Improving transmission loss performance of aluminum extrusion in railway vehicles using lightweight material

This study developed a method for improving the transmission loss performance of aluminum extrusion by reinforcing the inner space of the extruded material with a lightweight material, such as acrylic plastic. First, the dynamic characteristics of the aluminum extrusion were analyzed, and the characteristics of noise transmission were evaluated through an acoustic mode analysis of the air layer for the inner space of the extruded material. Furthermore, to improve the transmission loss performance of the aluminum extrusion, methods were developed for increasing the vibration stiffness and altering the acoustic mode of the inner space. Additionally, a simulation analysis of the vibration mode and a response analysis based on the excitation of sound were performed to validate the proposed model; the effectiveness of the model for noise and vibration reduction was compared with that of the existing model. This analysis was conducted using models wherein the acrylic plastic was partially and totally inserted into the interior space of aluminum extrusion. The results indicated that the noise performance of the short reinforcement model with the partially inserted acrylic plastic was improved by 3 dB and that of the long reinforcement model with the totally inserted acrylic plastic was degraded by > 4 dB compared with the existing aluminum panel.


Introduction
The sources of noise in railway vehicles are generally distributed outside the vehicles rather than inside. 1,2he main source of noise in railway vehicles is rolling noise caused by the contact between the wheels and rails due to the fine roughness of their steel surfaces, which generates vibrations. 3In addition, when a railroad car travels at a high speed, the irregular flow that occurs around the vehicle gives rise to airflow noise. 4wing to the different sources of noise outside railway vehicles, the noise level is high in the entire frequency range.Furthermore, because the noise generated outside flows inside through the body of the vehicle, the noise blocking performance of the vehicle body has a significant impact on the vehicle's interior.
Aluminum extrusion can be considered as panels with specific shapes and structures.Various studies on panels have been conducted using the wave finite-element (WFE) method.The WFE method was extended to predict the noise transmission through -and radiation from -infinite panels. 5Various example applications are presented herein to illustrate the approach, including a thin isotropic panel; an antisymmetric, cross-ply sandwich panel; and a symmetric panel with an orthotropic core.Moreover, the vibroacoustic responses of infinite, plane, one-or two-dimensionally periodic structures were predicted including the forced response, sound transmission, and radiation. 6This study affords a straightforward and efficient approach for estimating the vibroacoustic responses of general plane periodic structures.
In order to analyze aluminum extrusions, various researches were conducted in terms of vibroacoustic performance.For example, modeling approach for the vibroacoustic behavior of aluminum extrusions used in railway vehicles was carried out. 7In this research, extruded panels were represented using global and local mode subsystems.Moreover, an approximate model for the modal density of extruded panels was developed and verified using finite element models.Additionally, sound transmission loss of extruded panels was studied using analytical approaches such as the coupled wavenumber finite element method and wavenumber boundary element method. 8ecause aluminum extrusion in railway vehicles significantly impacts the weight of the vehicle, research has focused on reducing the weight of the vehicle by altering the shape of the aluminum profiles.Typically, topology optimization is used to optimize the aluminum profiles occupying the largest portions of the aluminum body. 9,10The weight of the railroad car can be reduced by approximately 8.5% while maintaining its rigidity.However, because the optimized shape depends on certain aspects of stiffness, it has different effects from noise improvement.
A study was conducted to improve the structure of the aluminum extrusion -the basic structure of a vehicle body -with regard to vibration in railway vehicles.Several methods were studied for reducing the intermittent shocks in railroad vehicles and the vibrations generated in the ground by running vehicles. 11,12urthermore, these studies suggested ways to reduce noise at a specific frequency due to impact for reducing vehicle vibration.In addition, research has been conducted to reduce vehicle vibration by reinforcing the material of the vehicle. 13However, in these studies, the effects of these methods on the actual vehicle were not sufficiently examined through analysis of transmission loss, which influences the reduction of indoor noise caused by the influx of external noise.
In a prior study, an analytical method based on transmission loss was used to analyze the indoor noise in railway vehicles.Statistical energy methods are mainly used to analyze the overall indoor noise in railway vehicles 14 and the combined effect of various noise sources around the railway vehicle on the indoor noise depending on the energy flow.In another study, an acoustic structure analysis was conducted to analyze the transmission loss of aluminum extrusions in railway vehicles. 15,16These studies provide essential data for related research, along with a method for analyzing and predicting the transmission losses of aluminum extrusions.However, the application of practical methods to actual railway vehicles is limited.
Various studies have been conducted to reinforce the shape of aluminum in railway vehicles for noise reduction. 17In particular, the degree of noise improvement due to filling the empty space inside aluminum with sound-absorbing materials was analyzed.Additionally, various methods to improve the interior noise of railway vehicles were proposed for the analysis of the shapes of the extrusion profiles and the effect of the filling materials.Thus, research on the improvement of aluminum extrusion has focused on blocking external noise, which is inevitably generated when the vehicle travels at high speeds, in different frequency ranges. 18owever, this approach limits the performance of the sound-absorbing material filled inside aluminum as the material hardens over time.
Therefore, this study entailed the development of a method for improving the transmission loss performance of aluminum extrusion by reinforcing the inner space of the extruded material using a lightweight material, such as acrylic plastic.First, a dynamic characteristics analysis of the aluminum extrusion was performed, and the characteristics of noise transmission were analyzed through acoustic mode analysis of the air layer of the inner space of the extrusion.To enhance the transmission loss performance of the aluminum extrusion, a method for increasing the vibration stiffness and altering the acoustic mode of the inner space of the extrusion was devised.A simulation analysis was performed to examine the effectiveness of the proposed method.Moreover, the effectiveness of the proposed model for noise and vibration reduction was compared with that of an existing model by using an analysis of the vibration modes and responses based on the excitation of sound.

Theoretical approach to improve transmission loss performance of aluminum extrusion
This study entailed an investigation of a method for improving the transmission loss performance of aluminum extrusion using a lightweight material.For a simple flat plate, the transmission loss of the panel is affected by the stiffness, frequency, density of the medium, and sound speed.In the region below the undamped natural frequency, the transmission loss is expressed as follows 19 : where s is the coefficient of the stiffness per unit area (N/m), f represents the frequency (Hz), r 0 represents the density of the medium (kg/m 3 ), and c represents the speed of sound (m/s).This equation confirms that the transmission loss performance improves as the spring constant increases below the first resonance frequency.
The transmission loss of a single panel in the frequency domain above the resonant frequency is given as follows: where m represents the mass per unit area (kg/m 2 ).This equation confirms that the mass per unit area significantly influences the transmission loss in the region above the resonance frequency.Aluminum extrusion exhibits a highly complex shape compared with a single flat plate, as shown in Figure 1.The aluminum extrusion used in railroad vehicles has a complex structure connecting various ribs inside the outer two double panels.There exists an empty space inside the aluminum extrusion, which is surrounded by ribs and panels.
When a noise source excites the external flat panel of a railway vehicle, the noise is transmitted to the ribs and panel in the form of vibrations.Simultaneously, the inner cavity exhibits an acoustic mode.The propagated noise and vibration are then transmitted to the opposite flat panel for noise transmission.
As mentioned previously, to improve the transmission loss performance of aluminum extrusion, the mass per unit area should be increased by increasing the panel thickness.According to the aforementioned relational expression, if the thickness is doubled for a single panel, the transmission loss improves by 6 dB.However, as the panel thickness increases, the weight of the vehicle increases; therefore, additional energy is needed to propel the vehicle.
Another method for improving the transmission loss involves increasing the spring constant of the vehicle, which generally includes increasing the thickness of the body frame.However, this study aimed to apply a method that involves inserting a lightweight material into the inner space of the aluminum extruded material of a railroad car; thus, the method of minimizing the increase in the weight of the vehicle using a light material was considered.Furthermore, by considering the acoustic resonance mode of the inner space when the panel is inserted into the aluminum extrusion cavity, this method can effectively block noise transmission in the related frequency region.
The theoretical aspects of the acoustic mode in the cavity are as follows. 20The sound in the space within the cavity can be expressed using the acoustic wave equation as follows: where f represents the acoustic velocity potential, and c represents the speed of sound in the medium.
According to the relationship between the vibration velocity of particles in the air and the pressure, the acoustic velocity potential can be expressed as follows: where u, v, and w represent the displacements along the three axes in the three-dimensional (3D) space.It is assumed that the effect of vibration due to the sound propagation of the material surrounding the cavity is negligible.Assuming that the acoustic velocity potential vibrates with the original frequency (w), it can be determined by separating the variables for each direction considering the phase difference (c), as follows: Suppose that the cavity is rectangular and that the lengths along the x-axis, y-axis, and z-axis are a, b, and c, respectively.Ignoring the effect of vibration on each wall, the following boundary conditions can be derived: On the basis of this equation, the acoustic potential velocity can be expressed as follows: where n, m, and l are integers representing the numbers of sound modes generated in the cavity.Equation (7)  indicates that the sound mode is related to the side lengths of the cavity.This implies that if the size of the cavity is artificially changed, the acoustic mode that exists in the cavity can change.
To further examine the changes in the internal acoustic mode according to the cavity size, an acoustic simulation was performed based on a specific cavity.First, a case involving an air layer of a tetrahedron that has a side length of 1 m, as shown in Figure 2, was considered.The lowest possible acoustic frequency in the cavity is 171 Hz.In the acoustic mode, the sound vibrates alternately by dividing the air layer in half.If an acoustic excitation of the same frequency occurs externally, more noise and vibration may be transmitted owing to resonance.
Figure 3 shows the acoustic mode inside a tetrahedron with a side length reduced by half (0.5 m).Here, because the length decreases in the same direction, the lowest resonant frequency is 343 Hz.Therefore, when a 171 Hz sound or vibration is generated on the outside, the transmission of noise and vibration in the relevant frequency domain decreases owing to the absence of an internal acoustic resonance mode, compared with that in the resonance frequency domain.This study reviewed the acoustic mode of the inner cavity of the aluminum extruded material to reduce the internal noise transmission.

Analysis of aluminum extrusion model
The previous section presents a review of a method for improving the transmission loss performance based on the specific shape of the aluminum extrusion.As shown in Figure 4, the aluminum extrusion, which constitutes the basic skeleton of a railway vehicle, has a doubleplate structure comprising differently shaped ribs.Aluminum extrusions of the same shape, having dimensions of 1 3 1 3 0.05 m 3 (length 3 width 3 height), in an actual railway vehicle was investigated.The aluminum material had a density of 2730 kg=m 3 , a Young's modulus of 69 3 10 9 Pa, and a Poisson's ratio of 0.33.This study employed the finite-element method to confirm the dynamic properties of the aluminum extrusion by implementing an analysis model, as shown in Figure 5(a).The analysis was performed using the commercial software COMSOL Multiphysics; a mesh size of 54,810 was employed.In this paper, free boundary conditions were used to conduct modal analysis in order to obtain natural frequencies of the model.The results confirmed that the first natural vibration frequency of the aluminum extrusions was approximately 158 Hz.As shown in Figure 5(b), the central part of the aluminum panel vibrated vertically with respect to both ends.The secondary resonance frequency was 194 Hz.In this frequency range, the central part of both ends of the aluminum extruded material vibrated vertically, as shown in Figure 5(c).Table 1 presents the natural frequencies of the aluminum extrusion as observed in this study.In the case of 3D model analysis, it has the advantage of being able to reflect more of the shape of the actual model, but has the disadvantage of taking a lot of analysis time and cost.Especially in the case of aluminum panels, it takes a lot of effort to set the mesh because there are various ribs.Therefore, in this study, analysis was performed using a two-dimensional model   to simply predict the research results.In the case of the 2D model, it was modeled the same as the actual model, and the same values of material properties were used.The vibration modes of the aluminum extrusions are attributed to the vibration of the flat panel at both ends; however, the complex internal rib shapes also had a significant influence.Therefore, many natural vibration modes were observed in various frequency domains.
Next, the effect of noise transmission under the excitation of external sound was analyzed; it was necessary to analyze the aluminum structure as well as the area of air through which the sound propagated.In order to calculate acoustic phenomenon, mesh sizes should be small enough for simulation of the sound propagation.Therefore, the mesh size should be selected according to the wavelength of the simulation.In accordance with the audible frequency range of humans and the main noise generated by actual vehicles, the frequency range of the target noise was set as 20-5000 Hz.Because the maximum noise frequency was considered as 5000 Hz, the maximum size of the finite element was set as ł 0.0115 m to obtain meaningful analysis results.However, the number of finite elements increases exponentially when the analysis is performed with a 3D shape, thereby increasing the analysis time and cost.Therefore, the analysis was simplified by using a twodimensional (2D) model.Figure 6 shows the model implemented for transmission loss analysis.COMSOL was used for the analysis, and the number of finite elements was 42,071.In order to examine the effect of the transmission loss by the panel, an analysis was performed based on the boundary condition with fixed points at both ends.The model was constructed such that 1 Pa noise was incident from the outside of the panel to the inside through the aluminum panel.Transmission loss was calculated by using inlet and outlet sound pressures simulated from analysis modeling.
As shown in Figure 7, the transmission loss exhibited significant fluctuations in the range of 7.2-58.5 dB.The largest transmission loss was observed in the lowfrequency region, at approximately 80 Hz.Additionally, the transmission loss rapidly decreased at 160, 630, 1000, and 1600 Hz owing to the resonance.Figure 8 shows the analysis results for the sound pressure and stress at 1000 Hz and 1600 Hz, where the transmission loss decreased rapidly.It was observed that the noise transmitted to the inner cavity was scarcely blocked.Furthermore, an analysis of the shape of the structural vibration at the relevant frequency revealed that the noise blocking effect could not be generated, owing to the resonance of the internal rib.Therefore, it is crucial to reduce vibrations generated from the thin ribs by reinforcing the inner cavity to increase the transmission loss of the aluminum extrusion.
Figure 9 shows the analysis results for the acoustic mode of the inner cavity of the panel.Acoustic mode is closely related to a specific dimension of the cavity.As a result, each cavity had different acoustic mode.The aluminum extrusions comprised various inner spaces that exhibited an acoustic mode; that is, the vibration of sound generated outside the vehicle could be easily transmitted to the inside.The results indicated that the triangular shape had one rounded vertex with an acoustic mode of 2520 Hz, whereas the rectangular shape had two vertices at a right angle with an acoustic resonance frequency of 3238 Hz.The frequency domains were present in regions below 5000 Hz, which were considered the frequency domains of interest for the analysis.Therefore, to improve the transmission loss performance of the aluminum extrusion, it is crucial to artificially divide the internal acoustic mode while improving the rigidity of the cavity to transfer the acoustic modes to the high-frequency region of 5000 Hz.

Improvement of transmission loss performance using lightweight material
This study essentially aimed to develop methods for improving the transmission loss performance by reinforcing aluminum extrusions using lightweight acrylic  plastic.A plastic acrylic material having a density of 1190 kg=m 3 (only 44% of aluminum extruded, i.e. 2730 kg=m 3 ), as shown in Figure 10, was selected.The acrylic material had a Young's modulus of 3.2 3 10 9 Pa and a Poisson's ratio of 0.35.The thickness of the plastic acrylic was 0.0029 m, and the areal density, which has a significant effect on the transmission loss, was 3.45 kg=m 2 .The areal density of the plastic acrylic was only 21% of that of the aluminum extrusion (16.38 kg=m 2 ).Owing to its light weight and easy manufacturing process, plastic acrylic can be advantageous for minimizing the increase in the weight of the vehicle.
It is essential to improve the rigidity of the inner space of the aluminum extrusions and change the internal acoustic mode for improving the transmission loss performance of the aluminum extrusions.Therefore, methods for partially reinforcing the inner space of the aluminum extrusion and reinforcing the whole using acrylic plastic were developed.Figure 11 shows a model wherein 0.0029 -m-thick and 0.1 -m-long acrylic plastic is inserted, which prevents the aluminum extruded material from bending into the inner space under the influence of external vibrations.In this case, the acrylic plastic reinforcement was fastened to the ribs.Compared with the existing panel, the weight increase was only 0.76 kg, that is, 2.9%.In this case, the acrylic plastic reinforcement is stuck to the ribs.Figure 12 shows another model wherein 0.0029 -m-thick and 1 -m-long aluminum acrylic    is inserted into the inner space of the aluminum extrusion.With this attachment, the weight of the panel is increased by 3.79 kg, that is, 13.3%.Because this material is inserted into the entire inner space, the vibration generated in the empty space of the aluminum extrusion can be reduced.Furthermore, because the empty space is divided artificially, the noise transmission can be reduced by altering the acoustic mode.In particular, considering that the overall amount of acoustic space decreases, the acoustic resonance mode may change in the high-frequency region compared with the original aluminum extrusion.This is an effective method for reducing sound transmission in the frequency region of interest by moving the acoustic vibration mode outside the frequency region of interest.Long-type acrylic plastics were designed for modification of acoustic modes in the cavity inside aluminum extrusions.In contrast, short-type acrylic plastics were intended to increase the stiffness of the boundary areas of the panel.The latter type could not divide the internal space of the acoustic modes.These devices were designed to increase the stiffness on both sides of the supporting positions of the ribs.
The eigenfrequency and eigenmode of the proposed model were analyzed, as shown in Figure 13.For the long-type acrylic plastic reinforcement, the primary and secondary resonant frequencies were 171 and 263 Hz, respectively.These were higher than the first and second resonant frequencies of the existing aluminum extrusion material (158 and 194 Hz, respectively), confirming that the internal rigidity improved owing to the acrylic plastic.In addition, the overall distortion mode of the proposed model was examined.For the existing aluminum extrusion model, the bending of the overall structure occurred at the first resonant frequency owing to vertical vibrations, whereas for the proposed model, it occurred at the second resonant frequency.
Figure 14 shows the cross-sectional structure for the existing aluminum extrusion and the internal reinforcement model.Compared with the existing aluminum model, the interior space of the proposed model is divided further.In the proposed model, the structure of the extrusion is reinforced via the insertion of the acrylic plastic, whose shape matches that of the existing inner space.In addition, the size of all the spaces inside the aluminum extrusion is reduced by half or one-third to artificially change the acoustic resonance frequency for effective noise reduction.
Table 2 presents the natural frequencies of the aluminum extrusion and internal reinforcement model with acrylic plastic.While the existing aluminum extrusion model had a frequency range of 158-715 Hz up to the sixth resonant frequency, the acrylic plastic reinforcement model had a frequency range of 199-1131 Hz.The increase in the resonant frequency in each mode indicated that the rigidity was improved.Furthermore, as shown in Figure 15, comparing the modes at the first resonant frequency revealed that the bending mode occurred at 158 Hz for the existing aluminum extrusion model.For the reinforcement model, the primary resonance frequency was 199 Hz owing to the reinforcement  of the acrylic inside.Furthermore, the transmission of noise and vibration can be more effectively blocked in the proposed model considering that the resonance mode decreases in the frequency region of interest.
The methods for reducing sound propagation were analyzed by artificially changing the internal acoustic space and improving the internal rigidity.Figure 16 shows a comparison of the internal acoustic modes of the aluminum extrusion and the internal reinforcement model.For the existing aluminum extrusion model, the triangular-inner space model exhibited a resonance frequency of 2518 Hz.Furthermore, the internal space was divided in half, and the sound was generated in an alternating manner.The rectangular shape had a resonance mode of 3230 Hz, and the inner space was divided in half to generate sound in an alternating manner.The frequency region of interest was 20-5000 Hz.The aim was to alter the existing resonant frequency to a frequency outside the region of interest by artificially reducing the inner space.The results of the acoustic mode analysis indicated that the frequencies of the triangular and rectangular shapes changed from 2518 to 4493 Hz and from 3230 to 5006 Hz, respectively.Therefore, by artificially changing the internal sound field mode, the propagation of the sound mode can be effectively reduced.The design purpose of this research is to shift natural frequencies of internal cavities of aluminum extrusions to higher frequencies of 5000 Hz which is the upper boundary region for evaluating transmission loss of the panel.Furthermore, inserting Acrylic plastics in the internal spaces of the aluminum extrusions enhances stiffness of the panel.
In railway vehicles, the acoustic excitation generated outside the vehicle is transmitted to the inside through the vehicle frame.A transmission analysis was performed using COMSOL based on acoustic excitation for the aluminum extrusion and plastic acrylic reinforcement models to consider the influx of noise from railway vehicles, as shown in Figure 17.This analysis was based on the condition that sound with a magnitude of 1 Pa is excited from 20 to 5000 Hz on the outer surface.

Experimental validation of improvement models
The effect of the internal acrylic plastic reinforcement on the noise transmission loss was investigated according to the aluminum extrusion model.The aluminum extrusion had a square shape with a length, width, and thickness of 1, 1, and 0.05 m, respectively, similar to that used in actual railroad vehicles, as shown in Figure 19.The inner panel had a thickness of 0.002 m.A reinforced model with acrylic plastic inserted into the flat plate of the aluminum extruded material was manufactured.The long reinforcement model with acrylic plastic had the same length as the 1.0 -m-long aluminum extrusion material, whereas the short reinforcement model, in which the same material was inserted, was manufactured with a length of 0.1 m on both ends.The sound insulation performance of the specimen was evaluated, as shown in Figure 20. 21The volumes of the sound source and receiving rooms were 249 and 325 m 3 , respectively.The sound source was generated using JBL's SRX 700, and the noise was measured using a 40AE (1/2$) microphone from G.R.A.S. Measurement data acquisition and analysis were performed using PAK MK2 (Muller-BBM).Furthermore, 0.3 -m-thick    concrete was used in spaces except for the specimen of the test wall to block the transmission of sound sources, as shown in Figure 21.A test specimen was installed at the center of the wall, and the transmission loss was determined by measuring the reverberation time.
In the sound source and receiving rooms, the microphone was installed 0.7 m from the wall boundary.A minimum distance of 0.7 m was maintained between each microphone, and the measurements were performed at six different positions.After measuring the sound pressure level in each microphone, the average sound pressure level (L) was calculated as follows 21 : where L i represents the sound pressure level measurement value (dB) at the ith fixed measurement point, and n represents the number of measurement points.Using this measured value, the sound reduction index (R) was calculated as follows: where L 1 and L 2 represent the average sound pressure levels in the sound source room and receiving room (dB), respectively, S represents the sample area (m 2 ), and A represents the sound absorption power of the receiving room (m 2 ).
Figure 22 shows the acoustic reduction index measurement results for the existing aluminum extrusion and internal reinforcement models.This result provides shows the transmission loss by the reverberation experiment of the real panel.The noise reduction index of the existing aluminum model was measured as 37 dB, whereas that of the model reinforced at both ends by using 0.1 -m-long acrylic plastic inside the aluminum extrusion material was 40 dB, indicating that the transmission loss was improved by 3 dB.Figure 23 shows a comparison of the noise reduction indices at different frequencies.The results indicated that the noise reduction was improved by .4.4 dB in the 1250 Hz region and was increased overall in the entire frequency region of 200-5000 Hz, indicating that the transmission loss can be effectively improved by reinforcing the inner space of the aluminum extrusion at both ends.In particular, the Young's modulus of the acrylic plastic was approximately 4.5% of that of the aluminum extrusion.The results confirmed that noise could be effectively reduced by .3 dB by using a 0.5 -cm-thick material with low stiffness.
For the model wherein the lengths of the acrylic plastic and aluminum extrusion were equal, the noise reduction index was measured as 41 dB, indicating that the noise can be reduced by .4 dB compared with the conventional aluminum extrusion material.Furthermore, the noise reduction was improved by .5.4 dB at 1250 Hz.
In this region, vibrations can be easily transmitted for a simple 2D model owing to the vibration of a thin aluminum panel in the original model.Moreover, it was confirmed that noise could be effectively reduced by the acrylic plastic reinforcement in the interior space.Furthermore, the noise reduction index of the model improved in the entire frequency range of 200-5000 Hz.Moreover, compared with the existing aluminum extrusion, the noise performance improved in the range of 2500-3150 Hz.Various acoustic modes of the inner space of the aluminum extrusion were scattered in these frequency regions, and the noise reduction index was improved by altering the acoustic mode through the insertion of the lightweight panel into the inner space.

Conclusion
This study entailed the development of a method for improving the transmission loss performance of aluminum extrusions in railway vehicles by reinforcing the inner space of the extruded material using a lightweight material, such as acrylic plastic.The dynamic characteristics of the aluminum extrusion were analyzed, and the characteristics of noise transmission were evaluated by conducting an acoustic mode analysis of the air cavity for the internal space.Furthermore, we investigated methods for increasing the vibration stiffness and changing the acoustic mode of the inner space of the aluminum extrusion to improve its transmission loss performance.The effectiveness of the proposed model for noise and vibration reduction compared with the existing model was confirmed through an analysis of the vibration mode, wherein the acrylic plastic was inserted into the extruded material and evaluated under the excitation of sound.The transmission of vibrations due to the excitation of sound from the outside could be effectively reduced by reinforcing the empty space inside the aluminum extrusion with a lightweight material.In addition, a method for changing the resonance frequency was devised by analyzing the acoustic resonance mode of the inner space of the aluminum extrusion.To validate the proposed method, a specimen was manufactured, and a transmission loss test was performed in a reverberation room.Compared with the existing aluminum panel, the noise performance of a short reinforcement model with partially inserted acrylic plastic was improved by 3 dB, and that of a long reinforcement model with totally inserted acrylic plastic was degraded by .4 dB.It was concluded that the noise reduction performance of the short reinforcement model with the partially inserted acrylic plastic can be improved in the entire frequency  range of 200-5000 Hz by using a lightweight material with 5.6% rigidity, compared with the aluminum extrusion.Furthermore, it was confirmed that the noise could be effectively reduced by changing the internal sound field mode in the long reinforcement model with acrylic plastic.

Declaration of conflicting interests
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figure 1 .
Figure 1.Aluminum extrusion profile of a railway car body.

Figure 3 .
Figure 3. Acoustic mode of the hexahedral cavity with a side length reduced by half (Pa, 343 Hz).

Figure 4 .
Figure 4. Aluminum extrusion of a railway vehicle.

Figure 6 .
Figure 6.Analysis model of transmission loss of the aluminum extrusion.

Figure 7 .
Figure 7. Transmission loss of the aluminum extrusion in the frequency domain.

Figure 9 .
Figure 9. Acoustic mode analysis for the inside of the cavity of the aluminum extrusion.

Figure 11 .
Figure 11.Short type of the acrylic plastic reinforcement.

Figure 12 .
Figure 12.Long type of the acrylic plastic reinforcement.

Figure 13 .
Figure 13.Structural analysis of the long type acrylic plastic reinforcement: (a) first natural frequency (171 Hz) and (b) second natural frequency (263 Hz).

Figure 14 .Figure 15 .
Figure 14.Cross-sectional analysis of the existing aluminum extrusion and internal reinforcement model.

Figure 16 .
Figure 16.Comparison of the internal acoustic modes of the aluminum extrusion and the internal reinforcement model: (a) original aluminum plate and (b) acrylic plastic reinforcement model.

Figure 18 .
Figure 18.Comparison results for the surface vibration under external acoustic excitation.

Figure 17 .
Figure 17.Analysis model for the surface vibration under external acoustic excitation.

Figure 19 .
Figure 19.Aluminum extrusion and the internal acrylic plastic reinforcement.

Figure 20 .
Figure 20.Transmission suite for the reverberation test.

Figure 21 .
Figure 21.Specimen installation for evaluating the noise reduction performance.

Figure 22 .
Figure 22.Noise reduction indices of the original aluminum extrusion and internal reinforcement models (one-third Oct-band).

Figure 23 .
Figure 23.Comparison of the noise reduction index results for internal reinforcement models (one-third Oct-band).

Table 1 .
Analysis of the natural vibration of the aluminum extrusions.