Development and evaluation of a pseudo-force approximation applied to nonlinear dynamic contacts and viscoelastic damping

Abstract

A pseudo-force approximation method is used to study the nonlinear dynamic contacts and the effect of viscoelastic damping of beam-mass-beam systems. A pseudo-contact element with nonlinear stiffness and damping approximated by polynomial functions is defined and evaluated. To improve the system dynamic responses, viscoelastic damping is introduced into the systems using the standard linear model. The nonlinear forces derived from surface elasticity, penetration, instant contact velocity and viscoelastic damper are added to an excitation force vector to avoid reformation of system matrices. The system's equations of motion are directly integrated using the Wilson-θ method with minor modifications to accommodate the dynamic contacts and the viscoelastic damping. A design equation is also proposed to estimate the required viscoelastic dampers.