Static and Dynamic Nonlinear In-Plane Effect in the Response of a Cantilevered Plate With Tip Mass Load: Theory and Experiment

Abstract

Abstract In this article, two nonlinear effects are investigated. One is the effect of the static stiffness nonlinearity in changing the linear dynamic natural frequency, and the other is the combination of nonlinear stiffness and nonlinear inertia effects in changing the nonlinear dynamic transient response due to a change in the initial release state of the system. A theoretical model has been developed for a cantilevered thin plate with a range of length-to-width ratio using beam theory and considering both stiffness and inertial nonlinearities in the model. Lagrange's equation was used to deduce nonlinear inertia and stiffness matrices for a modal representation. Some insights into how these nonlinear components influence the beam response are presented. Measurements with both a hammer test and also a release test of cantilevered thin plates were done using different configurations and tip mass values. Results from static and dynamic analyses using the linear and the nonlinear theoretical models show good agreement between theory and experiment for natural frequencies and the amplitude displacements versus time.