Accepted Manuscript. Vibro-acoustic response and sound transmission loss characteristics of truss core sandwich panel filled with foam

Transcription

1 Accepted Manuscript Vibro-acoustic response and sound transmission loss characteristics of truss core sandwich panel filled with foam M.P. Arunkumar, Jeyaraj Pitchaimani, K.V. Gangadharan, M.C. Leninbabu PII: S (18) DOI: Reference: AESCTE 4483 To appear in: Aerospace Science and Technology Received date: 5 January 2018 Revised date: 17 February 2018 Accepted date: 17 March 2018 Please cite this article in press as: M.P. Arunkumar et al., Vibro-acoustic response and sound transmission loss characteristics of truss core sandwich panel filled with foam, Aerosp. Sci. Technol. (2018), This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

2 Vibro-Acoustic Response and Sound Transmission Loss Characteristics of Truss Core Sandwich Panel Filled with Foam M. P. Arunkumar Department of Mechanical Engineering Koneru Lakshmaiah Education Foundation, Vaddeswaram, Andhra Pradesh, India Jeyaraj Pitchaimani 1, K. V. Gangadharan Department of Mechanical Engineering National Institute of Technology Karnataka Surathkal, Mangalore, India M. C. Leninbabu School of Mechanical and Building Sciences VIT university, chennai campus, Tamilnadu, India Abstract This paper presents the studies carried out for improving the acoustic behavior of truss core sandwich panel, which is mostly used in aerospace structural applications. The empty space of the truss core is filled with polyurethane foam (PUF) to achieve better vibro-acoustic and sound transmission loss characteristics. Initially equivalent elastic properties of the foam filled truss core sandwich panel are calculated. Then, the vibration response of the panel under a harmonic excitation is obtained based on the equivalent 2D finite element model. Finally, the vibration response is given as an input to the Rayleigh integral code built in-house to obtain the acoustic and sound transmission loss characteristics. The results revealed that PUF filling of the empty space of the truss core, significantly reduces resonant amplitudes of both vibration and acoustic responses. It is also observed that foam filling reduces the overall sound power level significantly. Similarly, sound transmission loss studies revealed that, sudden dips at resonance frequencies are significantly reduced. Also an experiment is conducted on forced vibration response of honeycomb core sandwich panel to show that equivalent 2D model can be used for predicting sound power level and transmission loss behavior. Keywords: Sandwich panel, 2D equivalent model, Sound Transmission Loss, Acoustic response, Truss Core and Foam Filled. 1 Corresponding author Preprint submitted to Aerospace Science and Technology March 23, 2018

3 1. Introduction Sandwich panels are mostly used in aerospace structural applications, which require high mechanical strength with lesser weight. While designing these sandwich panels, it is important to consider acoustic comfort along with strength and weight requirements. For example, the sandwich panels used in fuselage of the aircraft are subjected to harmonic excitations which leads to radiation and transmission of sound in the passenger s cabin. Mellert et al. [1] performed experimental studies on the impact of sound and vibration on health, travel comfort and performance of flight attendants and pilots. Their results revealed that noise level has a significant effect on health indices, especially when the level increases with time. In order to improvise the acoustic comfort, the present work focuses on the effect of filling foam in the empty space of truss core sandwich panel. Schematic diagram of a foam-filled truss core sandwich panel and that of different geometric parameters associated with the corresponding unit cell are shown in Figure 1a and 1b respectively. Analytical solutions to predict the vibro-acoustic response from a vibrating sandwich panel is quite difficult due to the complexity in both geometry and material property variations. However these kind of complex problems can be solved with the help of available commercial finite element solvers. But, it is associated with certain disadvantages including development of the finite element model and pre-processing issues while analyzing the 3D sandwich panels. In order to avoid these disadvantages, the complex sandwich panel can be modelled as an equivalent 2D model. Recently Arunkumar et al. [2] derived effective elastic properties of foam-filled truss core sandwich panel based on the force distortion relationship to perform the 2D analysis. They compared their results with 3D finite element model with respect to free vibration frequencies. The present work discusses about forced vibration response which is predicted from the equivalent 2D finite element model. From the forced vibration response, sound radiation and transmission loss characteristics are evaluated using Rayleigh integral. Numerous research works have been carried out to predict the accurate equivalent elastic properties of complex sandwich panels. Libove and Hubka [3] derived the equivalent Young s and shear modulus for corrugated core sandwich panels. They used the homogenization theory to derive equivalent elastic properties that can be used for all types of corrugated core, where the unit cell of the sandwich panel is symmetrical about the vertical plane. Lok and Cheng [4] derived the equivalent elastic properties of the truss core sandwich panel by comparing the force-distortion relationship of the unit cell of the truss core with the element of a thick plate. Carlsson et al. [5] derived the equivalent properties of corrugated core sandwich panels using first order shear deformation theory and showed that bending and twisting stiffness are predominant in face sheets of the sandwich panel. The stiffness properties of a corrugated board are evaluated based on the finite element model of the micro mechanical representation of the corrugated 2

4 (a) (b) Figure 1: (a) Schematic diagram of foam filled truss core sandwich panel, (b) Dimensions of unit foam filled truss core sandwich panel 3

5 board [6]. Hao et al. [7] reported that the honeycomb plate theory is suitable for deriving the equivalent properties of a sandwich panel with honeycomb core. Numerous research works have been carried out to predict free vibration response of sandwich panels. Lok and Cheng [[8], [9]] investigated the free vibration response of clamped and simply supported truss core sandwich panels based on the equivalent stiffness properties. Their analytical results are in very good agreement with the numerical solutions. The free vibration response of composite sandwich plates was analyzed by Nayak et al. [10] using finite element model based on Reddy s higher order theory. Free vibration behavior of laminated sandwich plate was analyzed using enhanced plate theories by Kim [11], who validated the accuracy of the result with the exact 3D solution. Aydincak [12] studied the dynamic behavior of honeycomb core sandwich panel using an equivalent 2D finite element model. Aydincak [12] concluded that the accuracy of the equivalent model highly depends on the derived elastic properties and that reduces numerical error and computational time. Wang et al. [13] extended the higher-order dynamic formulation of foam core sandwich beams to the case of composite sandwich plates. The vibration results for the thin and thick composite sandwich plates obtained using the extended formulation were consistent with the predictions of the higher order mixed layer wise theory for laminated and sandwich plates. Franco et al. [14] studied about the reduction of noise in sandwich structure with honeycomb and truss core by choosing the suitable geometrical parameter. Jeyaraj et al. [15] studied the vibration and acoustic behavior of an isotropic plate under a thermal environment. Jeyaraj et al. [[16], [17]] studied the vibration and acoustic response of a composite plate and visco-elastic sandwich plate in a thermal environment with inherent material damping. They reported that the inherent damping reduces resonant amplitudes of vibration and acoustic response. Wang et al. [18] predicted the sound transmission loss characteristics of a sandwich panel by statistical energy method. Their results matches well with the experimental work. Boudjemai et al. [19] performed a numerical study on free vibration response of honeycomb panels, used in the satellites structural design. They conducted free vibration experiments on a honeycomb panel and compared the results with numerical results and found that both the results are in excellent agreement. Petrone et al. [20] predicted free vibration behavior of ecologically friendly sandwich panels experimentally and compared the results with finite elements based numerical method results. Arunkumar et al. [[21],[22]] analyzed the influence of nature of core on vibration and acoustic response of sandwich aerospace structures. They found that there is a significant influence of shear stiffness on vibration and acoustic response of triangular core sandwich panel. Boorle [23] analyzed the bending, vibration and vibro-acoustic behavior of composite sandwich plates with corrugated core. Petrone et al. [24] investigated sound power radiated from aluminum foam sandwich panel numerically and validated the results experimentally. Petrone et al. [25] filled natural fiber in the core of the honeycomb sandwich panel to improve the acoustic response. 4

6 Numerous research works are published on sound transmission loss (STL) characteristics of sandwich panels. Zhou and Crocker [26] investigated the STL behavior of sandwich panel with plane weave fabric reinforced graphite composite face sheets. Their results based on statistical energy analysis are in good agreement with the experimental results. Dalessandro et al. [27] reviewed different models and methods used for the investigation of vibro-acoustic characteristics of sandwich panels with different core types. Chandra et al. [28] investigated acoustic response and sound transmission loss behavior of functionally graded plate experimentally. Griese et al. [29] studied the effects of core geometry on sound transmission behavior of honeycomb core sandwich panel. Arunkumar et al. [30] analyzed the effect of nature of core on sound transmission behavior of aircraft sandwich panels and found that a change in web angle has a significant effect on STL characteristics. Arunkumar et al. [31] analyzed vibro-acoustic response of honeycomb core sandwich panel with composite laminate facings and found that the inherent damping associated with composite facing reduces the resonant amplitudes and increases the STL significantly. The sandwich panel must be heavy and large in size in order to achieve the desired acoustic comfort. In order to achieve better acoustic comfort, most designers increase the thickness of face sheet or height of the core. This results in increased weight, and thus, more space is occupied. This drawback can be overcome by filling the foam in empty space of the core. Foams are light in weight compared to conventional metals and are anticipated to provide better damping with out altering the structural stiffness of the panel. The intention of the present work is to improve the vibro-acoustic response and sound transmission characteristics by filling foam in the empty space of truss core sandwich panel. 2. Methodology Initially, the equivalent properties of foam-filled truss core sandwich panel are obtained based on the relationship given by Arunkumar et al.[2]. The equivalent properties are derived based on force vs. distortion relationship. Based on the assumption that foam and truss are firmly fixed together, the equivalent stiffness properties of truss core can be summed up with the relevant equivalent stiffness properties of the foam. Equations used to calculate the equivalent stiffness properties are summarized 5

7 as below. D x = E(I c + td2 2 )+E Fo(I t (I c + td2 2 )) D y = EI f 1 γ2 I c I c + I f + E f0 d 3 c 12 D xy = 1 2 Gtd2 d 2 t + 1 pst c 6 D Qx = Gt c ( ) 2 dc p t t c + sd c 3pd + G f0 d c (1) D Qy = 1 δ y d + δ z p + G fo d c Moreover, the equivalent elastic modulus E x and E y, and equivalent shear modulus G xy, G xz and G yz are calculated by equating the stiffness of the sandwich panel to the rectangular orthotropic plate. D x = E xh 3 12 ; D y = E yh 3 12 ; D xy = G xyh 3 6 D Qx = k 2 G xz h; D Qy = k 2 G yz h (2) Subsequently, the sandwich panel is modeled by extracting the mid surface of the panel. Then the panel is descritized using four node quadrilateral layered structural shell element (SHELL 181). The response of free vibration is obtained by solving the following equation: (K ωkm) 2 φ k = 0 (3) where, K is the structural stiffness matrix, M is the structural mass matrix, ω k is the circular natural frequency of the sandwich panel and φ k is the corresponding mode shape. Further, the vibration response under harmonic excitation is obtained from the general equation of motion as follows where, MÜ + C U + KU = F(t) (4) C = 2ζ ω K (5) where, C is the damping matrix calculated using Equation 5, ζ refers damping ratio, ω refers excitation frequency, F(t) the applied load vector (assumed time-harmonic), Ü, U and U are the acceleration, velocity and displacement vector of the panel. To calculate the free and forced vibration response of the sandwich panel, the commercial finite element software ANSYS is used. 6

8 Harne et al. [32] considered a damping ratio of 0.01 and for aluminum and polyurethane foam respectively for their structural acoustic studies on sandwich structures. In the present work, a damping ratio of 0.01 is assumed for truss core sandwich panel made up of aluminum and a damping ration of is considered for foam-filled aluminum truss core sandwich panel. It is assumed that the foam, core and face sheet of the panel are held together rigidly and that there is no relative motion between them. So the effective damping ratio of 0.155, which is sum of damping ratio of aluminum and polyurethane foam (PUF), is considered for response studies on PUF-filled sandwich panel. Equation 4, is solved for each excitation frequency to obtain the forced vibration response under a steady state harmonic excitation. The complex normal velocities at each node for each excitation frequency is given as an input to the Rayleigh integral to calculate the sound radiation characteristics. p(r) = jωρ 0 2π w(r s ) e jk r rs ds (6) r r s where, p(r) is the complex pressure amplitude, ρ 0 is the density of the medium, w(r s ) is the normal particle velocity at the surface point, and k is the acoustic wave number, r r s is the distance between the surface and the field point. Next, sound power is obtained from Equation 7 W = 1 ( ) 2 Re p(r)ẇ (r)ds (7) where W refers to sound power, and ẇ (r) refers to complex conjugate of the acoustic particle velocity. Sound power level is obtained from Equation 8 SWL =10log W W ref (8) where, W ref is equal to Watts. Sound transmission loss is obtained from Equation 9 τ = TL =10log 10 ( 1 τ ) T ransmitted power Incident power (9) (10) Transmitted sound power can be calculated using Equation 7 and the incident sound power is obtained from Equation 11 W i = p2 i cosθab (11) 2ρc where p i refers incident pressure 1 N/m 2, θ refers incidence angle (rad), A and B refers length and width of the panel respectively, ρ refers density of air (kg/m 3 ) and c refers speed of sound (m/s). 7

9 Figure 2: Dimension of truss core sandwich panel unit cell [8]. 3. Validation Studies 3.1. Validation of Free Vibration Response of Truss Core Sandwich Panel Without Foam In order to validate the free vibration response of truss core sandwich panel without foam, based on an equivalent 2D model, a truss core sandwich panel of size 1.2 m 2 m with 8 identical truss core that was analyzed by Lok and Cheng [8] is considered in this study. Here, the natural frequencies calculated based on 3D and its equivalent 2D finite element model from the present approach are compared with the results reported by Lok and Cheng [8], which are based on closed form solutions. The dimension and properties of the unit cell are p =75mm, f 0 =25mm, d =46.75 mm, t f = t c =3.25 mm, E =80 GPa, the Poisson s ratio ν =0.3, and material density ρ = 2700 kg/m 3 as shown in Figure 2. The elastic properties for the 2D equivalent model are calculated based on relations given in Lok and Cheng [8]. Natural frequencies of the panel predicted using present approaches are in good agreement with the results reported by Lok and and Cheng [8] as seen in Table 1. It is also observed that there is no significant change in free vibration mode shapes obtained based on 3D and equivalent 2D models as shown in Table Validation for Free Vibration Frequencies of Foam Filled Truss Core Sandwich Panel The dimension of truss core sandwich panel analyzed in section 3.1 is considered for the validation of free vibration frequencies of foam-filled truss core panel. It is assumed that empty spaces of a truss core panel is filled with PUF. The material properties of PUF are Young s modulus of

10 Table 1: Validation of free vibration results with Lok and Cheng [8] for the panel without foam filling Free vibration frequency (Hz) Mode 3D Model Equivalent 2D Model Lok and Cheng [8] Present absolute % error Lok and Cheng [8] Present absolute % error 1, , , , , , , , , , Table 2: Comparison of free vibration modes predicted by 3D and 2D finite element models for the panel with out foam filling Mode 3D FE model Equivalent 2D FE model (1,1) (1,2) (2,2) (3,2) 9

11 Table 3: Comparison of natural frequencies of foam filled truss core sandwich panel predicted by 3D and its equivalent 2D model. Free vibration frequency (Hz) Mode 3D Model Equivalent 2D Model absolute % error 1, , , , , , , , Pa and a density of 30 kg/m 3 [32]. Here, the equivalent properties for 2D finite element model are calculated from Equation 1. In the 3D model, the mid surfaces associated with the stiff facing layers and webs are modeled using SHELL181 elements while the volume of the foam is modeled using SOLID185 elements. SHELL 181 is a 4-node layered structural shell element formulated based on first order shear deformation theory while SOLID185 is an 8-node structural solid element. In the case of equivalent 2D model, the mid surface of the entire foam filled panel is extracted i.e., a rectangular area and meshed with SHELL 181 elements. Free vibration frequencies of the foam filled sandwich panel obtained from the equivalent 2D finite element model are in good agreement with the frequencies calculated based on the 3D finite element model as seen in Table 3. Some of the free vibration mode shapes of the foam filled truss core sandwich panels obtained using both the 3D and 2D finite element models are compared in Table 4, which showed that there is no significant variation Comparison with Experimental Results Free and forced vibration response of the honeycomb core sandwich panel predicted experimentally are compared with the results predicted numerically based on the equivalent model used by Hao et al. 10

12 Table 4: Comparison of free vibration modes predicted by 3D and 2D finite element models Mode 3D FE model Equivalent 2D FE model (1,1) (1,2) (2,2) (3,2) 11

13 [7]. Elastic properties based on honeycomb plate theory are given in Equation 12. E x = E y = 4 3 ( t l ) 3 E; G xy = G xz = ( ) 3 3 t 2 γ E l γ 3 t l G; γ xy = 1 3 E x = e 11e 22 e 2 12 e 22 ; E y = e 11e 22 e 2 12 ; G xz = e 44 G yz = e 55 ; G xy = e 66 ; e 11 γ xy = e [ 12 (h + d) 3 h 3] e f11 + h 3 e c11 ; e 11 = e 22 (h + d) [ 3 (h + d) 3 h 3] e f22 + h 3 e c22 e 22 = (h + d) 3 [ (h + d) 3 h 3] e f12 + h 3 e c12 e 12 = (h + d) 3 e 44 = d h + d e f44 + h h + d e c44 e 55 = d h + d e f55 + h h + d e c55 [ (h + d) 3 h 3] e f66 + h 3 e c66 e 66 = (h + d) 3 1 e c11 = e c22 = 1 γxy 2 E x (12) e c44 = G xz,e c55 = G yz,e c66 = G xy ; e f11 = e f γ 2 Ee f44 = e f55 = kg, e f66 = G ρ eq = dρ f + hρ c h + d where e fij, e cij are the stiffness parameters of the face sheet and the core respectively. E x and E y, G xy and G yz are the equivalent Young s modulus and shear modulus of core respectively. E x and E y, G xy and G yz refers to the over all equivalent properties of sandwich panel. μ is the Poisson s ratio of the face sheet, h is one half of the core height, t is the cell wall thickness, l is the side wall length, d is the thickness of the face sheet, ρ f and ρ c are the density of face and core respectively. k is the effective coefficient in the range 0.0 and Impact Hammer Test In order to compare the natural frequencies obtained through experiment with the numerical results, the impact hammer test was carried out. The honeycomb core sandwich panel is clamped to the portion of 0.25 m in the mid-bottom of panel for the height of 0.04 m. Figure 4 shows the experimental set up used to carry out the modal analysis. For this experiment, the sandwich panel with honeycomb core made up of Al 3003 and the face sheet made up of Al 6061 were purchased from Honeycomb India Pvt Ltd. Young s modulus of Al 3003 and Al 6061 alloy are given as 70 and 68.9 GPa respectively. Density 12

14 Table 5: Experimental and numerical comparison of free vibration response Natural frequency (Hz) Mode Experimental Numerical of Al 3003 and Al 6061 alloy is 2730 and 2700 kg/m 3, respectively. The dimension of honeycomb core sandwich panel as mentioned in Figure 3a and Figure 3b is a and b =1m, h =6.8 mm, d =0.5 mm, s =6.2 mm, and t =0.001 mm. Experimental modal analysis is performed and the predicted natural frequencies are compared with the numerical results as shown in Table 5. From Table 5, it is clear that the experimental result matches well with the numerical results Forced Vibration Response Similar to the free vibration frequencies, experimentally calculated forced vibration response excited under harmonic forcing condition is also compared with the ANSYS results. Figure 5 shows the schematic diagram of the experimental set up used for the forced vibration experiment. The signal generator is connected to an amplifier, which is in turn connected to an electro dynamic shaker. The honeycomb structure is fixed at the bottom in the centre by a clamping system. An accelerometer is mounted on the honeycomb structure. Signal acquired in the sensor is passed through NI 9234 DAQ for signal processing, and the honeycomb structure is excited through shaker. The force transducer is attached to the stringer which excites the honeycomb structure. The force transducer is used to acquire the force signal and it is controlled through the LABVIEW program. Figure 6 shows the experimental set up for forced vibration response. Here, the panel is excited with the magnitude of 1 N harmonic signal at (0.3, 0.3) m and the acceleration data is obtained at (0.1, 0.765) m. The obtained time domain signal for each excitation frequency is transferred to frequency domain by the in built Fast Fourier Transform (FFT) analyzer in LABVIEW software. The calculated forced vibration response is compared with the numerical result and it is shown Figure 7. From Figure 7, it is clear that forced vibration response of experimental data matches well with the numerical value which is calculated based on the equivalent 2D model. 13

15 (a) (b) Figure 3: (a) Dimension of honeycomb core sandwich panel, (b) Dimension of unit cell honeycomb core 14

16 Figure 4: Experimental set up for modal analysis Figure 5: Schematic diagram of experimental set up to obtain forced vibration response Figure 6: Experimental set up for forced vibration response 15

17 Figure 7: Numerical and experimental comparison of forced vibration response at resonance frequencies (Hz) 3.4. Validation for Element Type SHELL 181 In order to validate the accuracy of using SHELL 181 element for the analysis of sandwich panel, the work carried out by Kulkarni and Kapuria [33] based on layer wise theory is considered. This validation study is carried out, to ensure the shear effect through thickness is captured by SHELL 181 while calculating the vibration response. The sandwich panel with composite laminate face having a length to thickness ratio of 20 is considered. The sandwich panel (0/90/core/90/0) with core height of 0.8h, and top and bottom face sheet of thickness 0.05h is considered. Here, h is the total height of the sandwich panel. The properties of face sheet material as given by Kulkarni and Kapuria [33] E x = 276 GPa, E y = E z =6.9 GPa, G xy = G xz = G yz =6.9 GPa, ν xy = ν xz =0.25,ν yz =0.3. The properties of core material are given as E x = E y = E z = GPa, G xy = GPa, G xz = GPa, G yz = GPa, ν xy = ν xz = ν yz = Kulkarni and Kapuria [33] predicted the free vibration frequencies using finite element model based on zig-zag theory and compared their results with 3D exact solution. They represented the natural frequencies in the non dimensional form as given by ρcore ω n = 100ω n a (13) E xy where a is the side of the plate, E xy is Young s modulus of the face sheet material. SHELL 181 has been used in the present work to model the sandwich panel and the results obtained matches well with the results reported by Kulkarni and Kapuria [33] as seen in Table 6. 16

18 Table 6: Comparison of non-dimensional natural frequencies ω n with zigzag theory and 3D exact solution Mode 3D exact solution [33] Zigzag theory [33] Present FE model Figure 8: Validation of sound transmission loss calculation with experimental data 3.5. Validation of Sound Transmission Loss Evaluation Sound transmission loss behavior of sandwich panel calculated experimentally by Lee and Kondo [34] is considered, in order to validate the present approach. Lee and Kondo [34] also validated their results using analytical solutions. A sandwich panel has a dimension of 0.3 m 0.2 m with core height 2 mm and a face sheet thickness 0.5 mm. Density of face sheet and core material are 2720 kg/m 3 and 1.60 kg/m 3 respectively. Young s modulus and shear modulus of face sheet and core materials are given as Pa and Pa respectively. Poisson s ratio of face sheet and core materials is given as 0.33 and 0.4 respectively. Sound transmission loss calculated based on the present method is in good agreement with the experimental and analytical data [34] as seen in Figure 8. 17

19 Table 7: Dimension of zed core, cellular core, trapezoidal core and triangular core in mm Type of parameter core p d f t = t c Cellular core Trapezoidal core Triangular core Results and Discussions The specific objective of the present work is to analyze the vibro acoustic and transmission loss behavior of truss core sandwich panel filled with PUF. A truss core sandwich panel having three different types of core topology such as cellular, trapezoidal and triangular core with and with out PUF filling is considered for this investigation Effect of Filling Foam on Free Vibration Behavior of Truss Core Sandwich Panel Influence of filling foam in empty spaces of truss core sandwich panel on free vibration response characteristics is presented in this section. PUF with Young s modulus E = Pa, Poisson s ratio γ =0.4 and density ρ =30kg/m 3 [32] is filed in the empty space of the panel. Square panel with a side of 1.5 m having ten identical units is considered. To estimate the elastic properties for rectangular or cellular and triangular core, it is considered that f/p varies from 0 f/p 0.5 for truss cores. In that, the ratio f/p = 0relates to a triangular truss core, and f/p = 0.5 corresponds to a cellular truss core. In order to maintain the equal weight for all cases, same cross sectional area is considered and the dimensions of the sandwich panels with out foam are calculated, and the results are given in Table 7. Further, mass of the panel without foam filling is obtained. Now, in order to keep the same mass for sandwich panel filled with foam, thickness of face sheet associated with the foam filled sandwich panel is modified as 1.4 mm, 1.2 mm and 1 mm for cellular, trapezoidal and triangular core sandwich panel respectively. Influence of filling foam on free vibration behavior is shown in Table 8. From Table 8, it is clear that the triangular core sandwich panel has high natural frequencies due to its high transverse shear stiffness compared to cellular core and trapezoidal core sandwich panel. It is also evident that the effect of filling foam increases natural frequencies in all types of core due to contribution of PUF in transverse shear stiffness Effect of Filling Foam on Vibro-Acoustic and Transmission Loss Characteristics Influence of filling foam in empty spaces of truss core sandwich panel on dynamic and acoustic response characteristics is presented in this section. In order to investigate the forced vibration response of sandwich panel, it is excited with a force of 1 N at a chosen point. The lower left corner of the plate 18

20 Table 8: Influence of foam filling on free vibration behavior of truss core sandwich panel Natural frequency (Hz) S. No Cellular core Trapezoidal core Triangular core With-out With foam With-out With foam Without With foam foam foam foam is chosen as the excitation location chosen in the present analysis (1.05 m, 1.05 m). This is based on the condition that it should not be a vibration nodal point for any modes in the chosen excitation frequency range. The excitation frequency range is chosen as Hz based on the coincidence frequency of the panel analyzed. Based on the convergence study the panel is meshed with elements for all the cases analyzed. It is also ensured that the chosen mesh size satisfies the six elements per wave length requirement for numerical vibro-acoustics analysis. Figure 9 and Figure 10 shows the forced vibration response of truss core sandwich panel with and with out foam respectively. From Figure 9, it is clear that the resonant amplitude of all type of sandwich panel are in the same level irrespective of the nature of core. Similarly from Figure 10, one can observe that resonant amplitudes are reduced significantly due to the enhanced damping provided by PUF filling. The effect of core topology of truss core sandwich panel is shown in Figure 11. From Figure 11, it is clear that triangular core has reduced number of radiation modes in the interested frequency range due to the high shear stiffness of the triangular core sandwich panel. It is also evident that triangular core sandwich panel has lower sound power level compared to other two cases till its first resonance frequency. Influence of foam filling on sound power level associated with cellular core is shown in Figure 12. The figure shows that the resonant amplitude of sound power level for cellular core is reduced significantly. This can be attributed to the effect of damping on resonant frequencies for cellular core when poly urethane foam is filled. It is also clear that there is no significant change in the stiffness controlled region, i.e., up to first resonant frequency. Similarly, sound power level for trapezoidal core and triangular core sandwich panels are shown in Figure 13 and 14 respectively. From these figures, it is very clear that sound power level is reduced significantly in all resonance amplitudes for foam filled 19

21 Figure 9: Effect of core topology of truss core sandwich panel with out foam on Vrms Table 9: Effect of filling foam on over all sound power level Sound Power Level (db) Influence Cellular core Trapezoidal core Triangular core Without Foam With Foam Reduction in SPL sandwich panel. This is attributed to the damping property of PUF. The effect of foam filling on over all sound power level is given in Table 9. This table also shows very clear that foam filling significantly reduces the over all sound power level to around 12 db in each case. Sound pressure radiated at 100 Hz and 600 Hz are analyzed to investigate the effect of foam filling on the directivity pattern of sound radiation. The results given in Figure 15a and Figure 15b indicates that foam filling reduces the amplitude of sound pressure radiation significantly. The effect of core topology on sound transmission loss characteristics of truss core sandwich panel is shown in Figure 16. From Figure 16, it is seen that in triangular core sandwich panel, there are not many sudden dips in the excitation frequency range, whereas for cellular core and trapezoidal core, there are many dips in the transmission loss curve. It is attributed to the shear stiffness properties of the core geometry. The effect of foam filling is shown in Figure 17, 18 and 19 for cellular, trapezoidal and triangular core respectively. From the Figures 17, 18 and 19 one can say, that the effect of filling foam is significant when the sudden dips are avoided at resonance frequencies. Nearly 20 db is reduced at resonance. This is attributed to the high damping property of PUF. 20

22 Figure 10: Effect of core topology of truss core sandwich panel filled with foam on Vrms Figure 11: Effect of core topology on Sound Power Level 21

23 Figure 12: Sound power level of cellular core Figure 13: Sound power level of trapezoidal core 22

24 Figure 14: Sound power level of triangular core 5. Conclusion Vibro-acoustic response and sound transmission loss behavior of truss core sandwich panel is compared with foam-filled truss core sandwich panel. In the present approach, the equivalent model derived for foam filled truss core sandwich panel is used to predict the vibro-acoustic response characteristics. The effects of damping ratio of PUF are also studied. The below mentioned key points are observed in the present analysis. Effect of core topology on SPL is only significant in particular frequency zones. When the over all SPL is considered, the effect of core topology is not significant. Resonance amplitude of SPL of foam-filled sandwich panels are efficiently reduced. Sudden dips at resonance frequencies are fully reduced. In the octave band analysis, the effect of foam filling is significant in all frequency zones. From the results obtained in this manuscript, it is clear that, if the truss core sandwich panel is filled with polyurethane foam, it would avoid high transmission noises at resonance i.e., around 20 db of noise can be reduced in all core type of truss core sandwich panel analyzed. Acknowledgement The author/s acknowledge the contribution of Centre for System Design (CSD): A Centre of Excellence at NITK Surathkal pertaining to issuance of technical equipment/product service/experimental facility. The technical support received from the members of SOLVE: The Virtual NITK Surathkal 23

25 (a) (b) Figure 15: (a) Sound Pressure Level at 100 Hz, (b) Sound Pressure Level at 600 Hz 24

26 Figure 16: Effect of core topology on STL Figure 17: STL of cellular core 25

27 Figure 18: STL of trapezoidal core Figure 19: STL of triangular core 26

28 ( is deeply appreciated. Declaration of Conflicting Interests The authors declare that they have no conflict of interest. Funding This research received no specific grant from any funding agency in the public, commercial, or not-forprofit sectors. 27

29 References [1] V. Mellert, I. Baumann, N. Freese, R. Weber, Impact of sound and vibration on health, travel comfort and performance of flight attendants and pilots, Aerospace Science and Technology 12 (1) (2008) [2] M. P. Arunkumar, J. Pitchaimani, K. V. Gangadharan, Bending and free vibration analysis of foam-filled truss core sandwich panel, Journal of Sandwich Structures & Materials doi: / [3] C. Libove, R. E. Hubka, Elastic constants for corrugated-core sandwich plates, Tech. rep., NACA Document (1951). [4] T.-S. Lok, Q.-H. Cheng, Elastic stiffness properties and behavior of truss-core sandwich panel, Journal of Structural Engineering 126 (5) (2000) [5] L. A. Carlsson, T. Nordstrand, B. Westerlind, On the elastic stiffnesses of corrugated core sandwich, Journal of Sandwich Structures and Materials 3 (4) (2001) [6] M. Biancolini, Evaluation of equivalent stiffness properties of corrugated board, Composite Structures 69 (3) (2005) [7] L. Hao, L. Geng, M. Shangjun, L. Wenbin, Dynamic analysis of the spacecraft structure on orbit made up of honeycomb sandwich plates, in: Computer Science and Automation Engineering (CSAE), 2011 IEEE International Conference on, Vol. 1, IEEE, 2011, pp [8] T. Lok, Q. Cheng, Free vibration of clamped orthotropic sandwich panel, Journal of Sound and Vibration 229 (2) (2000) [9] T.-S. Lok, Q.-H. Cheng, Free and forced vibration of simply supported, orthotropic sandwich panel, Computers & Structures 79 (3) (2001) [10] A. Nayak, S. Moy, R. Shenoi, Free vibration analysis of composite sandwich plates based on reddy s higher-order theory, Composites Part B: Engineering 33 (7) (2002) [11] J.-S. Kim, Free vibration of laminated and sandwich plates using enhanced plate theories, Journal of Sound and Vibration 308 (1) (2007) [12] I. Aydincak, Investigation of design and analyses principles of honeycomb structures, Ph.D. thesis, Middle East Technical University (2007). [13] T. Wang, V. Sokolinsky, S. Rajaram, S. R. Nutt, Consistent higher-order free vibration analysis of composite sandwich plates, Composite Structures 82 (4) (2008)

30 [14] F. Franco, K. A. Cunefare, M. Ruzzene, Structural-acoustic optimization of sandwich panels, Journal of Vibration and Acoustics 129 (3) (2007) [15] P. Jeyaraj, C. Padmanabhan, N. Ganesan, Vibration and acoustic response of an isotropic plate in a thermal environment, Journal of Vibration and Acoustics 130 (5) (2008) [16] P. Jeyaraj, N. Ganesan, C. Padmanabhan, Vibration and acoustic response of a composite plate with inherent material damping in a thermal environment, Journal of Sound and Vibration 320 (1) (2009) [17] P. Jeyaraj, C. Padmanabhan, N. Ganesan, Vibro-acoustic behavior of a multilayered viscoelastic sandwich plate under a thermal environment, Journal of Sandwich Structures and Materials (2011) [18] T. Wang, S. Li, S. Rajaram, S. R. Nutt, Predicting the sound transmission loss of sandwich panels by statistical energy analysis approach, Journal of Vibration and Acoustics 132 (1) (2010) [19] A. Boudjemai, R. Amri, A. Mankour, H. Salem, M. Bouanane, D. Boutchicha, Modal analysis and testing of hexagonal honeycomb plates used for satellite structural design, Materials & Design 35 (2012) [20] G. Petrone, V. DAlessandro, F. Franco, B. Mace, S. De Rosa, Modal characterisation of recyclable foam sandwich panels, Composite Structures 113 (2014) [21] M. P. Arunkumar, J. Pitchaimani, K. V. Gangadharan, M. C. Leninbabu, Effect of core topology on vibro-acoustic characteristics of truss core sandwich panels, Procedia Engineering 144 (2016) [22] M. P. Arunkumar, J. Pitchaimani, K. V. Gangadharan, M. C. L. Babu, Influence of nature of core on vibro acoustic behavior of sandwich aerospace structures, Aerospace Science and Technology 56 (2016) [23] R. K. Boorle, Bending, vibration and vibro-acoustic analysis of composite sandwich plates with corrugated core, Ph.D. thesis, University of Michigan-Dearborn (2014). [24] G. Petrone, V. D Alessandro, F. Franco, S. De Rosa, Numerical and experimental investigations on the acoustic power radiated by aluminium foam sandwich panels, Composite Structures 118 (2014) [25] G. Petrone, S. Rao, S. De Rosa, B. Mace, F. Franco, D. Bhattacharyya, Initial experimental investigations on natural fibre reinforced honeycomb core panels, Composites Part B: Engineering 55 (2013)

31 [26] R. Zhou, M. J. Crocker, Sound transmission loss of foam-filled honeycomb sandwich panels using statistical energy analysis and theoretical and measured dynamic properties, Journal of Sound and Vibration 329 (6) (2010) [27] V. DAlessandro, G. Petrone, F. Franco, S. De Rosa, A review of the vibroacoustics of sandwich panels: Models and experiments, Journal of Sandwich Structures and Materials 15 (5) (2013) [28] N. Chandra, S. Raja, K. N. Gopal, Vibro-acoustic response and sound transmission loss analysis of functionally graded plates, Journal of Sound and Vibration 333 (22) (2014) [29] D. Griese, J. D. Summers, L. Thompson, The effect of honeycomb core geometry on the sound transmission performance of sandwich panels, Journal of Vibration and Acoustics 137 (2) (2015) [30] M. P. Arunkumar, J. Pitchaimani, K. V. Gangadharan, M. C. L. Babu, Sound transmission loss characteristics of sandwich aircraft panels: Influence of nature of core, Journal of Sandwich Structures and Materials (2016) [31] M. P. Arunkumar, M. Jagadeesh, J. Pitchaimani, K. V. Gangadharan, M. C. L. Babu, Sound radiation and transmission loss characteristics of a honeycomb sandwich panel with composite facings: Effect of inherent material damping, Journal of Sound and Vibration 383 (2016) [32] R. L. Harne, C. Blanc, M. C. Remillieux, R. A. Burdisso, Structural-acoustic aspects in the modeling of sandwich structures and computation of equivalent elasticity parameters, Thin-Walled Structures 56 (2012) 1 8. [33] S. Kulkarni, S. Kapuria, Free vibration analysis of composite and sandwich plates using an improved discrete kirchhoff quadrilateral element based on third-order zigzag theory, Computational Mechanics 42 (6) (2008) [34] C. Lee, K. Kondo, Noise transmission loss of sandwich plates with viscoelastic core, in: 40th Structures, Structural Dynamics, and Materials Conference and Exhibit, 1999, p

32 本文献由 学霸图书馆 - 文献云下载 收集自网络, 仅供学习交流使用 学霸图书馆 ( 是一个 整合众多图书馆数据库资源, 提供一站式文献检索和下载服务 的 24 小时在线不限 IP 图书馆 图书馆致力于便利 促进学习与科研, 提供最强文献下载服务 图书馆导航 : 图书馆首页文献云下载图书馆入口外文数据库大全疑难文献辅助工具