The damping problem in non-linear viscoelastic frames under varying temperature

A theoretical consideration of the damping problem in frame engineering structures made of functionally graded materials with non-linear viscoelastic behaviour is carried-out. The frames studied are under external mechanical load and varying temperature. In particular, damping in a two-legged frame with supports on different levels is analyzed. The frame is subjected to a cyclic side load with simultaneous variation of the temperature. The material of the frame is functionally graded in the thickness direction. Thus, the material properties change smoothly along the thickness. Equilibrium equations are used for determining the curvature and the neutral axis coordinates in the members of the frame structure. The damping energy density is integrated in the volume of the frame members in order to find-out the damping energy in the whole frame structure. A parametric investigation is performed by using the solution of the damping energy in order to clarify the influence of various factors (the frame geometry, loading, etc.) on the damping phenomenon at different temperatures.