Size-dependent analysis of piezoelectric nanobeams including electro-mechanical coupling

•The nonlinear size-dependent formulation of Timoshenko piezoelectric nanobeam is developed.•The nonlinear analysis of nanobeam under mechanical and electrical loading of nanobeam is investigated.•The consistent size-dependent theory are utilized to investigate the size dependent electromechanical behavior of nanobeam.•The electromechanical behaviors of nanobeam in piezoelectric and inverse processes are investigated.

In this paper, nonlinear formulation of the size-dependent piezoelectric Timoshenko nano-beam is developed based on the consistent size-dependent piezoelectricity theory. Nonlinear basic equations as well as linear and nonlinear boundary conditions of the piezoelectric nanobeam are derived using Hamilton’s principle and the variational method. To derive these equations, the von Karman strain is employed to model the nonlinear geometric model for the nanobeam behavior. To evaluate the formulation derived, static deformation and free vibration of the hinged-hinged piezoelectric beam is investigated in the special case. The results of the formulation derived are investigated under different parameters, and linear and nonlinear effects of the new size-dependent formulation with the classical theory are compared.

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