CMS Methods for Efficient Damping Prediction for Structures With Friction

Friction in joints significantly contributes to the observed overall damping of mechanical structures. Especially if the material damping is low, the frictional effects in joints and clamping boundary conditions dominate the structural damping. The damping and the stiffness of the structure are nonlinear functions of the system states and consequently of the excitation signal and amplitude. If these nonlinear effects should be incorporated in the design process, transient simulations must be employed in order to predict and analyze the damping for a given excitation, though they need excessive computation power due to the nonlinear constitutive laws and the high contact stiffnesses. As one approach to alleviate transient simulations, the application of component mode synthesis (CMS) methods to structures with friction is investigated exploiting the linearity of the jointed substructures. The nonlinear frictional effects and the normal contact is modeled by constitutive laws implemented in a zero–thickness–element formulation. The necessary considerations for accurate damping prediction by the reduced models, the accuracy and the computational times for transient simulations are presented. The found model reduction techniques allow a strong reduction of the computation time which in turn makes it a promising tool for model updating and predictive parameter studies. As an application example, a beam–like structure with attached friction damper is investigated in simulations and the obtained numerical results after model updating are compared to experiments. Nomenclature x, q physical, generalized coordinate vector M ,K,M̂ , K̂ mass and stiffness matrix, hat indicates reduced mass and stiffness matrices F ,BT,BN right–hand–side load vectors g, gref gap vector, gap vector of reference solution urel relative displacement FN,1, FN,2 normal forces applied by the left and right bolt E,Eref strain energy, strain energy of reference solution μ friction coefficient cN,0, cN,1, cT stiffness parameters in normal and tangential direction g0, g1 gap parameters for normal contact law ω, f angular frequency, frequency