Investigating dynamic transient behavior of Timoshenko cantilever beam by theoretical analysis, numerical calculation and experimental measurement

Abstract

Polyvinylidene fluoride (PVDF) is a piezoelectric polymer that has been used in many sensing applications. To precisely determine the impact loading history, a special technique is developed by attaching the PVDF film on the top and bottom surfaces of a cantilever beam where a dynamic impact is applied directly on the top side. The Laplace transform method is employed to investigate the transient response of the displacement and strain for a Timoshenko cantilever beam subjected to impact loading. The Durbin method is used to perform the Laplace inverse transformation to construct the transient responses for displacement and strain in the time domain. After confirming the correctness of the experimental boundary conditions, the impact loading history obtained from the experimental measurement is used for the Timoshenko and Bernoulli–Euler beam theories to investigate the transient responses for different slender ratios. The strain and displacement of cantilever beams are measured experimentally by PVDF films and fiber optics sensors separately. A three-dimensional finite element cantilever beam model is implemented to perform the numerical calculation of the transient response. By comparing the theoretical analysis and the finite element simulation against measurements from corresponding experiments, this research shows that the transient response of strain and displacement for a cantilever beam can be accurately evaluated using the Timoshenko beam theory if the slender ratio is greater than 50.