Dynamic analysis of porosity dependent functionally graded sigmoid piezoelectric (FGSP) plate

Abstract

This paper analyzes the vibration behaviour of the functionally graded sigmoid piezoelectric (FGSP) plate subjected to electrical and mechanical loading of a porous and non-porous plate. The sigmoid law is used for the variations of material properties along with the direction of thickness with different porosity types, i.e. even and uneven types. The plate incorporates the geometrical nonlinearity with von Kármán strains and First-order shear deformation theory (FSDT) based displacement field. For getting the nonlinear governing equation from Hamilton's principle or energy principle and higher-order numerical formulation with nine nodded isoperimetric elements and the six degrees of freedom per node. The perfect FGSP plate shows multi-periodic excitation with two strong attractors for SSSS boundary conditions, while quasi-periodic responses and 3-T periodic responses are observed for CCCC and CFFF boundary conditions. For evenly distributed porous SSSS FGSP square plate, the center displacement increases with an increase of the porosity from 0.2 to 0.4, while for un-evenly distributed porous center displacement reduces with a rise of the porous exponent from 0.2 to 0.4. The current analysis outcomes can be used for perfect and porous functionally graded piezoelectric smart structure applications under different electromechanical loading environments.