Simulating Nonlinear Beating Phenomena Induced by Dry Friction in Dynamic Systems

Self-excitation and beating phenomena are the result of nonlinear constitutive behavior of vibrating structures with nonlinear components. These behaviors require externally supplied excitation and can be induced by the combination of near equilibrium damping and nonlinear damping operating far from equilibrium. In this study, dry friction, a mechanism known for producing self-excitation in structures, is explored as a mechanism for producing beat phenomena in structures. The system consists of two masses connected via a linear spring with one of the masses damped via a grounded dashpot that is modeled using a five-parameter friction contact model. The system is modeled and solved using the RK-4 time-integration scheme. We perform system parameter identification of experimental data using the STFT (short-time Fourier transform) and wavelet-bounded empirical mode decomposition (WBEMD) to determine system model variables that may simulate the self-excitation and beat phenomena observed in the structural dynamics. Beat phenomena may also be a result of the existence of two or more closely separated damped natural frequencies. We also investigate the degree to which self-excitation in the structure is driving the nonlinear beat phenomenon as opposed to it being caused by choosing closely separated damped natural frequencies. We address this question using nonlinear normal modes (NNM) analysis which provides frequency-energy dependence of the modes as system parameters change. The approach developed here is useful for the design of energy harvesting and vibration isolation systems that are subjected to sliding friction.