Dynamic buckling analysis of bi-directional functionally graded porous truncated conical shell with different boundary conditions

In this study, the dynamic buckling of bi-directional functionally graded porous (BD-FG) truncated conical shell resting on an elastic foundation is investigated for different boundary conditions. The structure is under an axial compression loading at the two ends. First order shear deformation theory (FSDT) and Hamilton's principle are used to derive the governing equations. The material characteristics change according to modified power-law model across thickness and along length directions for even and uneven distributions of porosity pattern. The governing equations are solved numerically by means of the Generalized Differential Quadrature method. Afterwards, the Bolotin's method is employed for attaining the dynamic instability region of structure. The results are compared and validated with those cases from published papers. Subsequently, the effect of circumferential half wave number, geometrical parameters, power-law indexes, porosity volume fraction, boundary conditions, static load factor and elastic foundation parameters on the dynamic instability region are investigated.