Hygrothermal free vibration of multiple magneto-electro-elastic nanoplate system via higher-order nonlocal strain gradient theory

Abstract

The free vibration behavior of the coupled multiple magneto-electro-elastic nanoplate system embedded in Kelvin–Voigt visco-Pasternak medium incorporating hygrothermal effects is analyzed using the higher-order nonlocal strain gradient assumption. It should be noted that to obtain a more precise modeling of small-scale structures when using higher-order nonlocal strain gradient theory, both hardening and softening effects of materials are considered. The governing equilibrium equations are derived based upon the classical Kirchhoff thin plate approach and Hamilton’s variational principle. The complex eigenvalues of the system are presented in the exact closed-form solutions and are validated by numerical results found from the trigonometric technique. Numerical studies are carried out to demonstrate the effects of the number of magneto-electro-elastic nanoplates, material length scale parameters, initial external electric and magnetic fields, visco-Pasternak foundation, and hygrothermal loading on how the system damped frequency curves are varied.