Thermally Induced Vibration of Beams with Consideration of Rotary Inertia

Present research deals with the thermally induced vibrations of beams. The structure is made of an isotropic homogeneous material and is subjected to rapid surface heating on the upper surface while the lower one in thermally insulated. Based on the assumptions of uncoupled thermo-elasticity, the one-dimensional transient heat conduction equation is solved analytically. The transverse vibration equation of the beam is obtained with the aid of the Euler-Bernoulli assumption with consideration of the rotary inertia. This equation is also solved analytically for simply supported beams using the Fourier series expansion. The solution of this equation is divided into two parts, namely the quasi-static response and the complementary response. All of the results are presented in a dimensionless form and the obtained formula are compared with those provided by neglecting the inertia effects. Finally, graphical presentation of mid-span vibrations of the beam are given which accept the existence of thermally induced vibrations.