Sound transmission loss characteristics of sandwich aircraft panels: Influence of nature of core

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1 Original Article Sound transmission loss characteristics of sandwich aircraft panels: Influence of nature of core Journal of Sandwich Structures and Materials 2017, Vol. 19(1) 26 48! The Author(s) 2016 Reprints and permissions: sagepub.co.uk/journalspermissions.nav DOI: / jsm.sagepub.com MP Arunkumar 1, Jeyaraj Pitchaimani 1, KV Gangadharan 1 and MC Lenin Babu 2 Abstract Sandwich panel which has a design involving acoustic comfort is always denser and larger in size than the design involving mechanical strength. The respective short come can be solved by exploring the impact of core geometry on sound transmission characteristics of sandwich panels. In this aspect, the present work focuses on the study of influence of core geometry on sound transmission characteristics of sandwich panels which are commonly used as aircraft structures. Numerical investigation has been carried out based on a 2D model with equivalent elastic properties. The present study has found that, for a honeycomb core sandwich panel in due consideration to space constraint, better sound transmission characteristics can be achieved with lower core height. It is observed that, for a honeycomb core sandwich panel, one can select cell size as the parameter to reduce the weight with out affecting the sound transmission loss. Triangular core sandwich panel can be used for low frequency application due to its increased transmission loss. In foam core sandwich panel, it is noticed that the effect of face sheet material on sound transmission loss is significant and this can be controlled by varying the density of foam. Keywords Sandwich structure, sound transmission loss, 2D equivalent model, honeycomb, truss core topology, foam 1 National Institute of Technology Karnataka, Mangalore, India 2 School of Mechanical and Building Sciences, VIT University, Tamil Nadu, India Corresponding author: Jeyaraj Pitchaimani, National Institute of Technology Karnataka, Surathkal , Mangalore, India. pjeyaemkm@gmail.com

2 Arunkumar et al. 27 Introduction The advantage of high strength to weight ratio associated with sandwich panels has lead to its excessive demand in several engineering applications as structural members. The major short coming of these panels is their higher sound transmission during their service under dynamic conditions, as in the case of aircraft fuselage. High sound power level transmitted by these light weight sandwich panels will be an annoyance to the passengers in the aircraft. Mellert et al.[1] reported that undesirable sound has a significant effect on physical and mental wellness, travel comfortability and pursuance of flight attendants. Different types of core geometries used in the construction of sandwich panels are typically used in several engineering applications such as aircraft, marine, automobile and railway engineering are shown in Figure 1 [2]. Numerical methods are the most suitable method to analyse the dynamic behaviour of the sandwich panels, as the closed form solutions are very difficult due to their associated complexity [3]. The vibration response can be determined using 3D model as well as equivalent 2D finite element model. 3D FE model has the drawback of extremely larger post-processing time, mesh connectivity and higher computational cost to predict the response. In case of equivalent 2D model, it is effective for the dynamic analysis of sandwich panels in terms of accuracy of the solution and computational cost [4]. The equivalent 2D FE model is based on the equivalent Figure 1. Types of sandwich construction with different kinds of core [2]. (a) Foam core, (b) Honeycomb core, (c) Web core and (d) Truss core.

3 28 Journal of Sandwich Structures and Materials 19(1) orthotropic elastic properties of the sandwich panels. The accuracy of the result greatly depends on the elastic property used. The derivation of equivalent property of sandwich panel is originated by Libove and Hubka [5] in order to simplify the static and dynamic analysis of sandwich structures used in several engineering applications. Similar work was carried out by Lok and Cheng [6] to model the truss core sandwich panel. The analysis carried out by Libove and Hubka [5] suits only for symmetrical core sandwich panels. This has been overcome by Fung et al. [7]; they obtained the equivalent elastic properties of Zed and C core sandwich panels which come under unsymmetrical core sandwich panels. Lok and Cheng [8] carried out the free vibration analysis of clamped truss core sandwich panel using closed-form solution and validated their results with finite element solutions. Boudjemai et al. [9] studied the effect of face sheet, cell size and core height on free vibration behaviour of honeycomb core sandwich panel. In aerospace structures, generally porous or foam material is used to reduce noise and vibration [10]. Rayleigh integral method is the simplest and computationally effective method to calculate the sound radiation characteristics of baffled flat structural panels [11]. Sound transmitted by these sandwich panels are considered as disturbance in the view of acoustic comfort. In the field of acoustics, numerous research works are being carried out to control this noise. Since the sound transmission loss depends on stiffness, damping and mass, the unique core of sandwich panel can not solve all the acoustic problems [12]. The forecast of sound transmission loss and how it can be regulated by its own geometry must be explored. Petrone et al. [13] attained an improvement in damping value by filling the wool fibre in core, thereby achieving better acoustic performance in eco-friendly honeycomb cores for sandwich panels. Toyoda et al. [14] proved that using honeycomb in its back cavity enhances the sound absorption characteristics. The effect of stiffness and damping on sound transmission loss is improved by using aluminium sheets and fibre-reinforced concrete sheet as added on panels [15]. Wennhage [16] optimised the sandwich structure considering mechanical and acoustic constraints. Wennhage [16] demonstrated that the design considering acoustic comfort is heavier than the design considering mechanical strength. The effect of core geometry on sound transmission loss of a honeycomb core sandwich panel is studied by Griese et al. [17]. Griese et al. [17] showed the shift in natural frequency and resulting resonance by changing the stiffness in the core without compromising the mass. Chandra et al. [18] studied the vibro acoustic behaviour and sound transmission loss of functionally graded plate. They observed high fluctuation of sound transmission loss (STL) in high frequency range for the functionally graded plate. Sargianis and Suhr [19] analysed the acoustic performance of the sandwich panel using wave number analysis by varying the core thickness in Rohacell foam core and carbon fibre face sheet composite beams. Sargianis and Suhr [19] observed that low wave number amplitudes correspond to high structural damping value which relates to the reduction in sound level radiation in structures. The sound radiation characteristics of aluminium foam sandwich panel were studied by Petrone et al. [20]. They validated the experimental results with the numerical values.

4 Arunkumar et al. 29 The property of high stiffness to weight ratio of sandwich panel allows it to be more mechanically efficient, but the drawback is transmission of noise. From the literature survey, it is clear that the impact of sound and vibration on health, travel comfort and performance of flight attendants and pilots has a significant effect, especially when the level increases with time of work. Hence, it is necessary to design a sandwich panel with acoustic comfort. But a design which involves the acoustic comfort is always dense and large in size than the design considering mechanical strength alone. This drawback can be overcome by exploring the influence of core geometry on vibration and acoustic response of sandwich panel without increasing its weight and size. In the present study, the sound transmission loss of frequently used cores in aerospace engineering applications such as honeycomb, triangular, trapezoidal, cellular, zed, aluminium foam and rohacell foam with aluminium, titanium and epoxy carbon laminate face sheet is analysed based on equivalent 2D FE model. Initially, sound transmission loss behaviour of honeycomb core is analysed and the effect of its different design parameters is studied. Next in the order, sound transmission loss behaviour of different topology of truss core sandwich panel is analysed and compared with zed core. Further, sound transmission loss of aluminium foam and different types of face sheet material with Rohacell foam core sandwich panel are analysed and compared. Methodology The equivalent 2D FE model is used for analysing the free and forced vibration response of the sandwich panel and the calculated vibration response is given as an input to Rayleigh integral in order to obtain the sound transmission loss characteristics. To initiate with,. fundamentally, the sandwich panel is equalised as an continuous and homogeneous, and orthotropic plate by using the equivalent stiffness (such as bending stiffness, twisting stiffness and transverse shear stiffness) properties of the sandwich panel. Stiffnesses for an orthotropic plate with height h are given below D x ¼ E xh 3 12 ; D y ¼ E yh 3 12 ; D xy ¼ G xyh 3 6 D Qx ¼ k 2 G xz h; D Qy ¼ k 2 G yz h ð1þ where D x and D y are bending stiffnesses, D xy is twisting stiffness, and D Qx and D Qy are the transverse shear stiffnesses, E x and E y are the Young s modulus and G xy,

5 30 Journal of Sandwich Structures and Materials 19(1) G xz, G yz, are the shear modulus, and k 2 is the transverse shear correction factor. The derived equivalent elastic properties are continuous and homogenous, and orthotropic.. Next in order, the eigen value problem is solved to compute the natural frequencies and mode shapes of the panel under CCCC (clamped along the edges) boundary condition as follows. ½K! 2 k MŠf kg¼0 ð2þ where K is the structural stiffness matrix, M is the structural mass matrix, while! k is the circular natural frequency of the sandwich panel and k is the corresponding mode shape.. Further, the forced vibration response of the sandwich panel is found using the harmonic response analysis by applying a incident pressure of 1 N/m 2 on the sandwich panel. The general dynamic equation of motion for a sandwich structure is given below M U þ C _U þ KU ¼ FðtÞ ð3þ where C is the damping matrix, F(t) the applied load vector (assumed time-harmonic), and U, _U, and U are the acceleration, velocity, and displacement vector of the panel, respectively. By using commercial finite element software ANSYS, the present work has computed the free and forced vibration responses. To proceed with the finite element analysis, a four-noded layered structural shell element SHELL 181, which is available in ANSYS element library, is used. Based on the first-order shear deformation theory, the SHELL 181 element is formulated. The detail of formulation of SHELL 181 is to be referred with ANSYS manual.. The incident intensity multiplied by the area of plate, on which it acts, is used to calculate the incident acoustic power and it is given by W i ¼ p2 i cosab 2c ð4þ where p i is the incident pressure assumed to be a real constant 1 N/m 2, is the incidence angle (rad), a and b are the length and breadth of the plate, respectively, is the density of air (kg/m 3 ) and c is the speed of sound (m/s), respectively.. To estimate the transmitted sound pressure, the forced vibration response of the sandwich panel is given as an key to the Rayleigh integral. The velocity of the

6 Arunkumar et al. 31 plate and the radiated pressure is related in the Rayleigh integral and it is given below pðrþ ¼ j! Z 0 2 wðr s Þ e jkjr r sj jr r s j ds where p(r) is the complex radiated pressure amplitude, 0 is the density of the medium, wðr s Þ is the particle velocity at the surface point, k is the acoustic wave number, and jr r s j is the distance between the surface and the field point. The in-house built MATLAB code for the Rayleigh integral is used.. The computation of sound power transmitted from the vibrating panel is obtained from the relation given as W ¼ 1 I 2 Re pðrþ _w ðrþ ds ð6þ ð5þ where W refers sound power and _w ðrþ refers to the complex conjugate of the acoustic particle velocity.. Using equation (4) and equation (6), the prognostication of sound transmission loss in terms of decibels is given below TL ¼ 10log 10 1 ð7þ where is the transmission ratio, calculated by the ratio of transmitted power and incident power (i.e ratio of equations (4) and (6)). The in-house built MATLAB code for the Rayleigh integral has been used to obtain sound transmission loss features of the sandwich panel. Validation studies To determine the vibration response analysis, the commercial finite element software ANSYS has been used, whereas to evaluate the sound radiation characteristics, the code built-in-house using MATLAB for the Rayleigh integral has been used. To systematise the methodology which is tracked in the present work, the results obtained using the present attempt have been validated with the existing results available in the literature and presented in this section. Validation of natural frequency evaluation Free vibration frequencies of a sandwich panel of size 2 m 1.2 m with eight identical truss core sandwich analysed by Lok and Cheng [8] are considered for the validation

7 32 Journal of Sandwich Structures and Materials 19(1) Figure 2. Dimension of truss core sandwich panel unit cell [8]. of natural frequency evaluation. Geometrical dimensions and properties of the unit cell shown in Figure 2 are: p ¼ 75 mm, f 0 ¼ 25 mm, d ¼ mm, t f ¼ t c ¼ 3:25 mm, E ¼ 80 GPa, the Poisson ratio ¼ 0:3, and material density ¼ 2700 kg/m 3. Lok and Cheng [8] used a closed-form solution to obtain the natural frequencies of 3D model and its equivalent 2D model while the present method is based on FEM. SHELL 181 element available in ANSYS is used for both the 3D model and its equivalent 2D model analyses carried out in this present work. To systematise the model of 3D sandwich panel, the unit cell is modelled and meshed, and then an array of cell is created to develop the entire model. SHELL 181 element meshes the mid surfaces associated with the facings and core of the sandwich panel. While meshing the 3D model, it is ensured that there is no undesirable connectivity issue between the core geometry and face sheet of the respective sandwich panel. A plate with same breadth and width of the sandwich panel is referred to be an equivalent 2D model which is created as a geometric model with rectangular area of dimensions 2m 1.2 m. The frequency reports of Lok and Cheng [8] are well matched with the free vibration frequencies obtained from ANSYS for both 2D and 3D model as shown in Table 1. The maximum error associated with equivalent 2D model is around 3%. There is no significant variation in mode shapes of the sandwich panel obtained using both the 3D model and equivalent 2D model as seen in Table 2. Validation of sound transmission loss In order to validate the proposed method to predict the sound transmission loss, the available experimental data in the literature for sandwich panel analysed by

8 Arunkumar et al. 33 Table 1. Validation of free vibration results with Lok and Cheng [8]. Free vibration frequency (Hz) 3D Model Equivalent 2D Model Mode Lok and Cheng [20] Present Absolute percentage error Lok and Cheng [20] Present Absolute percentage error 1, , , , , , , , , , Lee and Kondo [21] is considered. Lee and Kondo [21] also analysed analytically and compared their results with experimental tests. Lee and Kondo [21] analysed a sandwich panel of size 303 mm 203 mm with top and bottom face sheet of thickness 0.5 mm and core thickness 2 mm, density of face sheet and core material is 2720 kg/m 3 and 1.60 kg/m 3, respectively. Young s modulus and shear modulus of face sheet and core material are given as 73.2 GPa and 4.12 GPa, respectively. Poission s ratio of face sheet and core material is given as 0.33 and 0.4. Sound transmission loss predicted using the proposed method, matches well with experimental and analytical data [21] as seen in Figure 3. Results and discussions In this part, the sound transmission loss of sandwich panels which is generally used as cores for aerospace structures is analysed. The following are the various sandwich panels evaluated in the present work: (i) aluminium panel with honeycomb core; (ii) aluminium panel with trapezoidal, triangular, cellular and zed core; (iii) aluminium and rohacell foam core sandwich panels with aluminium, titanium and carbon-epoxy facings. A plane acoustic pressure with an amplitude of 1 N/m 2 is investigated for normal (with incident angle 90 ) and oblique (with incident angle 45 ) incident cases and the corresponding transmission loss behaviour has been investigated. The yield of various cores on sound transmission loss is examined. The mechanism of sound transmission through the sandwich panel is by the deformation of bottom skin which undergoes normal deflection when the incident

9 34 Journal of Sandwich Structures and Materials 19(1) Table 2. Mode shape validation of equivalent 2D FEM model with 3D FEM model. Mode 3D FEM model Equivalent 2D FEM model (1,1) (1,2) (2,2) (3,2) (4,2) sound is in the form of a pressure normal to the surface. The core transmits this motion to top skin to cause similar deformation. This deformation of top skin resembles the pumping action which causes sound waves in air above [22]. Assumption in the study is constrained only to the incident pressure wave. The deformation of the skin is maximum, when there is normal incident sound in the form of pressure normal to the bottom skin, and therefore no shear. When the panel is subjected to oblique incident, the part of the deflection is reduced due to the shear deformation, thereby reduction in the transmitted sound pressure.

10 Arunkumar et al. 35 Figure 3. Validation of sound transmission loss calculation with experimental data. In this study, for oblique incident of pressure, there will be slightly increased transmission loss and reduced sound power level is anticipated. (Note: No other changes are made in response for oblique incident, and the study is interested only on the variation in deformation of the panel when subjected to normal and oblique incident, thereby anticipating to see the changes in transmitted sound power.) The transmission loss can be interpreted by dividing the sound transmission loss (STL) curve into three distinct regions such as stiffness sensitive, damping sensitive and mass sensitive region. The stiffness-sensitive region related to the portion of the curve from zero to first resonance frequency. In the stiffness region, the STL increases with increase in stiffness. The damping-controlled region relates to a narrow band frequency close to resonance frequencies. Here, STL agrees to damping and very small damping may result in thumbs down sharp STL. A structural damping ratio of 0.01 has been assumed for all the cases analysed in the present work. As there are several damping controlled region in the chosen excitation frequency range, it is plotted in logarithmic scale to lucidly show the effect of damping on STL curve. The mass-controlled region corresponds to the portion of the STL curve after the first resonance frequency. In this region, the STL curve is proportional to the mass, and increase in mass will increase the db efficiently. Since there are many damping-sensitive region, appearing within the mass dominant region, the multiple peaks and valleys are observed towards the high frequency section. Due to several reasons, for the finite plate, the transmission loss is defective at the first resonance frequency. At the resonance vibration response of a finite plate can be theoretically infinite and this is on major scale, being controlled by damping value, ultimately resulting in sharp dips in the STL curve. As there is area normalisation in computing the incident power, the transmitted coefficient () can

11 36 Journal of Sandwich Structures and Materials 19(1) Figure 4. Honeycomb core sandwich panel [24]. (a) Dimension of honeycomb core sandwich panel, (b) Dimension of unit cell honeycomb core. be more than unity. This does not mean the transmitted power is greater than the incident power. This occurrence is due to the valuation of incident power in the normalisation process. There is high coherency between the observations made in this section and the observation made by Huang [23]. Studies on honeycomb core sandwich panel By comparing the sandwich panels with different type of cores, the sandwich panel with honeycomb core is geometrically more complicated. The dimensionality and the unit cell of the honeycomb core sandwich panel are shown in Figure 4(a) and (b), respectively. The effect of face sheet thickness, core height and cell size of honeycomb core on sound transmission loss behaviour is analysed. Equivalent elastic properties of sandwich panel with honeycomb core The equivalent properties for honeycomb core sandwich panel are derived based on honeycomb plate theory as given by Hao et al. [25]. Assumptions made for deriving the equivalent elastic properties are. The facing plates are thin compared to the core thickness.. During distortion of the panel, straight lines normal to the middle panel do not remain straight.. The hexagonal cell is perfectly regular. The honeycomb core sandwich panel of size 1.5 m 1 m is chosen for the investigation in the present work. E x ¼ E y ¼ 4 3 t pffiffiffi E; 3 l G xz ¼ p ffiffi t 3 l G; xy ¼ 1 3 pffiffi 3 3 t G xy ¼ 2 E l

12 Arunkumar et al. 37 E x ¼ e 11e 22 e 2 12 e 22 ; E y ¼ e 11e 22 e 2 12 e 11 ; G xz ¼ e 44 G yz ¼ e 55 ; G xy ¼ e 66 ; xy ¼ e 12 e 22 e 11 ¼ ½ðh þ d Þ3 h 3 Še f11 þ h 3 e c11 ðh þ d Þ 3 ; e 22 ¼ ½ðh þ d Þ3 h 3 Še f22 þ h 3 e c22 ðh þ d Þ 3 e 12 ¼ ½ðh þ d Þ3 h 3 Še f12 þ h 3 e c12 ðh þ d Þ 3 ; e 44 ¼ d h þ d e f44 þ e 55 ¼ d h þ d e f55 þ h h þ d e c55 h h þ d e c44 e 66 ¼ ½ðh þ d Þ3 h 3 Še f66 þ h 3 e c66 ðh þ d Þ 3 ; e c11 ¼ e c22 ¼ 1 1 xy 2 E x 1 e c44 ¼ G xz, e c55 ¼ G yz, e c66 ¼ G xy ; e f11 ¼ e f E e f44 ¼ e f55 ¼ kg, e f66 ¼ G; eq ¼ d f þ h c h þ d ð8þ where e fij and 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, whereas E x and E y, G xy and G yz refer to the overall equivalent properties of sandwich panel. 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, f and c are the densities of face and core, respectively. k is the effective coefficient in the range Sound transmission loss characteristics Effect of face sheet thickness. Core height (15 mm), cell size (2 mm) and cell wall thickness (0.04 mm) of honeycomb core are assumed to be constant and the face sheet thickness is varied as 0.5 mm, 1.5 mm and 2 mm to analyse the effect of face sheet thickness on sound transmission loss of the sandwich panel with honeycomb core. Based on the convergence study, the mesh size of is used. This mesh size also satisfies the six elements per wavelength requirement for numerical vibroacoustics. Figure 5(a) shows the effect of face sheet thickness on sound power level for both normal and oblique incidence. From Figure 5(a), the sound power level has its peak value in the resonance frequencies whereas the STL curve has sharp dips in the resonance frequencies because of high transmission of sound power. Figure 5(b) shows the sound transmission loss of normal and oblique angle of incidence for 0.5 mm, 1.5 mm and 2 mm. From Figure 5(b), it is clear that the STL curve has the inverse pattern of SPL as anticipated. From Figure 5(b), STL for various face sheet thicknesses are clearly distinguished

13 38 Journal of Sandwich Structures and Materials 19(1) Figure 5. Effect of face sheet thickness for honeycomb core sandwich panel. (a) Sound power level, (b) Sound transmission loss. in the stiffness-controlled region. Face sheet of 2 mm thickness has high sound transmission loss in the stiffness controlled region. This can be attributed to high stiffness when compared with the other two cases. The negative transmission loss is seen in first resonance frequency due to the reasons as discussed earlier. Many damping-sensitive regions appear in the mass-dominant region and hence multiple peaks and valleys are observed in the higher frequency segment. The massdominant zone is also clearly distinguished because of increase in overall mass of the panel due to increase in face sheet thickness. From the above discussion, it is clear that effect of face sheet thickness on sound transmission loss is significant in all the three regions of the STL curve. The same kind of variation has been observed in the STL behaviour for the oblique incidence also as seen in Figure 5(b). One can observe from Figure 5(a) and (b) that for oblique incident, sound radiation is lower and sound transmission loss is higher than the normal incident excitation as discussed earlier. Effect of core height. The effect of core height on sound transmission loss of the honeycomb core sandwich panel is studied by varying the core height as 10 mm, 15 mm and 20 mm and by keeping cell size (2 mm) and wall thickness (0.04 mm) as constant. In order to keep the sound transmission loss in a desirable level by reducing the panel size in due considerations with the space constraints, the face sheet thickness of 2 mm, 1.5 mm, 0.5 mm are selected, respectively, in the increasing order of the core height of 10 mm, 15 mm and 20 mm, respectively. It is done so to increase the stiffness and equivalent density while varying the core height. Based on the convergence study, the mesh size of is used. This mesh size also satisfies the six elements per wavelength requirement for numerical vibroacoustics. Figure 6(a) shows the effect of core height on sound power level for both the normal and oblique incidences variation of sound power radiated with respect to core height that has been given in Figure 6(a). From Figure 6(a), it is clear that resonant amplitude of sound power is influenced by the core height.

14 Arunkumar et al. 39 Figure 6. Effect of core height on acoustic behaviour for honeycomb core sandwich panel. (a) Sound power level, (b) Sound transmission loss. Figure 6(b) shows the influence of core height on STL. From Figure 6(b), one can observe the anti-peaks, and the stiffness-sensitive region curves are not clearly distinguished. This indicates that stiffness of the panel is not enhanced by increase in core height, due to the counter balance effect of face sheet thickness and core height. But in the mass-controlled region, anti-peaks in the curves are clearly distinguished which indicates that increase in face sheet thickness increases the mass significantly compared to the stiffness. Due to this approach, the higher sound transmission loss is achieved in the mass-controlled region with lesser core height. The effect of damping is clearly seen in the resonance frequencies, and due to this multiple peaks and valleys are seen in higher frequency segment. From this result, it is clear that, it is possible to achieve good transmission properties in lower core height sandwich panel in due consideration to space constraint. From the assumption made for oblique incident, the same trend is observed for sound transmission loss and sound power level analysis. Effect of cell size. The effect of cell size of the honeycomb core sandwich panel on sound transmission loss behaviour is studied by varying the cell size as 2 mm, 3 mm and 4 mm and keeping a same core height (15 mm), face sheet thickness (1 mm) and cell wall thickness (0.04 mm). Based on the convergence study, the mesh size of is used. This mesh size also satisfies the six elements per wavelength requirement for numerical vibroacoustics. Figure 7(a) shows the effect of cell size on sound power level for both normal incidence and oblique incidences. Influence of cell size on sound power variation and sound transmission loss is shown in Figure 7(a) and (b), respectively. Due to the counter-balance variation between the mass and stiffness, both the sound power radiated and transmission loss variation are not sensitive to the cell size. From Figure 7(a) and (b), it is also observed that there is no distinguished variation in peaks of curve in both stiffness and mass-sensitive region. The effect of damping in all resonance frequency is clear and sound transmission loss in the damping-controlled region is proportionally the same since the same damping ratio of 0.01 is assumed for all the cases.

15 40 Journal of Sandwich Structures and Materials 19(1) Figure 7. Effect of cell size on acoustic behaviour for honeycomb core sandwich panel. (a) Sound power level, (b) Sound transmission loss. Figure 8. Different types of core topologies. (a) Trapezoidal core, (b) Triangular core, (c) Cellular core and (d) Zed core. Studies on sandwich panel with triangular, trapezoid, cellular and zed cores In order to study the effect of core topology of truss core sandwich panel on sound transmission loss, three different cores such as triangular, trapezoidal and cellular cores are considered and the results are compared with Zed core sandwich panel. The schematic diagram of different cores that are analysed in this section is shown in Figure 8. Equivalent elastic properties for triangular, trapezoid, cellular and zed core sandwich panel An aluminium truss core sandwich panel analysed by Lok and Cheng [6] of size 1.5 m 1.5 m having 10 identical units is compared with 20 discrete zed cores to contain the same number of web cores. To estimate the elastic properties for rectangular or cellular and triangular core, it is considered that f/p varies from

16 Arunkumar et al f=p 0:5 for truss cores. In that, the ratio f=p ¼ 0 relates to a triangular truss core, and f=p ¼ 0:5 corresponds to a cellular truss core. In order to maintain the same weight for all cases, the same cross-sectional area is considered and the dimensions of the sandwich panels are calculated and shown in Table 3. The assumptions adopted for deriving the elastic properties are. the deformation of the panel is small.. the facing plates are thin compared to the core thickness.. during distortion of the panel, straight lines normal to the middle panel do not remain straight.. the panel width is many times the unit pitch. Equivalent stiffness properties for truss core sandwich panel are given by Lok and Cheng [6] as given below D x ¼ EðI c þ I f Þ; D y ¼ EI f ; 1 2 I c I c þi f D xy ¼ 2GI f ; 1 D Qy ¼ 1 d ðc y þ f y Þþ 1 p zc D Qx ¼ Gt c d2 t pst c þ 1 6 ðd c t t c þ sd c 3pd p Þ 2 x ¼, y ¼ D y D x ; I c ¼ st cd 2 c 12p ; I f ¼ td2 2 _ ð9þ Equivalent stiffness properties for zed core sandwich panel given by Fung et al. [7] is given below D x ¼ Eh2 t 2ð1 2 Þ þ E ci c 2p ; D y ¼ Eh2 t 2ð1 2 Þ D xy ¼ 1 2 Gh2 t; Table 3. Dimension of zed core, cellular core, trapezoidal core and triangular core in millimetres. Parameter Type of core P d f t ¼ t c Zed core Cellular core Trapezoidal core Triangular core

17 42 Journal of Sandwich Structures and Materials 19(1) 1 ð h2 t 2 D Qx ¼ G þ E ci c 2pE Þht w c s c g E C 24E t wg 3 D Qy ¼ 1 2 EI p 2 6 þ 1 2 c E c I c pag 2 h 2 þ pg3 6h 2 ð10þ where E and E c are the elastic modulus of facing material and core material, respectively. c y, f y and zc are deflection parameters described in Lok and Cheng[6]. I f and I c are the moment of inertia of face sheet and core, respectively. x and y are the Poisson s ratio along the x- and y axis, respectively. The equivalent stiffness properties for truss and Z core are calculated based on equations (9) and (10) derived by Lok and Cheng [6] and Fung et al. [7], respectively, and the calculated values are listed in Table 4. From Table 4, it can be seen that E x, E y, G xy, and G xz increases when the f/p ratio decreases and the G yz increases when the f/p ratio increases. Acoustic response characteristics In order to study the acoustic response, based on the convergence study, the mesh size of is used. This mesh size also satisfies the six elements per wavelength requirement for numerical vibroacoustics. The influence of various truss core and zed core on sound transmission loss variation is shown in Figure 9. From Figure 9, it is clear that in the stiffness-controlled region, the sound transmission loss of triangular core sandwich panel is high due to its increased transverse shear stiffness compared to other panels as shown in Table 4. This reflects a distinct variation of STL associated with triangular core in the stiffness region also. In the masscontrolled region, distinguished curve is not seen; since STL is proportional to Table 4. Equivalent properties of zed core, cellular core, trapezoidal core and triangular core. Equivalent properties Type of core Zed core Cellular core Trapezoidal core Triangular core E x (Pa) 2: : : : E y (Pa) 1: : : : G xy (Pa) 5: : : : G yz (Pa) 4: : : : G xz (Pa) : : : xy yz

18 Arunkumar et al. 43 Figure 9. Sound transmission loss of rectangle, trapezoidal, triangular and zed core sandwich panel. the mass, STL of the panel is not sensitive to the nature of truss curve. This can be attributed to the equal weight associated with different core sandwich panels. In damping-sensitive region, there is negative value in the first resonance frequency. The multiple peaks and valleys are seen in higher frequency range due to influence of damping effect at resonance frequencies. It is seen that the peaks and valleys for triangular core sandwich panel are less due to the shift in natural frequency, which is due to higher stiffness. Less number of dips in STL curve associated with triangular core sandwich panel indicates good acoustic performance in the frequency range Hz. From the results observed in this analysis, one can select a triangular core sandwich panel for low frequency application due to its increased transmission loss in stiffness-sensitive region and also less dips in the mass-controlled region in STL. The STL variation with different cores for normal and oblique incidents is observed. However, the amplitude of STL is relatively high for the oblique incident due to shear loss in plate compared to normal incidence. Studies on foam core sandwich panels Aluminium and rohacell foam are used as core material in most of the foam core sandwich panels that are used in aerospace structural applications. Three different face sheet materials such as aluminium, titanium and laminated carbon-epoxy are considered in this section. Their material properties are shown in Table 5. Polymethacrylimide-based foam, Rohacell 110 WF rigid foam, is used for the sound transmission loss analysis. The relative density of 10% is considered for all the foam core analysed in this section. Polymethacrylimide s density is given as 1100 kg/m 3. The properties of Rohacell 110 WF are selected from the standard

19 44 Journal of Sandwich Structures and Materials 19(1) Table 5. Material properties of face materials analysed in foam core sandwich panels [9]. S.No Material Young s modulus (GPa) Density (kg/m 3 ) 1 Aluminium Titanium Epoxy carbon Figure 10. Foam core sandwich panel. data sheet based on ASTM D 638. The density for Rohacell 110 WF given in data sheet is 110 kg/m 3 which is 10% of the density of polymethacrylimide. The Young s modulus for the same is 180 MPa. The formula to calculate the aluminium foam properties such as Young s modulus is given by Petrone et al. [20], which is used in the present work. Equivalent elastic properties for foam core sandwich panels The dimension of foam core sandwich panel is shown in Figure 10. In the present analysis, c ¼ 8 mm, d ¼ 10 mm, t ¼ 1 mm, l ¼ 1 m and b ¼ 0.8 m is considered. Equivalent elastic properties for foam core sandwich panel given by Ashby and Gibson [26] is given below ðeiþ eq ¼ E fbtc 2 2 ðaeþ eq ¼ 2A f E f þ A c E c ð11þ ðagþ eq ¼ bcg c where E f and E c refer to Young s modulus of face and core material, respectively. A f and A c are the cross-sectional area of face and core, respectively; I refers to the

20 Arunkumar et al. 45 second moment of area of sandwich panel. t, b,d,c, l are the geometric properties shown in Figure 10. The detailed derivation of the equivalent properties can be referred in Gibson and Ashby [26]. The equivalent density ( eq ) and relative density ( r ) of the foam core sandwich panel can be calculated from the equation (12) eq ¼ 2 ft þ c, r ¼ c t eq s ð12þ where f and c are density of face sheet and core, respectively. s is the density of core material. The properties of the face sheet material used in this section with reference to Boudjemai et al. [9] are shown in Table 5. Acoustic response characteristics In order to study the acoustic response, based on the mesh convergence and also to satisfy the six elements per wavelength requirement, a mesh size of is used. The STL variation of the sandwich panel with different foam and face is shown in Figure 11. Distinct variation of STL in the three different regions can be observed in Figure 11. In the stiffness-sensitive region, the effect of stiffness in epoxy carbon face sheet is high when compared to the other face sheet materials due to its high stiffness. The effect of damping is high in the first resonance frequency which leads to negative STL. Multiple peaks and valleys are seen in the mass predominant region due to damping effect. After the first resonance frequency, in the masscontrolled region, the Rohacell foam with titanium face sheet has high sound Figure 11. Sound transmission loss of foam core with different face sheet material.

21 46 Journal of Sandwich Structures and Materials 19(1) transmission loss because of its high density because it has high mass compared to other materials considered in this analysis. Due to the decrease in mass density for Epoxy carbon face sheet, the sound transmission loss is less after the first resonance frequency. Many peaks and valleys are seen in the mass-controlled region due to damping effect. Negative transmission loss is seen in the first resonance frequency due to small damping. The same trend is observed for both normal incidence and oblique incidence. From the results it is clear that the effect of material on sound transmission loss is significant and this can be controlled by varying the density of foam for various material sheets to keep the sound transmission loss with in a desirable level. Conclusion Influence of nature of core and materials on sound transmission loss of different kinds of sandwich panels typically used in aerospace structural application has been investigated using combined 2D equivalent FEM model and Rayleigh integral. The below mentioned key points are made with respect to sound transmission loss of sandwich panels:. In honeycomb core sandwich panel, the effect of face sheet thickness on sound transmission loss is significant.. In due consideration to space constraint, the desirable sound transmission loss can be achieved in lower core height honeycomb core sandwich panel.. One can select cell size as the parameter to reduce the weight without affecting the sound transmission loss.. One can select triangular core sandwich panel for low frequency application due to its increased transmission loss in stiffness-sensitive region and also over all less dips in mass-controlled region.. In foam core sandwich panel, it is noticed that the effect of material on sound transmission loss is significant and this can be controlled by varying the density of foam for various material sheet to keep the sound transmission loss in desirable level. These validated results can be used in the design of structures considering acoustic comfort for aerospace structures. Declaration of Conflicting Interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) received no financial support for the research, authorship, and/or publication of this article.

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