Wave transmission across laminated composite plate in the subsonic flow Investigating Two-variable Refined Plate Theory
Latin American Journal of Solids and Structures
The main aim of this paper is to employ an extension of two-variable Refined Plate Theory (RPT2) to determine Sound Transmission Loss (STL) across laminated composite plate in contrast to external excitation. It should be noted that RPT2 known as a second type of Refined Plate Theory which includes the extension term in displacement field. To achieve this goal, firstly, the lateral displacements are expanded by considering three parts, including shear, bending and extension term to provide an
... erm to provide an analytical model based on two-variable Refined Plate Theory without considering the effect of the shear correction coefficient in governing equations. Secondly, vibro-acoustic analysis is administered by incorporating the laminated composite plate equation beside the acoustic wave equation, simultaneously. Consequently, the power transmission through the structure is specified due to a plane sound wave. Beside, in order to illustrate the accuracy of the present formulation (RPT2), the obtained STL is compared with those available in literature. However, the application of present study (RPT2) is clarified in the acoustical designs due to presenting more precise results in comparison with Classical Plate Theory. Eventually, the numerical results are achieved to determine the influences of various properties on STL. of Solids and Structures, 2018, 15(5), e39 2/20 composed of two plastic plates with an ER mid layer. In the following, the STL of the lightweight all-metallic panels was achieved by Xin and Lu (2010) sandwiching corrugated cores as well as employing the space-harmonic method. It should be considered that two parallel panels are connected uniformly with distributed rotational and translational springs. Besides, an analytical model of STL proposed through finite as well as infinite aero elastic panels in convected fluids. It is essential to mention that the influence of mean flow on sound transmission was presented by three various condition, including existence of mean flow on radiating, incident and also the both sides. Then, the Classic Shell Theory was employed by Daneshjou et al. (2011) to designate the STL of doublewalled cylindrical shell subjected to porous core. Following the last work, the acoustic behavior of the panels subjected to air gap insulation was interpreted Arunkumar et al. (2016) . Koval (1980) studied the transmission as well as the reflection at plane displacement discontinuity surface in second gradient solid. In this regard, another work by Vashishth and Sukhija (2015) was suggested across the reflection and transmission of plane wave from a fluid-piezothermoelastic solid interface. Consequently, Tang et al. (1996a Tang et al. ( , 1996c considered honeycomb core as an intermediate layer to enhance the amount of STL. Moreover, the STL was calculated in Tang et al.(1996b) work through the cylindrical shell sandwiching a layer impinged upon an exterior turbulent boundary layer. As it's obvious, the importance of using laminated composite shell is unavoidable. For this reason, Daneshjou et al. (2007 Daneshjou et al. ( , 2009 ) absorbed their regard to determine STL of the laminated composite as well as orthotropic circular cylindrical shells. Just recently, an analytical model of double-walled sandwich shells was offered by Liu and He (2016) to illustrate the influence of air gap flow on STL by employing the Love's theory to obtain the shell motion. It should be noted that they considered elasticity theory to determine the motion of the isotropic thick polymer core. However, Talebitooti and Khameneh (2017) , a complete model of power transmission on the double-walled laminated composite cylindrical shells along with air-gap was proposed applying three-dimensional equations of anisotropic elasticity. In the following, Talebitooti et al. (2017a) employed the Genetic Algorithm to optimize the sound transmission of the structure subjected to porous material. Besides, Talebitooti et al. (2016) presented an analytical model across the specifications of the laminated composite cylindrical shell based on Third-order Shear Deformation Theory in the existence of external mean flow. Likewise, the displacements are derived as a cubic order of the thickness coordinate. Consequently, the equations of vibration related to cylindrical shell are combined with acoustic wave equation to clarify sound transmission into such structure. As another consequence, the vibroacoustic behavior of the laminated composite doubly curved shell was analyzed by Talebitooti et al. (2017b) in another paper based on considering Shear Deformation Shallow Shell Theory. In another work, Talebitooti et al. (2018a, b), Third order Shear Deformation Theory was employed through sound transmission of the orthotropic doubly curved composite shell. They also inspected the influence of porous core on acoustic transmission of the doubly curved composite shell. Literature clearly demonstrates that, although the STL on the variety of laminated theories has been presented and discussed, there is no investigation of STL through the plate employing an extension of two variables Refined plate theory (RPT2), so far. Earlier, to analyze the equation of motion of the plate, Classical thin Laminated Plate Theory was taken into account in which transverse shear and rotation effects are completely ignored. However, it should be noted that since the effect of transvers shear especially for thick plate become important, then, First-order Shear Deformation Theory (FSDT) is used to fulfill this end. Likewise, FSDT was developed based on stress approach for the first time by Reissner (1944 Reissner ( , 1945 with inserting the effect of transvers shear in its equations. Later, Reissner's theory was extended by Mindlin (1951) which is well-known as Mindlin's theory based on displacement approach. It is necessary to mention that FSDT was proposed by entering shear correction coefficient as well as regarding constant transvers shear stress through the thickness of the plate. Finally, it is noteworthy that the theory which is followed in this paper is well-known as RPT2, without entering shear correction factor (which is recognized as interesting feature of this theory) in its equations to interpret the behavior of STL in the existence of airflow. Besides, in the present formulation (RPT2) the effects of shear, extension and bending are taken into account in its transverse displacement while in other theories including FSDT as well as HSDT are being neglected. However, the importance of employing the RPT2 in comparison with other theories including FSDT and HSDT is clarified in a work done by Kim et al. (2009) as a result of demonstrating the accurate results. Furthermore, this procedure is applicable for Naviour closed form solution in the free vibration state. As another aspect, although the present study (RPT2) does not have the complicated process such HSDT, but the obtained result present the accuracy of the current formulation or sometimes the better results could be observed. It is not also refused to note that the present formulation appears much more effective in transverse deflection as well as buckling in comparison to HSDT, as a result of demonstrating accurate results. Consequently, the obtained STL from present study (RPT2) is compared with those of literature to demonstrate the validity of the present results in entire range of frequency. Furthermore, in numerical result section the effects of various properties on STL are presented and discussed.