Dynamic analysis of flexible linkage mechanisms under uniform temperature change

Deformation and stresses are produced not by mechanical forces alone, but by temperature variation as well. The additional stresses of a flexible mechanism caused by the temperature change should not be ignored. The generalized equations of motion for flexible linkage mechanisms, in which the thermal effects are taken into account, are developed by utilizing the virtual work method and the finite element theory in this paper. Since the determination of thermal stresses plays an important role in the design of mechanisms operating at elevated temperatures, the stress–strain relationship should include the effects of temperature. Based on the closed-form numerical algorithm, the equations are solved and the recursive scheme is proved to be efficient and converged in a few iterations for the cases examined. The Runge–Kutta method is also applied to study the transient response of the temperature change. Numerical solution results show that a small change of temperature will cause a significant change of the stresses of a flexible mechanism. The effects of temperature change should not be ignored when analyzing the dynamic performance of flexible mechanisms.