The Lumped Parameter Method for Elastic Impact Problems

Abstract

Transverse impact problems have recently been solved by several different methods including Timoshenko's integral equation method, the energy method, and the finite element method. This paper presents a lumped parameter method (LMP) for impact analysis, which is attractive for the solutions of impact of complex bodies. The advantages are in its simplification of mathematical formulation, computational efficiency, and improved understanding of the coupling effect of excited modes on the occurrence of multiple impacts. Experimentally obtained information of the dynamic characteristics of these impacting bodies permit easy extension to nonsimple body shapes.

Mathematical Modelling and Simulation Analysis of an Aircraft Wing Using SimMechanics

“…The natural frequencies can be predicted using the theoretical Eq. (10). It is noteworthy to say that the previously existing formulas for deflection properly fit in with the simulated wing model.…”

“…The usefulness of the lumped parameter method is introduced in Refs. [10,11], and it is an effective method for predicting the contact force of elastic colliding bodies. In addition, the advantages of this method are in its simplification of mathematical formulation, computational efficiency, and better understanding of the coupling effect of the excited modes on the occurrence of multiple impacts.…”

Dynamic response of composite laminated beams under asynchronous/repeated low-velocity impacts of multiple masses

“…This approach requires a knowledge of contact laws that, in the case of composite laminates, are obtained from static indentation tests [9]. Many researchers used the Hertzian contact law for isotropic materials and the Euler-Bernoulli beam theory then arrived at the non-linear integral governing equation [10][11][12]; especially for moderate indentations [13,14].…”

Equivalent Static Force in Heavy Mass Impacts on Structures

“…493because impact duration, equation(10), and maximum displacement, equation (14), are already 494 well-known from the proposed formulation.…”