The third superharmonic resonance of inclined beam subjected to harmonic excitation in temperature field

Based on nonlinear vibration equation of inclined beam subjected to harmonic excitation in temperature field, the first approximate solution of the 3 superharmonic resonance of the nonlinear vibration system is obtained by means of the method of multiple scales for nonlinear oscillations. The jumping and hysteresis phenomena of amplitude frequency response curves of 3 superharmonic are obvious. Numerical analysis on the influence of temperature, excitation, dumping, and geometric parameter on amplitude frequency response curve are as follow. With the increasing of Elastic modulus, cross-sectional area, damping, and high, the amplitude and resonant region of the 3 superharmonic resonance decrease. With the increasing of Excitation amplitude, length, initial temperature and temperature coefficient, the amplitude and resonant region of the 3 Superharmonic resonance increase.