Effects of porosity and thermomechanical loading on free vibration and nonlinear dynamic response of functionally graded sandwich shells with double curvature


The fundamental frequencies and nonlinear dynamic responses of functionally graded sandwich shells with double curvature under the influence of thermomechanical loadings and porosities are investigated in this study. Two material models are considered. The continuity requirement of material properties throughout layers are fulfilled by newly introducing refined effects of two porosity types regarding the average of constituent properties weighted by the porosity volume fraction. The first-order shear deformation theory taking the out-of-plane shear deformation into account is employed to obtain the Lagrange equation of motions. The number of primary variables reduces from five to three after introducing the Airy stress function. The system of dynamic governing equations is obtained by utilizing the Bubnov–Galerkin procedure. The natural frequencies are analytically computed by solving eigenvalue problems, and the fundamental frequencies are acquired by further assumptions about the inertial force caused by the shell rotation variables. The nonlinear dynamic responses of the functionally graded spherical, cylindrical, and hyperbolic paraboloid shells under the influence of different geometry configurations, loading conditions, and porosity types and degrees are obtained by applying the fourth-order Runge–Kutta method. The numerical results are presented and verified with available studies in the literature. Although porosities are usually considered material defects weakening the structure performance, this study has proved clearly that porosities stiffen the shell structures to some extent.


Functionally graded sandwich shell
Thermomechanical loading
Nonlinear dynamic analysis
First-order shear deformation theory