Thermally induced vibration analysis of Timoshenko beams based on the micropolar thermoelasticity

In this paper, the free vibrations of beam-type structures subjected to rapid heating are analyzed within the framework of micropolar thermoelasticity using a novel numerical approach. The equations of motion are derived based on the micropolar elasticity theory and the Timoshenko beam theory using Hamilton’s principle. The transient 1D Fourier-type heat conduction equation is also used as the heat equation. The matrix representation of relations is given which can be efficiently utilized in numerical approaches. Solution in time domain is done by the Newmark algorithm based on the constant average acceleration technique. The generalized differential quadrature and variational differential quadrature techniques are also applied to discretize in space domain. Important effects including those of thermal shock and geometrical parameters on the thermally induced vibrations of micropolar Timoshenko beams with various boundary conditions are investigated.