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 subharmonicresonance of the forced vibration of a dampedpre-loaded clamped-clamped micro/nano Euler Bernoullibeam in the temperature field is studied using the modifiedstrain gradient theory. Using Himlton’s Principle and theDiscrete Galerkin’s Method (DGM), the nonlineargoverning equation for the vibration of the micro/nanobeam is derived. The Multiple Scale Method (MMS) is thenutilized to solve the governing equation analytically andobtain the frequency-response equation. The effect ofnonlinearity, three length scale parameters, excitationamplitude, damping, temperature change and the pre-stressaxial load on the response is illustrated and the results areanalyzed.