Free Vibration Characteristics of Bidirectional Graded Porous Plates with Elastic Foundations Using 2D-DQM

This manuscript develops for the first time a mathematical formulation of dynamical behavior bi-directional functionally graded porous plates (BDFGPP) resting on Winkler–Pasternak foundation using unified higher-order plate theories (UHOPT). The kinematic displacement fields are exploited to fulfill null shear strain/stress at bottom and top surfaces without needing factor correction. gradation materials is proposed in axial (x-axis) transverse (z-axis) directions according power-law distribution function. cosine function employed define porosity through z-direction. Equations motion terms displacements associated boundary conditions derived detail Hamilton’s principle. two-dimensional differential integral quadrature method (2D-DIQM) transform partial equations into system algebraic equations. Parametric analysis performed illustrate effect relations, indices, type, elastic foundations, geometrical dimensions, (BCs) natural frequencies mode shapes BDFGPP. coefficient frequency dependent type. coupling conditions, functions. model can be used designing BDFGPP nuclear, marine, aerospace, civil structures based their topology constraints.