Patent Publication Number: US-8991553-B2

Title: Silencing apparatus for vehicle

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to a silencing apparatus for a vehicle, which includes a muffler having a flattened sectional shape in which the width is greater than the height, an inlet pipe through which exhaust gas flows into an inside of the muffler, an outlet pipe through which the exhaust gas flows out of the inside of the muffler, a partition plate that divides the inside of the muffler into sound-deadening chambers, and a communication hole that extends through the partition plate. 
     2. Description of Related Art 
     As a silencing apparatus for a vehicle, there is a muffler provided in an exhaust system of an internal combustion engine. The muffler disposed beneath the floor of a vehicle generally has a flattened sectional shape in which the width is greater than the height, for example, an elliptical sectional shape, en elongated circular sectional shape, etc., for the sake of mountability. 
     A muffler having a flattened sectional shape that has a width W as shown in  FIG. 13A  will be considered. In this muffler, air column resonance occurs in the width direction thereof, with two opposite ends of the muffler in the width direction thereof being closed ends. The air column resonance lowers the sound deadening performance of the muffler. The wavelength λ of a standing wave that causes air column resonance in the muffler in the width direction thereof is “2W/n (n is an integer equal to or greater than 1)”. If the sonic velocity is represented by “C (≈20×vT where T is the gas temperature within the muffler)”, the frequency f of the air column resonance is represented as “C×m/2W (m is an integer equal to or greater than 1)”. In this air column resonance, the standing waves that most conspicuously appear are two standing waves, that is, a standing wave whose wavelength λ is twice the muffler width (λ=2W) as shown in  FIG. 13B , and a standing wave whose wavelength λ is equal to the muffler width (λ=W) as shown in  FIG. 13C . 
     In related art, as a countermeasure against high-frequency exhaust sound as in the air column resonance in the width direction of a muffler, a sub-muffler that has a high-frequency resonance structure or that is filled with a sound absorbing material is provided in the exhaust system, as in Japanese Patent Application Publication No. 2009-062922 (JP-A-2009-062922). 
     If the sub-muffler is appropriately designed, it is certainly possible to restrain increase of the exhaust sound that results from the air column resonances in the width direction of the muffler. However, if the sub-muffler is installed, corresponding increases in cost and mass are inevitable. Therefore, it is demanded to provide a vehicle silencing apparatus that effectively restrains the increase of exhaust sound caused by the air column resonances in the muffler width direction at a reduced cost. 
     SUMMARY OF THE INVENTION 
     The invention provides a silencing apparatus for a vehicle, which effectively restrains the increase of exhaust sound caused by air column resonances in the width direction of a muffler. 
     PRINCIPLE OF INVENTION 
     Firstly, the principle of the invention will be explained.  FIG. 1  shows the case where, in a sound-deadening chamber  51  formed within a muffler  50  with a flattened sectional shape having a width W, openings  52  and  53  leading to the outside of the sound-deadening chamber  51  are formed at a position that is apart by a length (W/2) equal to a half of the width W of the muffler  50  from one end of the muffler  50  in the width direction thereof (a right-side end in  FIG. 1 ) and a position that is apart by a length (W/4) equal to a quarter of the width W from the same end in the width direction, respectively. In this muffler  50 , there occurs air column resonance in the width direction caused by two standing waves, that is, a standing wave (λ=2W) whose wavelength λ is twice the width W of the muffler  50  and a standing wave (λ=W) whose wavelength λ is equal to the width W of the muffler  50 . 
     When focus is placed on the opening  52  provided at the position that is apart from the end by the length of W/2, a space to the right of the opening  52  in  FIG. 2A  is a space that is open to the outside through the opening  53 . On the other hand, a space to the left side of the opening  52 , which is hatched in  FIG. 2A , is a space that is not open to the outside, that is, a space that is closed to the outside. The closed space functions as an acoustic tube having a length of W/2. The acoustic tube achieves a sound absorbing effect, that is, the effect of reducing sound caused by the air column resonance with the wavelength λ of 2W (λ=2W) shown in  FIG. 13B , by producing a standing wave that is opposite in phase due to resonance as shown in  FIG. 2B . 
     When focus is placed on the opening  53  provided at the position that is apart from the end by the length of W/4, a space to the left side of the opening  53  is a space that is open to the outside through the opening  52  as shown in  FIG. 3A . On the other hand, a space to the right side of the opening  53 , which is hatched in  FIG. 3A , is a space that is not open to the outside, that is, a space that is closed to the outside. This closed space functions as an acoustic tube having a length of W/4. The tube achieves a sound absorbing effect, that is, the effect of reducing sound caused by the air column resonance with the wavelength λ of W (λ=W) shown in  FIG. 13C , by producing a standing wave that is opposite in phase due to resonance as shown in  FIG. 3B . 
     Thus, the sound-deadening chamber  51  of the muffler  50  in which the openings  52  and  53  are formed at the above-described positions achieves the sound-absorbing effect, that is, the effect of reducing sound caused by the most conspicuous air column resonances among the air column resonances in the width direction of the muffler  50 , that is, the air column resonances with the wavelength of λ=2W and the wavelength of λ=W. Therefore, by providing the muffler  50  in which openings (communication holes) leading to the outside are formed respectively at the position that is apart by the length equal to a half of the width W of the muffler  50  from one end of the muffler  50  in the width direction and the position that is apart by the length equal to a quarter of the width W from one end of the muffler  50  in the width direction, it is possible to effectively restrain the increase of exhaust sound caused by the air column resonances in the width direction of the muffler, without a need to provide a sub-muffler. 
     A first aspect of the invention relates to a silencing apparatus for a vehicle. This silencing apparatus includes: a muffler having a flattened sectional shape in which a width is greater than a height; an inlet pipe through which exhaust gas flows into an inside of the muffler; an outlet pipe through which the exhaust gas flows out of the inside of the muffler; and at least one partition plate that divides the inside of the muffler into a plurality of sound-deadening chambers. Each of the at least one partition plate has at least one communication hole that extends through the partition plate. Within the muffler, at least one among an opening of the inlet pipe, an opening of the outlet pipe, and the at least one communication hole is disposed at a position that is apart by a length equal to a half of the width of the muffler from one end of the muffler in a width direction of the muffler, and at least one among the opening of the inlet pipe, the opening of the outlet pipe, and the at least one communication hole is disposed at a position that is apart by a length equal to a quarter of the width of the muffler from one end of the muffler in the width direction. 
     As described above, within the muffler, the opening or the communication hole, which leads to the outside of the sound-deadening chamber, is disposed at each of the position that is apart by the length equal to a half of the width W of the muffler from one end of the muffler in the width direction of the muffler and the position that is apart by the length equal to a quarter or the width W from one end in the width direction. This muffler achieves a sound absorbing effect, that is, the effect of reducing sound caused by the air column resonances with a wavelength λ of 2W (λ=2W) and a wavelength λ of W (λ=W), which most conspicuously appear among the air column resonances in the width direction of the muffler. Therefore, according to the foregoing configuration, it is possible to effectively restrain the increase of exhaust sound caused by the air column resonances in the width direction of the muffler, without a need to provide a sub-muffler. 
     In order to more reliably achieve the effect of reducing the exhaust sound, each of the opening of the inlet pipe, the opening of the outlet pipe, and the at least one communication hole may be disposed at either the position that is apart by the length equal to a half of the width of the muffler from one end of the muffler in the width direction, or the position that is apart by the length equal to a quarter of the width of the muffler from one end of the muffler in the width direction. 
     In each of the sound-deadening chambers, each of the position that is apart by the length equal to a half of the width of the muffler from one end of the muffler in the width direction of the muffler and the position that is apart by the length equal to a quarter of the width of the muffler from the same end in the width direction may be a position at which the opening of the inlet pipe, the opening of the outlet pipe, or one of the at least one communication hole is disposed. In this case, in all the sound-deadening chambers, the sound absorbing effect, that is, the effect of reducing sound caused by the air column resonances with the wavelength λ of 2W (λ=2W) and the wavelength λ of W (λ=W) is achieved, so that the increase of exhaust sound caused by the air column resonances can be more reliably restrained. 
     A second aspect of the invention relates to a silencing apparatus for a vehicle. This silencing apparatus includes: a muffler having a flattened sectional shape in which a width is greater than a height; an inlet pipe through which exhaust gas flows into an inside of the muffler; an outlet pipe through which the exhaust gas flows out of the inside of the muffler; and at least one partition plate that divides the inside of the muffler into a plurality of sound-deadening chambers. Each of the at least one partition plate has at least one communication hole that extends through the partition plate. An opening of the inlet pipe, an opening of the outlet pipe, and the at least one communication hole are disposed within the muffler. In each of the sound-deadening chambers, at least one among the opening of the inlet pipe, the opening of the outlet pipe, and the at least one communication hole is disposed at a position that is apart by a length equal to a half of the width of the muffler from one end of the muffler in a width direction of the muffler, and at least one among the opening of the inlet pipe, the opening of the outlet pipe, and the at least one communication hole is disposed at a position that is apart by a length equal to a quarter of the width from the same end in the width direction. 
     In the muffler in which the opening of the inlet pipe, the opening of the outlet pipe, and the at least one communication hole are disposed as described above, the sound absorbing effect, that is, the effect of reducing sound caused by the air column resonances with the wavelength λ of 2W (λ=2W) and the wavelength λ of W (λ=W) is achieved in all the sound-deadening chambers, so that the increase of exhaust sound caused by the air column resonances can be more reliably restrained. 
     In a fore-aft direction of the muffler, the inside of the muffler may be divided by the at least one partition plate into the sound-deadening chambers each of which has a length in the fore-aft direction of the muffler, which is greater than or equal to a quarter of the width of the muffler. In this muffler, the air column resonance in the width direction of the muffler appears particularly conspicuously. Hence, the foregoing aspects of the invention are particularly suitably applied to a vehicle silencing apparatus that includes the muffler. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Features, advantages, and technical and industrial significance of exemplary embodiments of the invention will be described below with reference to the accompanying drawings, in which like numerals denote like elements, and wherein: 
         FIG. 1  is a sectional view schematically showing a sectional elevation view of a muffler presented as a model for explaining the principle or the invention; 
         FIG. 2A  is a sectional view showing a manner of forming a closed space, that functions as an acoustic tube, when focus is placed on an opening that is formed at a position that is apart by a length equal to a half of the width from an end of the muffler in a width direction thereof, and  FIG. 2B  is a graph showing a waveform of a standing wave that is produced in the closed space; 
         FIG. 3A  is a sectional view showing a manner of forming a closed space that functions as an acoustic tube, when focus is placed on an opening that is formed at a position that is apart by a length equal to a quarter of the width from an end of the muffler in the width direction thereof, and  FIG. 3B  is a graph showing a waveform of a standing wave that is produced in the closed space; 
         FIG. 4A  is an elevation view showing an elevation structure of the muffler in a silencing apparatus for a vehicle in accordance with a first embodiment of the invention, and  FIG. 4B  is a sectional view showing a sectional plan structure of the muffler in the silencing apparatus for a vehicle in accordance with the first embodiment of the invention; 
         FIGS. 5A to 5C  are diagrams showing arrangements of openings and communication holes in sound-deadening chambers of the muffler; 
         FIG. 6  is a graph showing the amounts of sound deadening at wavelengths with regard to the muffler in accordance with the first embodiment, in comparison with the case where the positions of openings and communication holes are not optimized; 
         FIG. 7A  is a sectional view schematically showing a sectional plan structure of a muffler in a silencing apparatus for a vehicle in accordance with a second embodiment of the invention, and  FIG. 7B  is a back elevation view schematically showing a back structure of the muffler in the silencing apparatus for a vehicle in accordance with the second embodiment of the invention; 
         FIGS. 8A to 8C  are diagrams showing arrangements of openings and communication holes in sound-deadening chambers of the muffler; 
         FIG. 9A  is a sectional view schematically showing a sectional plan structure of a muffler in a silencing apparatus for a vehicle in accordance with a third embodiment of the invention, and  FIG. 9B  is a back elevation view schematically showing a back structure of the muffler in the silencing apparatus for a vehicle in accordance with the third embodiment of the invention; 
         FIGS. 10A to 10C  are diagrams showing, arrangements of openings and communication holes in sound-deadening chambers of the muffler; 
         FIG. 11A  is a sectional view schematically showing a sectional plan structure of a muffler in a silencing apparatus for a vehicle in accordance with a fourth embodiment of the invention, and  FIG. 11B  is a back elevation view schematically showing a back structure of the muffler in the silencing apparatus for a vehicle in accordance with the fourth embodiment of the invention; 
         FIGS. 12A to 12C  are diagrams showing arrangements of openings and communication holes in sound-deadening chambers of the muffler; and 
         FIG. 13A  is a sectional view showing a sectional elevation structure of a muffler having a flattened sectional shape, and  FIGS. 13B and 13C  are graphs each showing a waveform of a standing wave that is produced within the structure due to the air column resonance. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     First Embodiment 
     Hereinafter, a silencing apparatus for a vehicle in accordance with a first embodiment of the invention will be described with reference to  FIG. 4A  to  FIG. 6 . 
     As shown in  FIG. 4A , a muffler  1  has a flattened sectional shape (elliptical sectional shape) in which the width W is greater than the height H. As shown in  FIG. 4B , an inside of the muffler  1  is divided, in the fore-aft direction thereof, into three sound-deadening chambers, that is, a first sound-deadening chamber  4 , a second sound-deadening chamber  5 , and a third sound-deadening chamber  6 , by a first partition plate  2  and a second partition plate  3 . The sound-deadening chambers  4  to  6  are formed so that the length of each of the sound-deadening chambers  4  to  6  in the fore-aft direction of the muffler  1  is greater than or equal to a quarter of the width W of the muffler  1 . Arrows in  FIG. 4B  show flows of exhaust gas. In each embodiment, the first sound-deadening chamber, the second sound-deadening chamber, and the third sound-deadening, chamber are disposed in, the stated order in the fore-aft direction of the muffler. 
     An inlet pipe  7 , through which exhaust gas flows into the inside of the muffler  1 , is disposed at a position that is apart by a length (W/4) equal to a quarter of the width W of the muffler  1  from a right-side end (in  FIG. 4B ) of the muffler  1  in the width direction of the muffler  1  (the left-right direction in  FIG. 4B ). A distal end of the inlet pipe  7  has an opening in the second sound-deadening chamber  5 . On the other hand, an outlet pipe  8 , through which exhaust gas flows out of the inside of the muffler  1 , is disposed at a position that is apart by the length (W/4) equal to a quarter of the width W of the muffler  1  from a left-side end (in  FIG. 4B ) of the muffler  1  in the width direction. A distal end of the outlet pipe  8  has an opening in the first sound-deadening chamber  4 . 
     In the first partition plate  2 , a communication hole  9  that extends through the first partition plate  2  is formed at a center of the muffler  1  in the width direction, that is, a position that is apart by a length (W/2) equal to a half of the width W of the muffler  1  from the two opposite ends thereof in the width direction. Through the communication hole  9 , the first sound-deadening chamber  4  and the second sound-deadening chamber  5  communicate with each other. The second partition plate  3  is provided with communication pipes  10  and  11  that extend through the second partition plate  3 , at a position that is apart by the length (W/4) equal to a quarter of the width W of the muffler  1  from the right-side end (in  FIG. 4B ) of the muffler  1  in the width direction and at a position that is apart by the length (W/2) equal to a half of the width W of the muffler  1  from the right-side end (in  FIG. 4B ) of the muffler  1  in the width direction, respectively. The first and second communication pipes  10  and  11  form communication holes that extend through the second partition plate  3 . 
     As shown in  FIG. 5A , the first sound-deadening chamber  4  of the muffler  1  is open to the outside of the first sound-deadening chamber  4  through the opening of the distal end of the outlet pipe  8 , at the position that is apart by the length equal to a quarter of the width W of the muffler  1  from the left-side end (in  FIG. 5A ) of the muffler  1  in the width direction. The first sound-deadening chamber  4  is open to the outside of the first sound-deadening chamber  4  through the communication hole  9  at the position that is apart by the length equal to a half of the width W of the muffler  1  from the left-side end (in  FIG. 5A ) of the muffler  1  in the width direction. 
     On the other hand, as shown in  FIG. 5B , the second sound-deadening chamber  5  of the muffler  1  is open to the outside of the second second-deadening chamber  5  through the opening of the distal end of the inlet pipe  7  and through the first communication pipe  10 , at the position that is apart by the length equal to a quarter of the width W of the muffler  1  from the right-side end (in  FIG. 5B ) of the muffler  1  in the width direction. The second sound-deadening chamber  5  is also open to the outside of the second sound-deadening chamber  5  through the communication hole  9  and the second communication pipe  11 , at the position that is apart by the length equal to a half of the width W of the muffler  1  from the right-side end (in  FIG. 5B ) of the muffler  1  in the width direction. 
     As shown in  FIG. 5C , the third sound-deadening chamber  6  of the muffler  1  is open to the outside of the third sound-deadening chamber  6  through the first communication pipe  10  at the position that is apart by the length equal to a quarter of the width W of the muffler  1  from the right-side end ( FIG. 5C ) of the muffler  1  in the width direction. The third sound-deadening chamber  6  is open to the outside of the third sound-deadening chamber  6  through an opening of the second communication pipe  11  at the position that is apart by the length equal to a half of the width W of the muffler  1  from the right-side end ( FIG. 5C ) of the muffler  1  in the width direction. 
     As described above, in this muffler  1 , each of the opening of the inlet pipe  7 , the opening of the outlet pipe  8 , the first communication pipe  10 , the second communication pipe  11 , and the communication hole  9  is disposed at either the position that is apart by the length equal to a half of the width W of the muffler  1  from one end of the muffler  1  in the width direction or the position that is apart by the length equal to a quarter of the width W from one end of the muffler  1  in the width direction. In other words, in each of the first to third sound-deadening chambers  4  to  6 , at least one among the opening of the inlet pipe  7 , the opening of the outlet pipe  8 , the communication hole formed by the first communication pipe  10 , the communication hole formed by the second communication pipe  11 , and the communication hole  9  is disposed at the position that is apart by the length equal to a half of the width W of the muffler  1  from one end of the muffler  1  in the width direction, and at least one among the opening of the inlet pipe  7 , the opening of the outlet pipe  8 , the communication hole formed by the first communication pipe  10 , the communication hole formed by the second communication pipe  11 , and the communication hole  9  is disposed at the position that is apart by the length equal to a quarter of the width W of the muffler  1  from the same end of the muffler  1  in the width direction. 
     As described above, a sound-deadening effect, that is, the effect of reducing sound caused by the air column resonances can be achieved in a sound-deadening chamber in which openings leading to the outside of the sound-deadening chamber are formed respectively at the position that is apart by the length equal to a half of the width W of the muffler  1  from one end of the muffler  1  in the width direction and the position that is apart by the length equal to a quarter of the width W of the muffler  1  from the same end of the muffler  1  in the width direction. Therefore, in the muffler  1  in which the openings are disposed as described above, the sound-deadening effect, that is, the effect of reducing sound caused by the air column resonances can be achieved in each sound-deadening chamber. 
     The following mathematical expression (1) represents a sound deadening characteristic of a sound-deadening chamber that has two openings. The left side of the expression (1) represents the sound deadening characteristic of the muffler  1 , and the first term on the right side represents the sound deadening performance of the sound-deadening chamber as a closed space. The second term on the right side represents the sound deadening performance of an acoustic tube that is formed by a closed space extending from one opening to the other opening. Each of the third and fourth terms on the right side represents the sound deadening characteristic of an acoustic tube that is formed by a closed space extending from one opening to a closed end.
 
20 log| Z   3   Y   f |=20 log  m   23 +20 log|sin  kW|− 20 log|cos  kW   a |−20 log| kW   b |  (1)
 
where S 2  is the sectional area of the muffler, S 3  is the sectional area of the opening, m 23  is an expansion ratio (=S 2 /S 3 ), m is an integer equal to or greater than 1, C is 20×√T, T is the gas temperature, W is the width of the muffler, each of W a  and W b  is the length from one end of the muffler in the width direction to one opening, k is a wavelength constant (=2πf/c), Z 3  is the characteristic impedance of an acoustic tube, and Y f  is the equivalent open transfer admittance of a cavity portion.  FIG. 6  shows a relation between the frequency and the amount of sound deadening in the muffler  1  derived from the foregoing expression (1). In the case where W a  and W b  in the foregoing expression (1) are not appropriately adjusted, the amount of sound deadening considerably declines at the frequencies A and B as shown by a one-dot chain line in  FIG. 6 . The frequencies A and B are frequencies of the air column resonance whose wavelength is twice the width W of the muffler  1 , and of the air column resonance whose wavelength is equal to the width W.
 
     On the other hand, in the case where W a  is set at a half of the width W of the muffler  1  and W b  is set at a quarter of the width W of the muffler  1 , there is no region where the amount of sound deadening greatly declines, as shown in a thick solid line. This is because the frequency of the air column resonance coincides with the frequency at which the sound deadening effect of the acoustic tube formed by the closed space is achieved. The resonance frequencies when the inside of the muffler  1  is a space whose two ends are closed are represented by the following expression (2), and the resonance frequency when the inside of the muffler  1  is a space in which only one of the two ends is closed is represented by each of the following expressions (3) and (4). As is apparent from these expressions, if W a  is set at W/2 (W a =W/2) and W b  is set at W/4 (W b =W/4), the resonance frequencies when both ends are closed coincide with the resonance frequencies when one end is closed, so that the standing waves due to the air column resonance are reduced. 
                   f   =       C     2   ⁢   W       ×     m   ⁢     
     (     m   ⁢           ⁢   is   ⁢           ⁢   an   ⁢           ⁢   integer   ⁢           ⁢   equal   ⁢           ⁢   to   ⁢           ⁢   or   ⁢           ⁢   greater   ⁢           ⁢   than   ⁢           ⁢   1     )               (   2   )                 f   =     C     4   ⁢   Wa         ⁢     
     ⁢     (     in   ⁢           ⁢   the   ⁢           ⁢   case   ⁢           ⁢   where   ⁢           ⁢   m   ⁢           ⁢   is   ⁢           ⁢   1   ⁢     (     m   =   1     )       )             (   3   )                 f   =     C     4   ⁢   W   ⁢           ⁢   b         ⁢     
     ⁢     (     in   ⁢           ⁢   the   ⁢           ⁢   case   ⁢           ⁢   where   ⁢           ⁢   m   ⁢           ⁢   is   ⁢           ⁢   2   ⁢     (     m   =   2     )       )             (   4   )               
According to the silencing apparatus for a vehicle of the foregoing embodiment, the following effects can be achieved.
 
     (1) In this embodiment, within the muffler  1 , at least one among the opening of the inlet pipe  7 , the opening of the outlet pipe  8 , the communication hole  9 , and the communication holes formed in the second partition plate  3  by the first and second communication pipes  10  and  11  is disposed at the position that is apart by the length equal to a half of the width W of the muffler  1  from one end of the muffler  1  in the width direction. At least one among the opening of the opening of the inlet pipe  7 , the opening of the outlet pipe  8 , the communication hole  9 , and the communication holes formed in the second partition plate  3  is disposed at the position that is apart by the length equal to a quarter of the width W from one end of the muffler  1  in the width direction. Therefore, according to the foregoing configuration, it is possible to effectively restrain the increase of exhaust sound that is caused by the air column resonances in the width direction of the muffler, without a need to provide a sub-muffler. 
     (2) In this embodiment, each of the opening of the inlet pipe  7 , the opening of the outlet pipe  8 , the communication hole  9 , and the communication holes formed in the second partition plate  3  by the first and second communication pipes  10  and  11  is disposed at either the position that is apart by the length equal to a half of the width W of the muffler  1  from one end of the muffler  1  in the width direction or the position that is apart by the length equal a quarter of the width W of the muffler  1  from one end of the muffler  1  in the width direction. Therefore, the effect of reducing exhaust sound can be more reliably obtained. 
     (3) In the foregoing embodiment, in each of the first to third sound-deadening chambers  4  to  6 , each of the position that is apart by the length equal to a half of the width W of the muffler  1  from one end of the muffler  1  in the width direction and the position that is apart by the length equal to a quarter of the width W of the muffler  1  from the same end in the width direction is the position at which the opening of the inlet pipe, the opening of the outlet pipe, or the communication hole is disposed. That is, in the embodiment, in each of the first to third sound-deadening chambers  4  to  6 , at least one among the opening of the inlet pipe, the opening of the outlet pipe, and the plurality of communication holes is disposed at the position that is apart by the length equal to a half of the width W of the muffler  1  from one end of the muffler in the width direction, and at least one among the opening of the inlet pipe, the opening of the outlet pipe, and the plurality of communication holes is disposed at the position that is apart by the length equal to a quarter of the width W from the same end in the width direction. In the muffler in which the openings and the communication holes are disposed as described above, the sound absorbing effect, that is, the effect of reducing sound caused by the air column resonances with a wavelength λ of 2W (λ=2W) and a wavelength λ of W (λ=W) is achieved in all the sound-deadening chambers, so that the increase of exhaust sound caused by the air column resonances can be more reliably restrained. 
     Second Embodiment 
     Next, a silencing apparatus for a vehicle in accordance with a second embodiment of the invention will be described in detail below with reference to  FIGS. 7A and 7B  and  FIGS. 8A to 8C . 
     As shown in  FIGS. 7A and 7B , an inside of a muffler  20  with a flattened sectional shape is divided by a first partition plate  21  and a second partition plate  22  into three spaces, that is, a first sound-deadening chamber  23 , a second sound-deadening chamber  24  and a third sound-deadening chamber  25 . The sound-deadening chambers  23  to  25  are formed so that the length of each of the sound-deadening chambers  23  to  25  in the fore-aft direction of the muffler  20  is greater than or equal to a quarter of the width W of the muffler  20 . 
     An inlet pipe  26 , through which exhaust gas flows into the inside of the muffler  20 , is disposed at a position that is apart by a length (W/2) equal to a half of a width W of the muffler  20  from an upper-side end (in  FIGS. 7A and 7B ) of the muffler  20  in the width direction of the muffler  20  (the up-down direction in  FIGS. 7A and 7B ). A distal end of the inlet pipe  26  has an opening in the third sound-deadening chamber  25 . On the other hand, an outlet pipe  27 , through which exhaust gas flows out of the inside of the muffler  20 , is disposed at a position that is apart by the length (W/2) equal to a half of the width W of the muffler  20  from the upper-side end (in  FIGS. 7A and 7B ) of the muffler  20  in the width direction. A distal end of the outlet pipe  27  has an opening in the first sound-deadening chamber  23 . In the second sound-deadening chamber  24 , a side peripheral wall of the outlet pipe  27  is provided with a plurality of small holes. The outlet pipe  27  is open to the second sound-deadening chamber  24  through the small holes. 
     The first partition plate  21  is provided with a first communication pipe  28  that extends through the first partition plate  21 , at a position that is apart by a length (W/4) equal to a quarter of the width W of the muffler  20  from the upper-side end (in  FIGS. 7A and 7B ) of the muffler  20  in the width direction. A second communication pipe  29  that extends through the second partition plate  22  is disposed at the position that is apart by the length (W/4) equal to a quarter of the width W of the muffler  20  from the upper-side end (in  FIGS. 7A and 7B ) of the muffler  20  in the width direction. The first and second communication pipes  28  and  29  form a communication hole that extends through the first partition plate  21  and a communication hole that extends through the second partition plate  22 , respectively. 
     As shown in  FIG. 8A , the first sound-deadening chamber  23  of the muffler  20  is open to the outside of the first sound-deadening chamber  23  through the first communication pipe  28  at the position that is apart by the length equal to a quarter of the width W of the muffler  20  from a right-side end ( FIG. 8A ) of the muffler  20  in the width direction. The first sound-deadening chamber  23  is open to the outside of the first sound-deadening chamber  23  through the opening of the distal end of the outlet pipe  27  at the position that is apart by the length equal to a half of the width W of the muffler  20  from the right-side end ( FIG. 8A ) of the muffler  20  in the width direction. 
     As shown in  FIG. 8B , the second sound-deadening chamber  24  of the muffler  20  is open to the outside of the second sound-deadening chamber  24  through the first communication pipe  28  and the second communication pipe  29 , at the position that is apart by the length equal to a quarter of the width W of the muffler  20  from the right-side end ( FIG. 8B ) of the muffler  20  in the width direction. The second sound-deadening chamber  24  is open to the outside of the second sound-deadening chamber  24  through the small holes (openings) formed on the side peripheral wall of the outlet pipe  27 , at the position that is apart by the length equal to a half of the width W of the muffler  20  from the right-side end ( FIG. 8B ) of the muffler  20  in the width direction. 
     Furthermore, as shown in  FIG. 8C , the third sound-deadening chamber  25  of the muffler  20  is open to the outside of the third sound-deadening chamber  25  through the second communication pipe  29 , at the position that is apart by the length equal to a quarter of the width W of the muffler  20  from the right-side end ( FIG. 8C ) of the muffler  20  in the width direction. The third sound-deadening chamber  25  is open to the outside of the third sound-deadening chamber  25  through the opening of the distal end of the inlet pipe  26 , at the position that is apart by the length equal to a half of the width W of the muffler  20  from the right-side end ( FIG. 8C ) of the muffler  20  in the width direction. 
     As described above, in this muffler  20 , each of the opening of the inlet pipe  26 , the opening of the outlet pipe  27 , the first communication pipe  28 , and the second communication pipe  29  is disposed at either the position that is apart by the length equal to a half of the width W of the muffler  20  from one end of the muffler  20  in the width direction or the position that is apart by the length equal to a quarter of the width W from one end of the muffler  20  in the width direction. In other words, in each of the first to third sound-deadening chambers  23  to  25 , at least one among the opening of the inlet pipe  26 , the opening of the outlet pipe  27 , the communication hole formed by the first communication pipe  28 , and the communication hole formed by the second communication pipe  29  is disposed at the position that is apart by the length equal to a half of the width W of the muffler  20  from one end of the muffler  20  in the width direction, and at least one among the opening of the inlet pipe  26 , the opening of the outlet pipe  27 , the communication hole formed by the first communication pipe  28 , and the communication hole formed by the second communication pipe  29  is disposed at the position that is apart by the length equal to a quarter of the width W of the muffler  20  from the same end of the muffler  20  in the width direction. Therefore, in this embodiment, too, the effects described above as (1) to (3) can be achieved. 
     Third Embodiment 
     Next, a silencing apparatus for a vehicle in accordance with a third embodiment of the invention will be described in detail below with reference to  FIGS. 9A and 9B  and  FIGS. 10A to 10C . 
     As shown in  FIGS. 9A and 9B , an inside of a muffler  30  with a flattened sectional shape is divided by a first partition plate  31  and a second partition plate  32  into three spaces, that is, a first sound-deadening chamber  33 , a second sound-deadening chamber  34  and a third sound-deadening chamber  35 . The sound-deadening chambers  33  to  35  are formed so that the length of each of the sound-deadening chambers  33  to  35  in the fore-aft direction of the muffler  30  is greater than or equal to a quarter of a width W of the muffler  30 . 
     An inlet pipe  36 , through which exhaust gas flows into the inside of the muffler  30 , is disposed at a position that is apart by a length (W/2) equal to a half of the width W of the muffler  30  from an upper-side end (in  FIGS. 9A and 9B ) of the muffler  30  in the width direction of the muffler  30  (the up-down direction in  FIGS. 9A and 9B ). A distal end of the inlet pipe  36  has an opening in the third sound-deadening chamber  35 . On the other hand, an outlet pipe  37 , through which exhaust gas flows out of the inside of the muffler  30 , is disposed at a position that is apart by a length (W/4) equal to a quarter of the width W of the muffler  30  from a lower-side end (in  FIGS. 9A and 9B ) of the muffler  30  in the width direction. A distal end of the outlet pipe  37  has an opening in the first sound-deadening chamber  33 . 
     The first partition plate  31  is provided with a first communication pipe  38  that extends through the first partition plate  31 , at the position that is apart by the length (W/2) equal to a half of the width W of the muffler  30  from the upper-side end ( FIGS. 9A and 9B ) of the muffler  30  in the width direction. The second partition plate  32  is provided with a second communication pipe  39  that extends through the second partition plate  32 , at the position that is apart by the length (W/4) equal to a quarter of the width W of the muffler  30  from the upper-side end (in  FIGS. 9A and 9B ) of the muffler  30  in the width direction. The first and second communication pipes  38  and  39  form a communication hole that extends through the first partition plate  31  and a communication hole that extends through the second partition plate  32 , respectively. 
     As shown in  FIG. 10A , the first sound-deadening chamber  33  of the muffler  30  is open to the outside of the first sound-deadening chamber  33  through the opening of the distal end of the outlet pipe  37 , at the position that is apart by the length equal to a quarter of the width W of the muffler  30  from a left-side end ( FIG. 10A ) of the muffler  30  in the width direction. The first sound-deadening chamber  33  is open to the outside of the first sound-deadening chamber  33  through the first communication pipe  38 , at the position that is apart by the length equal to a half of the width W of the muffler  30  from the left-side end ( FIG. 10A ) of the muffler  30  in the width direction. 
     As shown in  FIG. 10B , the second sound-deadening chamber  34  of the muffler  30  is open to the outside of the second sound-deadening chamber  34  through the second communication pipe  39 , at the position that is apart by the length equal to a quarter of the width W of the muffler  30  from a right-side end ( FIG. 10B ) of the muffler in the width direction. The second sound-deadening chamber  34  is open to the outside of the second sound-deadening chamber  34  through the first communication pipe  38 , at the position that is apart by the length equal to a half of the width W of the muffler  30  from the right-side end ( FIG. 10B ) of the muffler  30  in the width direction. 
     Furthermore, as shown in  FIG. 10C , the third sound-deadening chamber of the muffler  30  is open to the outside of the third sound-deadening chamber  35  through the second communication pipe  39 , at the position that is apart by the length equal to a quarter of the width W of the muffler  30  from the right-side end ( FIG. 10C ) of the muffler  30  in the width direction. The third sound-deadening chamber  35  is open to the outside of the third sound-deadening chamber  35  through the opening of the distal end of the inlet pipe  36 , at the position that is apart by the length equal to a half of the width W of the muffler  30  from the right-side end ( FIG. 10C ) of the muffler  30  in the width direction. 
     As described above, in this muffler  30 , each of the opening of the inlet pipe  36 , the opening of the outlet pipe  37 , the first communication pipe  38 , and the second communication pipe  39  is disposed at either the position that is apart by the length equal to a half of the width W of the muffler  30  from one end of the muffler  30  in the width direction or the position that is apart by the length equal to a quarter of the width W from one end of the muffler  30  in the width direction. In other words, in each of the first to third sound-deadening chambers  33  to  35 , at least one among the opening of the inlet pipe  36 , the opening of the outlet pipe  37 , the communication hole formed by the first communication pipe  38 , and the communication hole formed by the second communication pipe  39  is disposed at the position that is apart by the length equal to a half of the width W of the muffler  30  from one end of the muffler  30  in the width direction, and at least one among the opening of the inlet pipe  36 , the opening of the outlet pipe  37 , the communication hole formed by the first communication pipe  38 , and the communication hole formed by the second communication pipe  39  is disposed at the position that is apart by the length equal to a quarter of the width W of the muffler  30  from the same end of the muffler  30  in the width direction. Therefore, in this embodiment, too, the effects described above as (1) to (3) can be achieved. 
     Fourth Embodiment 
     Next, a silencing apparatus for a vehicle in accordance with a fourth embodiment of the invention will be described in detail below with reference to  FIGS. 11A and 11B  and  FIGS. 12A to 12C . 
     As shown in  FIGS. 11A and 11B , an inside of a muffler  40  with a flattened sectional shape is divided by a first partition plate  41  and a second partition plate  42  into three spaces, that is, a first sound-deadening chamber  43 , a second sound-deadening chamber  44 , and a third sound-deadening chamber  45 . The sound-deadening chambers  43  to  45  are formed so that the length of each of the sound-deadening chambers  43  to  45  in the fore-aft direction of the muffler  40  is greater than or equal to a quarter of a width W of the muffler  40 . 
     An inlet pipe  46 , through which exhaust gas flows into the inside of the muffler  40 , is disposed at a position that is apart by a length (W/4) equal to a quarter of the width W of the muffler  40  from an upper-side end (in  FIGS. 11A and 1B ) of the muffler  40  in the width direction of the muffler  40  (the up-down direction in  FIGS. 11A and 11B ). A distal end of the inlet pipe  46  has an opening in the third sound-deadening chamber  45 . On the other hand, an outlet pipe  47 , through which exhaust gas flows out of the inside of the muffler  40 , is disposed at a position that is apart by a length (W/2) equal to a half of the width W of the muffler  40  from the upper-side end (in  FIGS. 11A and 11B ) of the muffler  40  in the width direction. A distal end of the outlet pipe  47  has an opening in the first sound-deadening chamber  43 . 
     The first partition plate  41  is provided with a first communication pipe  48  that extends through the first partition plate  41 , at a position that is apart by the length (W/4) equal to a quarter of the width W of the muffler  40  from a lower-side end ( FIGS. 11A and 11B ) of the muffler  40  in the width direction. A second communication pipe  49  that extends through the second partition plate  42  is disposed at the position that is apart by the length (W/2) equal to a half of the width W of the muffler  40  from the upper-side end ( FIGS. 11A and 11B ) of the muffler  40  in the width direction. The first and second communication pipes  48  and  49  form a communication hole that extends through the first partition plate  41  and a communication hole that extends through the second partition plate  42 , respectively. 
     As shown in  FIG. 12A , the first sound-deadening chamber  43  of the muffler  40  is open to the outside of the first sound-deadening chamber  43  through the first communication hole  48 , at the position that is apart by the length equal to a quarter of the width W of the muffler  40  from a left-side end ( FIG. 12A ) of the muffler  40  in the width direction. The first sound-deadening chamber  43  is open to the outside of the first sound-deadening chamber  43  through the opening of the distal end of the outlet pipe  47 , at the position that is apart by the length equal to a half of the width W of the muffler  40  from the left-side end ( FIG. 12A ) of the muffler  40  in the width direction. 
     As shown in  FIG. 12B , the second sound-deadening chamber  44  of the muffler  40  is open to the outside of the second sound-deadening chamber  44  through the first communication pipe  48 , at the position that is apart by the length equal to a quarter of the width W of the muffler  40  from the left-side end ( FIG. 12B ) of the muffler  40  in the width direction. The second sound-deadening chamber  44  is open to the outside of the second sound-deadening chamber  44  through the second communication pipe  49  at the position that is apart by the length equal to a half of the width W of the muffler  40  from the left-side end ( FIG. 12B ) of the muffler  40  in the width direction. 
     Furthermore, as shown in  FIG. 10C , the third sound-deadening chamber  45  of the muffler  40  is open to the outside of the third sound-deadening chamber  45  through the opening of the distal end of the inlet pipe  46 , at the position that is apart by the length equal to a quarter of the width W of the muffler  40  from the right-side end ( FIG. 12C ) of the muffler  40  in the width direction. The third sound-deadening chamber  45  is open to the outside of the third sound-deadening chamber  45  through the second communication pipe  49 , at the position that is apart by the length equal to a half of the width W of the muffler  40  from the right-side end ( FIG. 12C ) of the muffler  40  in the width direction. 
     As described above, in this muffler  40 , each of the opening of the inlet pipe  46 , the opening of the outlet pipe  47 , the first communication pipe  48 , and the second communication pipe  49  is disposed at either the position that is apart by the length equal to a half of the width W of the muffler  40  from one end of the muffler  40  in the width direction or the position that is apart by the length equal to a quarter of the width W from one end of the muffler  40  in the width direction. In other words, in each of the first to third sound-deadening chambers  43  to  45 , at least one among the opening of the inlet pipe  46 , the opening of the outlet pipe  47 , the communication hole formed by the first communication pipe  48 , and the communication hole formed by the second communication pipe  49  is disposed at the position that is apart by the length equal to a half of the width W of the muffler  40  from one end of the muffler  40  in the width direction, and at least one among the opening of the inlet pipe  46 , the opening of the outlet pipe  47 , the communication hole formed by the first communication pipe  48 , and the communication hole formed by the second communication pipe  49  is disposed at the position that is apart by the length equal to a quarter of the width W of the muffler  40  from the same end of the muffler  40  in the width direction. Therefore, in this embodiment, too, the effects described above as (1) to (3) can be achieved. 
     The following modifications or changes may be made to the foregoing embodiments. The arrangements of the openings of the inlet and outlet pipes and the communication holes may be made different from those in the foregoing embodiments. In such cases as well, it is possible to effectively reduce the exhaust sound caused by the air column resonances in the width direction of the muffler, as long as in each sound-deadening chamber, at least one among the opening of the inlet pipe, the opening of the outlet pipe, and at least one communication hole (opening) is disposed at a position that is apart by a length equal to a half of the width W of the muffler from one end of the muffler in the width direction, and at least one among the opening of the inlet pipe, the opening of the outlet pipe, and at least one communication hole (opening) is disposed at a position that is apart by a length equal to a quarter of the width W of the muffler from the same end in the width direction. 
     Although in each of the foregoing embodiments, the inside of the muffler is divided into three sound-deadening chambers, the number of sound-deadening chambers formed in the muffler may be appropriately changed. Also, the number of communication pipes and the number of communication holes may be changed. In any case, as long as in each sound-deadening chamber, at least one among the opening of the inlet pipe, the opening of the outlet pipe, and at least one communication hole (opening) is disposed at a position that is apart by a length equal to a half of the width W of the muffler from one end of the muffler in the width direction, and at least one among the opening of the inlet pipe, the opening of the outlet pipe, and at least one communication hole (opening) is disposed at a position that is apart by a length equal to a quarter of the width W of the muffler from the same end in the width direction, it is possible to effectively reduce the exhaust sound caused by the air column resonances in the width direction of the muffler. 
     Although in the foregoing embodiments, each sound-deadening chamber is formed so that the length thereof in the fore-aft direction of the muffler is greater than or equal to a quarter of the width W of the muffler, one or more or all of the sound-deadening chambers may be formed so that the length of each of the sound-deadening chambers in the fore-aft direction of the muffler is less than a quarter of the width W of the muffler. 
     In the foregoing embodiments, in each sound-deadening chamber, at least one among the opening of the inlet pipe, the opening of the outlet pipe, and at least one communication hole (opening) is disposed at a position that is apart by a length equal to a half of the width W of the muffler from one end of the muffler in the width direction, and at least one among the opening of the inlet pipe, the opening of the outlet pipe, and at least one communication hole (opening) is disposed at a position that is apart by a length equal to a quarter of the width W of the muffler from the same end in the width direction. However, if in at least one sound-deadening chamber, the air column resonance in the width direction of the muffler does not conspicuously appear, the arrangement of openings and communication holes in the at least one sound-deadening chamber may be made different from the above-described arrangements thereof.