Influence of contact constitutive equations on the vibro-impact response of structures

This paper investigates how different nonlinear constitutive equations for contact affect the dynamic response of a coupled structure composed of substructures with close dynamic characteristics. A general formulation based on nonlinear dynamic substructuring in the frequency domain is developed to analyze the vibro-impact behavior of three-dimensional structures. The substructure dynamics, which account for most degrees of freedom, are solved only once. Various constitutive equations representing the microscale interactions between surfaces are incorporated into the model through closed-form nonlinear equations without resolving the whole system. Two case studies are considered: first, a numerical evaluation of two rods separated by a small gap; second, an experimental and numerical analysis of 3D solid beams with clearance subjected to harmonic base excitation. This work focuses on modeling the contact behavior between small, lightweight plastic components, such as those used in hearing aids, wearable electronics, or acoustic sensor systems, where the vibrational response is crucial for device performance. The finite element method is used for the spatial discretization of each substructure, with node pairs in the contact region connected by nonlinear elements derived from six constitutive equations from contact theories. The multi-harmonic balance method, combined with nonlinear substructuring, is employed to obtain the system’s harmonic response efficiently. Experimental measurements validate the numerical results, and updating the macro-scale parameters of each model yields good agreement with the measurement. The findings emphasize the crucial role of damping, even in vibro-impact scenarios where friction effects are minimal. Moreover, the results highlight the influence of substructure dynamics in the nonlinear regime, where sequential contact and separation occur during vibration. • Nonlinear dynamic substructuring in the frequency domain is presented for vibro-impact. • Six contact constitutive equations are compared using the multi-harmonic balance method. • Measurements and numerical predictions are in good accordance for substructures with clearance. • Kelvin-Voigt contact model performs best for vibro-impact in small plastic assemblies.