Nonlinear dynamic analysis of an inclined micro-beam under a moving mass

Abstract

Nonlinear vibration of an inclined simply supported micro-beam under a moving mass is investigated for Euler–Bernoulli beam theory (EBT) and Timoshenko beam theory (TBT) respectively. Based on a modified couple stress theory (MCST) and the von-Karman geometric nonlinearity, the nonlinear coupled dynamic equations of the system are established through the Hamilton’s principle with the assumed mode method. A wide range of numerical examples are employed to study the influence of slenderness ratio, cross-section height, inclined angle, the size and velocity of the moving mass and the scale factor of the material on the solutions of nonlinear and linear, the solutions of EBT and TBT and the solutions of moving mass and moving load. By comparing the differences between the nonlinear and linear solutions under different parameters and beam theories, the importance and significance of nonlinear dynamic analysis of the inclined micro-beam are revealed.