Prediction and validation of the strongly modulated forced response of two beams undergoing frictional impacts

TL;DR

This paper models and validates the complex non-periodic response of two frictionally impacted beams under harmonic excitation, demonstrating good agreement with experimental data using advanced simulation techniques.

Contribution

It introduces a novel simulation approach combining component mode synthesis and set-valued laws to predict non-periodic vibro-impact dynamics in beam systems.

Findings

Simulation results closely match experimental measurements.

The approach effectively predicts strongly modulated non-periodic responses.

Modeling friction and impacts accurately captures complex dynamics.

Abstract

We consider two cantilevered beams undergoing frictional impacts at the free end. The beams are designed to be of similar geometry so that they have distinct but close natural frequencies. Under harmonic base excitation near the primary resonance with the higher-frequency fundamental bending mode, the system shows a strongly modulated non-periodic response. The purpose of this work is to analyze to what extent the non-periodic vibro-impact dynamics can be predicted. To this end, we use a recently developed modeling and simulation approach. The approach relies on component mode synthesis, the massless boundary concept and an appropriate time stepping scheme. Unilateral contact and dry friction are modeled as set-valued laws and imposed locally within the spatially resolved contact area. A linear model updating is carried out based on the natural frequencies and damping ratios identified in the regime without impacts. The nonlinear simulation of the steady-state response to forward and backward stepped sine excitation is compared against measurements. The results are in very good agreement, especially in the light of the uncertainty associated with the observed material loss in the contact region and the nonlinear behavior of the clamping.