Nonlinear dynamic responses of viscoelastic fiber–metal-laminated beams under the thermal shock

Abstract

The present study is concerned with the nonlinear dynamic responses for the viscoelastic fiber–metal-laminated beams subjected to thermal shock. First, the one-dimensional heat conduction equation with variable coefficients in the direction of thickness is established, and this equation is solved by differential quadrature method (DQM) and the fourth-order Runge–Kutta method. An effective numerical approach is presented to solve this kind of problem. The fiber layer is considered to be the standard linear material. Based on von Kármán geometric nonlinear theory and Timoshenko beam hypothesis, using Hamilton’s principle, the governing equations of dynamic for the fiber–metal-laminated beam under thermal shock are derived. The dynamic equations in terms of the displacements are discretized in spatial domain by adopting DQM and discretized in time domain by Newmark method synthetically. Then the Newton iteration method is used to solve the nonlinear algebraic equations at every grid of the time domain. Eventually, the temperature field in the beam and the dynamic displacement fields, and the stress responses of the beam are obtained. In numerical examples, the influences of temperature, geometric nonlinearity, and material parameters on the dynamic responses of the beam are discussed.