Dynamic responses to sinusoidal excitations of beams with frictional joints

We consider the dynamic responses of a beam with a frictional joint. The frictional force at the joint is modeled using the Coulomb friction model. The frictional force at the joint makes the nature of the boundary conditions at the joint uncertain. Therefore, this problem represents a type of nonlinear problems where the boundary conditions are coupled to the solutions. Using numerical integration of the resulting differential equations obtained by combining the finite element method and the Lagrange equations, we study the steady-state solutions of the system to sinusoidal excitations. We explore the dependence of the system responses to various parameters including the frictional force, the forcing frequency and the forcing amplitude. A result of special interest is the existence of an optimum friction force if the frictional joint is used to control the system response amplitude. We also examine the ways that friction affects the resonance frequency of the structure. Experiments are carried out, which agree qualitatively with the numerical results.