Investigating the thermal environment effects on free vibration of functionally graded skew plates with piezoelectric actuators using a meshfree method

In this study, free vibration analysis of FGM plate with piezoelectric layers in thermal environment is presented on the basis of the first-order shear deformation plate theory and a meshless method with radial point interpolation. Using this numerical method, the field variable is interpolated by nodes scattered in the mid-plate of the problem domain. As no relation between nodes exists, they can be scattered arbitrarily. The plate is made of a functionally graded material consisted of two different phases of metal and ceramic. In the piezoelectric FGM plates, the properties of core material are assumed to be graded through the thickness according by the power-law distribution while the electric potential is assumed to be a linear function through the thickness of each piezoelectric sub-layer. Two sets of electric boundary conditions exist for surfaces of the piezoelectric layers including: (1) a closed-circuit condition in which the electric potential is kept at zero (grounded); and (2) an open-circuit condition in which the electric potential remains free (zero electric displacements). In this work a closed-circuit electric boundary condition is adopted. Through the examinations, it is seen that with increase in volume fraction exponent and domination of the metal phase over the ceramic phase, a drop in the frequency occurs. The elevation of temperature also causes a frequency drop. However increase of the constraints of the plate increases the frequency of vibration. On the other hand, the effect of the thickness to length ratio of the FGM plate increases the frequency and increases the thickness of the piezoelectric layers firt causes a drop in the frequency and then increases it. The increase of skew angle in the constant volume fraction exponent causes increases the frequency and with increases the volume fraction exponent in constant skew angle a drop in the frequency gradually occurs.