Analyzing nonlocal nonlinear vibrations of two-phase geometrically imperfect piezo-magnetic beams considering piezoelectric reinforcement scheme

Abstract

This article deals with analyzing nonlinear free vibrations of nonlocal two-phase piezo-magnetic beam with geometric imperfection rested on viscoelastic substrate. The two-phase piezo-magnetic material is based on a composition of piezoelectric and magnetic constituents with desirable percentages. An assumption is that the nanobeam is rested in an initial position due to geometric imperfection. In addition, the equilibrium equations of nanobeam with piezo-magnetic properties are derived utilizing Hamilton’s principle and the von Kármán geometric nonlinearity. Then, an exact solution based on the Jacobi elliptic functions has been provided to obtain nonlinear vibration frequency. It is found that nonlinear vibration behavior of the nanobeam is dependent on the magnitude of induced electric voltage, magnetic field intensity, geometric imperfection, and viscoelastic substrate parameters.

Bending analysis of nanobeams based on the integral form of nonlocal elasticity using the numerical Rayleigh-Ritz technique

“…4 After that, the differential NET has been employed by several research workers in various problems mainly attributable to its simpler mathematical nature in comparison with the integral version in conjunction with reasonable accuracy. The first application can be found in the work of Peddieson et al 8 The reader is also referred to Refs., [9][10][11][12] , Refs., [13][14][15][16][17][18][19][20][21] and Refs., [22][23][24][25][26][27][28][29][30][31] as some examples for the problems of nanoscale beams, plates, and shells, respectively.…”