Dynamic responses of flexible linkage mechanisms with viscoelastic constrained layer damping treatment

Dynamic transient responses of high-speed flexible linkage mechanisms with viscoelastic constrained damping layer are studied in order to evaluate constrained layer damping treatment performances. A new type of shape function for three layer frame element containing a heavily damped viscoelastic layer, a base layer and a constraining layer is developed. The generalized equations of motion of flexible linkage mechanism systems with viscoelastic constrained damping layer are presented by utilizing finite element theory. The derivation and final form of the equations of motion provide the capability to model a multi-bar flexible linkage mechanism, to include the memory load caused by the damping material and the coupling terms of rigid body and elastic motion in a general representation. A recursion formula of calculation the memory load is developed and it permits calculation of the memory load efficiently. An approach to the solution of the equations of motion based on the Newmark direct integration method is offered. The responses of two flexible linkage mechanisms with damping treatment are analyzed. The analytical results illustrate the effectiveness of constrained viscoelastic layer damping treatment as passive control measures for flexible linkage mechanisms.