Nonlinear free vibration analysis of embedded flexoelectric curved nanobeams conveying fluid and submerged in fluid via nonlocal strain gradient elasticity theory

Abstract

In this study, harmonic balance method is employed to solve nonlinear equation of flexoelectric nanobeams by initial curvature and embedded in an elastic medium conveying viscous fluid and submerged in fluid. Fluid is assumed to be incompressible, laminar and Newtonian. Assuming Euler–Bernoulli’s beam theory with simply supported ends based on nonlocal strain gradient theory and Von-Karman nonlinear strain theory come to the nonlinear differential equation of motion. Using Galerkin method, the nonlinear partial differential equation reduces to ordinary differential equation. The effects of nonlocal and strain gradient parameters, maximum amplitude, nonlinear foundation, initial curvature, flexoelectric effect and … on the real and imaginary parts of the nonlinear natural frequencies are investigated. By increasing flexoelectric coefficient, natural frequency and critical velocity decreases and divergence and flutter instability occur earlier and the stability range becomes smaller. .