Geometric imperfection sensitivity of nonlinear vibration responses of laminated beams under thermal shock

Abstract

Initial geometric imperfections are bound to arise during a structure's service life or could emerge during the fabrication process. The exact influence of these geometric imperfections on the thermally-induced vibrations of the structure remains uncertain. This study represents the first endeavor to conduct a sensitivity analysis of geometric imperfections in the nonlinear vibration responses of laminated beams subjected to thermal shock. Considering uncoupled thermoelasticity theory, the temperature distribution is obtained using a one-dimensional Fourier-type transient heat conduction equation, and a nonlinear dynamic beam model accounting for initial geometric imperfections is developed based on the first-order shear deformation theory, Lagrange method, and Ritz method. An exact solution is implemented to capture the temporal temperature profile along the thickness of a beam subjected to a thermal boundary condition of the first kind (constant wall temperature). The sensitivity of various geometric imperfections to the nonlinear vibrations of laminated beams under thermal shocks is obtained using the Newmark scheme and Newton–Raphson iterative technique. A series of parametric studies is conducted to reveal the effects of different parameters on the nonlinear thermally induced vibration responses of the beams. Thermally induced vibration is shown to be sensitive to the initial geometric imperfections.