a case of a linear wave having a sufficiently small sound wave amplitude. When the amplitude becomes large enough to generate a shock wave, it is necessary to consider nonlinearity. Therefore, the propagation of low-frequency nonlinear sound waves is formulated below.

【0014】連続分布近似の下で,トンネル内を双方向
に伝わる非線形音波の挙動は次式で記述される:
Under the continuous distribution approximation, the behavior of a nonlinear sound wave propagating in a tunnel in both directions is described by the following equation:

【数5】 (複号同順)ここで,x,tは既に定義したようにトン
ネルの長さ方向の座標及び時間であり,uは音波によっ
て誘起されるx方向の速度成分である。一方,aはいわ
ゆる局所音速で,a0 とは異なり,空気の密度ρによっ
(Equation 5) Here, x and t are the coordinates and time in the length direction of the tunnel as defined above, and u is the velocity component in the x direction induced by the sound wave. On the other hand, a is the so-called local sound velocity, which is different from a 0 , depending on the density ρ of air.

【数6】 で定義される。数式5の右辺は容器列の効果を表してい
る。Nはトンネルの単位長さ当たりの容器の取り付け個
数で,1/dである(ただし,周方向にm個取り付けた
ときには,m/dとおく)。また,Bは容器のトンネル
取り付け部での断面積である。
(Equation 6) Is defined by The right side of Equation 5 represents the effect of the container row. N is the number of containers attached per unit length of the tunnel, and is 1 / d (however, when m are attached in the circumferential direction, it is m / d). B is the cross-sectional area at the tunnel mounting portion of the container.

【0015】個々の容器の体積Vは,容器取り付け間隔
当りのトンネルの体積Adに比べて十分小さいので,一
つ一つの容器はトンネル内を伝わる音波に対して大きな
影響を与えない。逆に言い換えれば,トンネル内の圧力
変動に対して,容器の応答が線形近似出来る。このと
き,容器取り付け部での流入速度vとトンネル内の変動
圧力p’とは,音響インピーダンスを用いると
Since the volume V of each container is sufficiently smaller than the volume Ad of the tunnel per container mounting interval, each container does not significantly affect the sound wave traveling through the tunnel. In other words, the response of the vessel to the pressure fluctuation in the tunnel can be linearly approximated. At this time, the inflow velocity v at the vessel mounting part and the fluctuating pressure p ′ in the tunnel are obtained by using acoustic impedance.

【数7】 で関係づけられる。ここで,Yは音響インピーダンスの
逆数である音響アドミッタンスで,B/ρ0 0 で無次
元されている。いま低周波の音波を考えているので,Y
を以下のように(−iω)で展開できるものとする:
(Equation 7) Are related by Here, Y is an acoustic admittance is the reciprocal of acoustic impedance, which is dimensionless in B / ρ 0 a 0. I'm thinking about low-frequency sound waves.
Can be expanded in (-iω) as follows:

【数8】 ここで,α,βは時間及びその3乗の次元をもつ定数で
ある。実際,この展開は,既に示した共鳴器や4分の1
波長管の場合には成立し,摩擦等による音波の散逸効果
を無視した場合,かなり一般的にいえる。本出願では,
容器はどのような形状であってもよいが,その音響アド
ミッタンスが,散逸効果を無視して考えたときに,数式
8のように展開できるものに限るものとする。これが必
要条件である。
(Equation 8) Here, α and β are constants having dimensions of time and its third power. In fact, this development is based on the resonators and quarters already shown.
This is true in the case of a wavelength tube, and it can be said that this is quite general when the effect of dissipating sound waves due to friction or the like is ignored. In this application,
Although the container may have any shape, it is assumed that its acoustic admittance is limited to one that can be developed as shown in Expression 8 when the dissipative effect is ignored. This is a necessary condition.

【0016】さて,(−iω)が∂/∂tの演算に対応
しているので,体積流量Bvは変動圧力p’によって次
のように与えられる:
Now, since (-iω) corresponds to the calculation of ∂ / ∂t, the volume flow rate Bv is given by the fluctuating pressure p 'as follows:

【数9】 この関係を数式5に用い,x軸の正方向への伝播に着目
し,変動圧力p’と流速uの関係p’〜ρ0 0 uを用
いると
(Equation 9) Using this relationship in equation 5, paying attention to the propagation in the positive direction of the x-axis, using the relationship p'~ρ 0 a 0 u of fluctuating pressure p 'flow velocity u

【数10】 と近似できる。いま変動圧力が十分小さいと仮定して,
この方程式の非線形項を無視して線形分散関係式を求め
ると,既に示したブロッホ波の分散関係式のqd<<1
の場合に一致することが確認される。数式10を一層コ
ンパクトな形にするために,遅延時間θ[=ω(t−x
/a0 ],トンネルの遠方場を記述する座標X[=εω
x/a0 ]をx,tに代わって導入する。ここで,ωは
音波の代表周波数,εは既に定義した大気圧に対する変
動圧力の最大値Δpの比に,(γ+1)/2γを掛けた
ものである。さらに,[(γ+1)/2]u/a0 をε
fとおくと,
(Equation 10) Can be approximated. Assuming now that the fluctuating pressure is sufficiently small,
When the linear dispersion relational expression is obtained by ignoring the nonlinear term of this equation, qd << 1 of the Bloch wave dispersion relational expression already described.
Is confirmed to match. To make Equation 10 more compact, the delay time θ [= ω (t−x
/ A 0 ], coordinates X [= εω describing the far field of the tunnel
x / a 0 ] is introduced instead of x, t. Here, ω is the representative frequency of the sound wave, and ε is the ratio of the previously defined maximum value Δp of the fluctuating pressure to the atmospheric pressure multiplied by (γ + 1) / 2γ. Further, [(γ + 1) / 2] u / a 0 is converted to ε
f

【数11】 なる,いわゆるコルテヴェーク−ド・フリース(Kor
teweg−de Vries)方程式(以下,単にK
−dV方程式)が導かれる。ここで,係数K及びΓはそ
れぞれ次のように与えられる:
[Equation 11] The so-called Corteweg-de-Fries (Kor
teweg-de Vries) equation (hereinafter simply K
−dV equation). Where the coefficients K and Γ are each given as follows:

【数12】 ここで,αが時間の単位をもっていることから,a0 α
は長さの次元をもち,これに断面積Bをかけると,体積
を与える。Ba0 αを容器の‘実質体積’Vと定義す
る。K,Γの具体的な値は,共鳴器の場合には,
(Equation 12) Here, since α has a unit of time, a 0 α
Has a dimension of length, multiplied by the cross-sectional area B to give a volume. Ba 0 α is defined as the 'real volume' V of the container. The specific values of K and Γ are

【数13】 となる。ここで,Ωは既に定義した共鳴器の固有周波数
ω0 と音波の代表周波数ωの比の自乗である。また,4
分の1波長管の場合
(Equation 13) Becomes Here, Ω is the square of the ratio between the natural frequency ω 0 of the resonator already defined and the representative frequency ω of the sound wave. Also, 4
In the case of a one-wavelength tube

【数14】 となる。[Equation 14] Becomes

【0017】K−dV方程式の解の性質は非常によく研
究されている。それによると,音波はもはや衝撃波を形
成せずに,パルス波状のいわゆるソリトン波列になるこ
とが知られている。個々のソリトンの具体的な波形は
The nature of the solution of the K-dV equation has been very well studied. According to this, it is known that a sound wave no longer forms a shock wave but becomes a so-called soliton wave train in the form of a pulse wave. The specific waveform of each soliton is

【数15】 で与えられ,Cはソリトンの波高,θ0 は位相である。
Cの最大値を決定するには,K−dV方程式の初期値問
題を解かねばならない。そのときCの値は,初期値の最
大値より大きくなることもあるが,いくつかのソリトン
列に分裂するときには,Cは初期値の2倍以下である。
数式15の波形を,Xを固定したある場所で時間の関数
を見ると,θの定義から分かるように,(C/12Γ)
1/2 ωの逆数がパルスの代表時間間隔(パルス幅)を与
える。換言すれば,(C/12Γ)1/2 ωは‘パルスの
代表周波数’とも見なすことができる。これから,パル
ス幅は,Cが大きくなる,もしくはΓが小さくなると,
狭くなる。従って,(C/12Γ)1/2 をどの程度の大
きさに設定するかが問題になる。それが1より大きくな
るにつれ,パルス幅が次第に狭くなり,極端に狭くなる
と,圧力波の波形勾配が大きくなりすぎ,衝撃波とは違
った新たな騒音問題が発生する恐れが生じる。
(Equation 15) Where C is the soliton wave height and θ 0 is the phase.
To determine the maximum value of C, the initial value problem of the K-dV equation must be solved. Then, the value of C may be larger than the maximum value of the initial value, but when splitting into several soliton trains, C is less than twice the initial value.
Looking at the waveform of Equation 15 from a function of time at a certain location where X is fixed, as can be seen from the definition of θ, (C / 12Γ)
The reciprocal of 1 / 2ω gives the representative time interval (pulse width) of the pulse. In other words, (C / 12Γ) 1/2 ω can be regarded as a 'representative frequency of a pulse'. From this, the pulse width becomes larger as C becomes larger or Γ becomes smaller.
Narrows. Therefore, how to set (C / 12Γ) 1/2 becomes a problem. As it becomes larger than 1, the pulse width becomes gradually narrower, and when it becomes extremely narrow, the waveform gradient of the pressure wave becomes too large, and a new noise problem different from the shock wave may occur.

【0018】最後に,解析で仮定した数式8の音響アド
ミッタンスの展開形の一般性について述べる。物理的に
は,α=0の場合は起こりえないが,β=0の場合は容
器形状により例外的に起こりうる。このとき,K−dV
方程式の3階微分が5階微分で置き換えられた方程式が
導かれる。この解でも,衝撃波は発生しないことが分か
っている。従って,衝撃波を防止する容器形状は,かな
り一般的にとることができる。
Finally, the generality of the expanded form of the acoustic admittance of Expression 8 assumed in the analysis will be described. Physically, it cannot occur when α = 0, but can occur exceptionally when β = 0 depending on the container shape. At this time, K-dV
An equation is derived in which the third derivative of the equation is replaced by the fifth derivative. Even with this solution, it is known that no shock wave is generated. Therefore, the shape of the container for preventing shock waves can be taken quite generally.

【0019】[0019]

【実施例】トンネル内の遠方場を伝播する圧力波は,ト
ンネルの断面にわたってほぼ平面波で,その周波数はい
わゆる‘低周波音波’であると予想される。その周波数
は,物理的な考察より,列車の長さをλ,列車の速度を
U,トンネルの(水力)直径をDとすると,大体a0
λもしくはU/Dと見積もられ,最高でもa0 /Dであ
ると考えられる。一方,その圧力レベルΔp/p0 の上
限は,列車断面積とトンネル断面積の比をχとすると
き,χM/(1−M)と見積もられる。ただし,Mは列
車のマッハ数で,U/a0 である。いま,λ=200
m,U=150m/s(540km/s),D=10
m,χ=0.1とすると,周波数は2〜3Hzから10
Hz程度で,いくら高くても30Hz以下の低周波数音
波である。また,音波レベルについては,最高0.1
(172dB SPL)程度は予想しておかねばならな
い。以上の見積もりから,圧力波の代表周波数ωを,1
0π rad/s(5Hz),圧力レベルは上限を想定
して,約0.08とする。これから,εを0.1と設定
する。パルス幅については,代表周波数の3倍まで(1
5Hz)許すと仮にすれば,Γ≧1/54=0.018
5に設定しなければならない。以下,幾つかの代表的な
実施例を示す。
DESCRIPTION OF THE PREFERRED EMBODIMENTS A pressure wave propagating in the far field in a tunnel is almost a plane wave over the cross section of the tunnel, and its frequency is expected to be a so-called 'low-frequency sound wave'. From physical considerations, the frequency is approximately a 0 /, where λ is the train length, U is the train speed, and D is the (hydraulic) diameter of the tunnel.
It is estimated to be λ or U / D, and is considered to be at most a 0 / D. On the other hand, the upper limit of the pressure level Δp / p 0 is estimated to be χM / (1−M), where 比 is the ratio of the train sectional area to the tunnel sectional area. However, M is the Mach number of the train, which is U / a 0. Now, λ = 200
m, U = 150 m / s (540 km / s), D = 10
Assuming that m and χ = 0.1, the frequency is 10 Hz from 2-3 Hz.
It is a low-frequency sound wave of about 30 Hz and no more than 30 Hz at most. Also, the maximum sound level is 0.1
(172 dB SPL) should be expected. From the above estimation, the representative frequency ω of the pressure wave is calculated as 1
0π rad / s (5 Hz), and the pressure level is about 0.08, assuming an upper limit. From this, ε is set to 0.1. The pulse width can be up to three times the representative frequency (1
5Hz) Assuming that it is allowed, Γ ≧ 1/54 = 0.018
Must be set to 5. Hereinafter, some typical embodiments will be described.

【0020】(実施例1) 図1の共鳴器列の例を示す。各共鳴器の形状は図1−
(3),図1−(4)に示す。空洞の体積Vを4m3
(2mx2mx1mの直方体に近い)をスロート3の断
面積Bを4π/100m2 (直径40cm),スロート
3の有効長さLを0.5mとすると,固有周波数はほぼ
14Hzとなる。この共鳴器をトンネル周方向に8個
(m=8)取り付け,長さ方向には4m間隔で取り付け
る(d=4m)と,K及びΩの値はそれぞれK=0.0
51/ε,Ω=7.4,Γ=0.069となり,設計条
件が満足される。
Embodiment 1 An example of the resonator array shown in FIG. 1 is shown. Figure 1 shows the shape of each resonator.
(3), shown in FIG. 1- (4). The volume V of the cavity 2 is 4 m 3
If the cross-sectional area B of the throat 3 is 4π / 100 m 2 (40 cm in diameter) and the effective length L of the throat 3 is 0.5 m, the natural frequency is approximately 14 Hz (closer to a rectangular parallelepiped of 2 mx 2 mx 1 m). When eight resonators (m = 8) are mounted in the tunnel circumferential direction and mounted at intervals of 4 m in the length direction (d = 4 m), the values of K and Ω are respectively K = 0.0.
51 / ε, Ω = 7.4, Γ = 0.069, which satisfies the design condition.

【0021】(実施例2) 図2の4分の1波長管を取り付けた例を示す。空洞
断面積Bを5m2 ,有効奥行きLを5mとすると,空洞
1の体積Vは25m3 となり,固有周波数は17Hzと
なる。この4分の1波長管をトンネル周方向に2個(m
=2)取り付け,長さ方向には10m間隔で取り付ける
(d=10m)と,K及びΩの値はそれぞれK=0.0
32/ε,Ω=11.6,Γ=0.023となり,設計
条件が満足される。
(Example 2) An example in which the quarter wavelength tube of FIG. 2 is attached is shown. Assuming that the sectional area B of the cavity 2 is 5 m 2 and the effective depth L is 5 m, the volume V of the cavity 1 is 25 m 3 and the natural frequency is 17 Hz. Two quarter-wave tubes (m
= 2) When attached at 10 m intervals in the length direction (d = 10 m), the values of K and Ω are respectively K = 0.0
32 / ε, Ω = 11.6, Γ = 0.023, which satisfies the design condition.

【0022】(実施例3) 図3に示す曲率をもった4分の1波長管を取り付けた例
を示す。断面積Bを4m2 ,有効奥行きLを7mとする
と,容器の体積Vは28m3 となり,固有周波数はほぼ
12Hzとなる。この4分の1波長管をトンネル周方向
に4個(m=4)取り付け,長さ方向には10m間隔で
取り付ける(d=10m)と,K及びΩの値はそれぞれ
K=0.071/ε,Ω=5.9,Γ=0.10とな
り,設計条件が満足される。これら三つの例では,圧力
レベル値をその上限であるε=0.1と想定したが,そ
れよりも低い場合には,Kの値が大きくなり,Γの値も
大きくなるので,問題はない。
(Embodiment 3) An example is shown in which a quarter-wave tube having the curvature shown in FIG. 3 is attached. Assuming that the sectional area B is 4 m 2 and the effective depth L is 7 m, the volume V of the container is 28 m 3 and the natural frequency is about 12 Hz. When four quarter-wave tubes are mounted in the tunnel circumferential direction (m = 4) and in the length direction at 10 m intervals (d = 10 m), the values of K and Ω are respectively K = 0.071 / ε, Ω = 5.9, Γ = 0.10, which satisfies the design condition. In these three examples, the pressure level value was assumed to be the upper limit, ε = 0.1, but if it is lower than that, there is no problem since the value of K increases and the value of Γ also increases. .

【0023】[0023]

【発明の効果】本出願による圧力波分散装置は,衝撃波
の発生を防止する効果はあるが,圧力波を減衰させる効
果は期待できない。これは,qd<<1なる低周波を考
えているので,大半の周波数はパスバンドに入るからで
ある。ただ,高周波数成分のうち,ストップバンドに入
る成分に対しては,減衰を起こすが,波全体としてはあ
まり減衰することなくトンネルに沿って伝播する。そこ
で,衝撃波の発生を防止すると共に,圧力波の遠方への
伝播を抑制するためには,ストップバンドをできるだけ
広くし,積極的にその減衰効果を利用することが効果的
になる。これはとりもなおさず,既に提案した圧力波減
衰装置と併用することに他ならない。現実に衝撃波を防
止し,また圧力波の遠方への伝播を抑制するには,図1
の圧力波分散装置と減衰装置とを組み合わせた図7に示
す形態が最適であると考えられる。もちろん,分散装置
としては図1の共鳴器に限らず,図2〜図4と組み合わ
せてもよい。
The pressure wave dispersion device according to the present invention has the effect of preventing the generation of shock waves, but cannot expect the effect of attenuating pressure waves. This is because most of the frequencies fall into the pass band because a low frequency of qd << 1 is considered. However, among the high-frequency components, components that fall into the stop band are attenuated, but the waves as a whole propagate along the tunnel without much attenuation. Therefore, in order to prevent the generation of a shock wave and to suppress the propagation of a pressure wave to a distant place, it is effective to make the stop band as wide as possible and positively use its damping effect. This is nothing but a combination with the already proposed pressure wave damping device. Figure 1 shows how to actually prevent shock waves and suppress the propagation of pressure waves to distant places.
The configuration shown in FIG. 7 in which the pressure wave dispersion device and the damping device are combined is considered to be optimal. Of course, the dispersing device is not limited to the resonator of FIG. 1 and may be combined with FIGS.

【図面の簡単な説明】[Brief description of the drawings]

【図1】トンネルの壁面に,その横断面の周方向に沿っ
て同じ共鳴器を8個を取り付けた例である。図1−
(1)はトンネルの横断面図,図1−(2)はトンネル
の長さ方向の側面図,図1−(3)は共鳴器の正面図,
図1−(4)は側面図,図1−(5)はア−アの断面図
である。図1−(3)の斜視部が開口部である。
FIG. 1 shows an example in which eight same resonators are attached to a wall surface of a tunnel along a circumferential direction of a cross section thereof. Figure 1
(1) is a cross-sectional view of the tunnel, FIG. 1- (2) is a side view in the length direction of the tunnel, FIG. 1- (3) is a front view of the resonator,
FIG. 1- (4) is a side view, and FIG. 1- (5) is a sectional view of the air. The perspective part in FIG. 1- (3) is the opening.

【図2】トンネルの壁面に空洞を設け,4分の1波長管
とした例である。空洞の奥行き方向(トンネルの長さ方
向に垂直)には,断面形状は一様な矩形であると,同じ
空洞をトンネル壁面相対する位置に対称的に取り付ける
ものとする。図2−(1)はトンネルのア−ア及びイ−
イでの横断面図,図2−(2)はトンネル側面図で,斜
線部が開口部である。
FIG. 2 shows an example in which a cavity is provided on the wall surface of a tunnel to form a quarter wavelength tube. In the depth direction of the cavity (perpendicular to the length direction of the tunnel), if the cross-sectional shape is a uniform rectangle, the same cavity shall be mounted symmetrically at a position facing the tunnel wall. Figure 2- (1) shows the tunnel air and air.
FIG. 2 (b) is a side sectional view of the tunnel, and the hatched portion is an opening.

【図3】トンネルの壁面に,4組の同じ4分の1波長管
を,その長さをトンネル横断面の周方向に沿って緩やか
に曲げて設置した例である。図3−(1)はトンネルの
横断面図,図3−(2)はトンネルの側面図,図3−
(3)は各4分の1波長管の正面図,図3−(4)はそ
の側面図である。斜線部が開口している。
FIG. 3 shows an example in which four sets of the same quarter-wave tubes are gently bent along the circumferential direction of the tunnel cross section on the wall surface of the tunnel. FIG. 3- (1) is a cross-sectional view of the tunnel, FIG. 3- (2) is a side view of the tunnel, FIG.
(3) is a front view of each quarter wavelength tube, and FIG. 3- (4) is a side view thereof. The shaded area is open.

【図4】トンネルの壁面に,4組の4分の1波長管を,
その長さ方向をトンネルの長さ方向に合わせて設置した
例である。この場合は,コンクリートで溝を設け,それ
に蓋をすることによって壁面内に空洞を作った例であ
る。図4−(1)はトンネルのア−ア及びイ−イでの横
断面図,図4−(2)はトンネルの側面図であり,斜線
部が開口している。
FIG. 4 shows four sets of quarter-wave tubes on the tunnel wall.
This is an example in which the length direction is set to match the length direction of the tunnel. In this case, a cavity is made in the wall by providing a groove with concrete and covering it with a lid. FIG. 4- (1) is a cross-sectional view at the air line and the eye line of the tunnel, and FIG. 4- (2) is a side view of the tunnel, where the hatched portion is open.

【図5】実施例1のトンネル内のブロッホ波の線形分散
関係式である。図5−(1)は,縦軸に共鳴器の固有周
波数ω0 で無次元化した周波数をとり,横軸には取り付
け間隔dで無次元にしたブロッホ波数qdの実部Re
{qd}を示す。図5−(2)は,縦軸に同じく固有周
波数ω0 で無次元化した周波数をとり,横軸には無次元
にしたブロッホ波qdの虚部Im{qd}を示す。虚部
が存在する周波数帯をストップバンドと呼び,それ以外
をパスバンドと呼ぶ。ストップバンドは無次元周波数が
1近傍の共鳴器の共鳴によるものと,それ以外のブラッ
グ反射によるものからなる。
FIG. 5 is a linear dispersion relational expression of a Bloch wave in a tunnel according to the first embodiment. In FIG. 5- (1), the vertical axis represents the dimensionless frequency at the natural frequency ω 0 of the resonator, and the horizontal axis represents the real part Re of the Bloch wave number qd dimensionless at the mounting interval d.
{Qd}. In FIG. 5- (2), the vertical axis indicates the frequency that is dimensionless at the natural frequency ω 0 , and the horizontal axis indicates the imaginary part Im {qd} of the dimensionless Bloch wave qd. The frequency band in which the imaginary part exists is called a stop band, and the others are called pass bands. The stop band is formed by resonance of a resonator whose dimensionless frequency is close to 1, and by other Bragg reflection.

【図6】実施例2のトンネル内のブロッホ波の線形分散
関係式である。図6−(1)は,縦軸に4分の1波長管
の最低次の固有周波数ω0 で無次元化した周波数をと
り,横軸には取り付け間隔dで無次元にしたブロッホ波
数qdの実部Re{qd}を示す。図6−(2)は,縦
軸に同じく固有周波数ω0 で無次元化した周波数をと
り,横軸には無次元ブロッホ波数qdの虚部Im{q
d}を示す。この場合,ω0 の奇数倍が全て4分の1波
長管の固有周波数に相当し,またブラッグ反射を起こす
周波数と一致する。この例では,ストップバンドはω0
の偶数倍では発生しない。
FIG. 6 is a linear dispersion relational expression of a Bloch wave in a tunnel according to the second embodiment. In FIG. 6- (1), the vertical axis indicates the dimensionless frequency at the lowest natural frequency ω 0 of the quarter-wave tube, and the horizontal axis indicates the dimensionless Bloch wave number qd at the mounting interval d. Indicates the real part Re {qd}. In FIG. 6- (2), the vertical axis represents the frequency that has been made dimensionless at the natural frequency ω 0 , and the horizontal axis represents the imaginary part Im {q of the dimensionless Bloch wave number qd.
d}. In this case, all odd multiples of ω 0 correspond to the natural frequency of the quarter-wave tube and coincide with the frequency at which Bragg reflection occurs. In this example, the stopband is ω 0
It does not occur at even multiples of.

【図7】図1に示す共鳴器列を取り付けたトンネルに,
以前に提案した圧力波減衰装置と組み合わせた例であ
る。減衰装置は,主トンネルに平行して補助トンネルを
設け,その内部を隔壁で適当な間隔に仕切ることによっ
て作られる空洞とトンネルとを連絡した構造をもつ。図
7−(1)はトンネルのア−ア及びイ−イでの横断面
図,図7−(2)は減衰装置の下面図であり,斜線部が
開口部である。
FIG. 7 shows a tunnel equipped with the resonator row shown in FIG.
This is an example in combination with a previously proposed pressure wave damping device. The damping device has a structure in which an auxiliary tunnel is provided in parallel with the main tunnel, and the inside of the auxiliary tunnel is partitioned by a partition wall at an appropriate interval, and the cavity and the tunnel are connected. FIG. 7- (1) is a cross-sectional view of the tunnel at the air line and the eye line, and FIG. 7- (2) is a bottom view of the damping device.

【符号の説明】[Explanation of symbols]

1 管状通路(トンネル) 2 空洞 3 スロート 4 主トンネル 5 圧力波減衰装置用の補助トンネル 6 圧力波減衰装置用の空洞 7 圧力波減衰装置用のスロート 8 補助トンネル内の隔壁 DESCRIPTION OF SYMBOLS 1 Tubular passage (tunnel) 2 Cavity 3 Throat 4 Main tunnel 5 Auxiliary tunnel for pressure wave damper 6 Cavity for pressure wave damper 7 Throat for pressure wave damper 8 Partition wall in auxiliary tunnel

Claims (1)

(57)【特許請求の範囲】(57) [Claims] 【請求項1】 高速列車用の管状通路1内の壁面に,一
定の体積を具備した閉鎖容器を埋め込むか,もしくは一
定の体積を具備した閉鎖空洞を設け,該容器又は空洞
一単位として,該一単位の一面を開口して管状通路1と
連通し,前記管状通路1の周方向に,同様の容器又は空
洞の複数単位を連設して容器列を構成し,また管状通路
1の長さ方向に,ある間隔をおいて該容器列を多数取り
付け,管状通路内を伝播する圧力波を構成する各周波数
の波の伝播速度に周波数依存性を発生させ,圧力波に
分散性を発生させ,圧力波形勾配の急峻化を抑制し,圧
力波形勾配が大きくなることにより不連続的に圧力波形
が変化する箇所が発生する衝撃波の発生を防止すること
を特徴とする高速列車用管状通路内の圧力波分散装置。
1. A closed container having a fixed volume is embedded in a wall in a tubular passage 1 for a high-speed train, or a closed cavity having a fixed volume is provided, and the container or the cavity is formed.
As one unit, one surface of the one unit is opened and a tubular passage 1 is formed.
Communicating with each other in the circumferential direction of the tubular passage
A container row is constructed by connecting a plurality of units of cavities, and a tubular passage
1 Take a number of the container rows at a certain interval in the length direction.
Give, by generating a frequency dependent on the speed of propagation of the wave of each frequency constituting a pressure wave propagating tubular passage, to generate dispersibility in the pressure wave, to suppress the steep pressure waveform gradient, pressure waveform A pressure wave dispersing device in a tubular passage for a high-speed train, wherein a shock wave in which a pressure waveform changes discontinuously due to an increase in gradient is prevented.
JP02875193A 1993-02-18 1993-02-18 Pressure wave dispersion device in tubular passage for high-speed train Expired - Lifetime JP3286372B2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP02875193A JP3286372B2 (en) 1993-02-18 1993-02-18 Pressure wave dispersion device in tubular passage for high-speed train

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP02875193A JP3286372B2 (en) 1993-02-18 1993-02-18 Pressure wave dispersion device in tubular passage for high-speed train

Publications (2)

Publication Number Publication Date
JPH074200A JPH074200A (en) 1995-01-10
JP3286372B2 true JP3286372B2 (en) 2002-05-27

Family

ID=12257118

Family Applications (1)

Application Number Title Priority Date Filing Date
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Country Status (1)

Country Link
JP (1) JP3286372B2 (en)

Families Citing this family (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2556439B2 (en) * 1993-11-18 1996-11-20 西日本旅客鉄道株式会社 Method of reducing air pressure noise at tunnel exit
JP4555560B2 (en) * 2003-11-25 2010-10-06 東日本旅客鉄道株式会社 Tunnel buffer
CN101929339A (en) * 2010-06-22 2010-12-29 西南交通大学 Micro-pressure wave mitigation structure in tunnel body of high-speed railway
KR101358906B1 (en) * 2011-12-07 2014-02-06 한국과학기술원 Tunnel structure for reducing micro pressure wave in tunnel
KR101356091B1 (en) * 2012-01-10 2014-01-29 한국과학기술원 Periodic Mechanical Resonance Structure in the Tunnel Wall to Reduce the Micro-pressure Wave in the High-speed Railway Tunnel
JP6356988B2 (en) * 2014-03-20 2018-07-11 大成建設株式会社 tunnel
CN111322085B (en) * 2020-03-19 2022-02-15 中南大学 Railway tunnel capable of relieving pressure fluctuation inside tunnel
CN115522951B (en) * 2022-10-25 2023-06-16 西南交通大学 Micro-air pressure wave structure of transverse channel low-air pressure control high-speed rail tunnel and control method

Also Published As

Publication number Publication date
JPH074200A (en) 1995-01-10

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