Size Dependent Nonlinear Secondary Resonance of a Damped Micro/Nano Beam with initial Axial Load in Temperature Field

In the present paper, the nonlinear super-harmonic and sub-harmonic resonance of the forced vibration of a damped pre-loaded clamped-clamped micro/nano Euler Bernoulli beam in the temperature field is studied using the modified strain gradient theory. Using Himlton’s Principle and the Discrete Galerkin’s Method (DGM), the nonlinear governing equation for the vibration of the micro/nano beam is derived. The Multiple Scale Method (MMS) is then utilized to solve the governing equation analytically and obtain the frequency-response equation. The effect of nonlinearity, three length scale parameters, excitation amplitude, damping, temperature change and the pre-stress axial load on the response is illustrated and the results are analyzed.