Nonlinear Vibroacoustic Analysis of Functionally Graded Plates in the Thermal Ambiance at Oblique Incidence

In this investigation, the analysis of the nonlinear vibroacoustic and sound transmission loss behaviors of plates made of functionally graded material is presented. It is assumed that the properties of the functionally graded plates are in the form of the simple power law scheme and continuous along the thickness, under thermal load and incident oblique plane sound wave as well as the first-order shear deformation theory. For this purpose, first, using Hamilton’s principle, the nonlinear partial differential equations of motion are derived by the displacement field function approach and by considering the nonlinear von Kármán strain-displacement relations. To solve the equations, using the Galerkin method, the nonlinear partial differential equations of motion lead to Duffing equation. Then, using the homotopy analysis method, the equation of the transverse movement of the plate is solved semi-analytically to obtain the nonlinear frequencies. Finally, the nonlinear vibration and acoustic response of functionally graded plates are studied by considering the variation of the important parameters such as aspect ratio, dimensionless amplitude, volume fraction power of functionally graded material, external acoustic pressure, incidence and azimuthal angles, temperature changes, phase portrait, sound transmission loss, velocity and average mean square velocity of drive point and sound power level of the functionally graded plate. Results show increasing the incidence angle leads increase in hardening effects and sound transmission loss, but growing the azimuthal angle does not have much effect on the frequency-response and sound transmission loss in the absence of the external mean flow. Also, increasing temperature changes lead to decrease in hardening effects and sound transmission loss.