An analytical and experimental investigation into overall dissipation of flexural mode in a periodically damped beam

Abstract

This study presents an innovative analytical model to estimate the overall energy dissipation in damped Euler–Bernoulli beams with uniform and non-uniform (stepped) cross-sections. The novelty lies in proposing a closed-form expression for an envelope function that closely matches the energy dissipation profile obtained from the time-domain response. Importantly, the study unveils a non-intuitive finding, which states that the rate of energy decay predominantly depends on the configuration (orientation) of the stepped beam. Both strain rate-dependent viscous damping and velocity-dependent viscous damping components are considered in the governing equations. An analytical formulation is developed to obtain the wave-number-dependent damped frequencies and damping ratios using the free-wave approach. The coefficient of energy decay, governing the envelope function, is expressed in terms of the damping ratios, natural frequencies, mode participation factors, and the ratio of flexural rigidities. Moreover, this study presents the experimental validation of the analytical formulation by estimating the settling times from free vibration tests on 3D-printed stepped beams with different configurations and further quantifies the damping coefficients of the stepped beam by applying the nonlinear least squares method to fit the peaks in the experimentally acquired acceleration response. The close agreement between analytical and experimental results establishes the accuracy and applicability of the proposed model for transient vibration mitigation.