Free vibration characteristics of trapezoidal nanoplate rested on viscoelastic substrate with arbitrary boundary conditions using differential quadrature method.

This study investigates the free vibration analysis of trapezoidal nanoplate resting on viscoelastic foundation based on first order shear deformation theory (FSDT) incorporating nonlocal elasticity theory, using differential quadrature (DQ) method. The nanoplate's governing equations of motion together with various associated boundary conditions have been discretized applying a mapping DQ method in the spatial domain. Then the complex natural frequencies of the trapezoidal nanoplates obtained by solving the eigen value matrix equation. Verification of the study is confirmed by comparing its numerical results with those available in the literature, then parametric study is thoroughly performed. A special attention is drawn to the role of geometrical parameters of nanoplate, stiffness and damping parameters of foundation, nonlocal parameter and boundary condition on natural frequencies characteristics. This research's results are useful for designing of the nanoelectromechanical systems (NEMS) efficiently and show the potential application of the system as highly sensitive nano-sensors and resonator in damped medium.