Analysis of one-dimensional response of an elastic body under dynamic loads

The methods of problem formulation and solution of an axially- loaded bar modelled as a continuous system were analyzed. The motions of continuous systems were obtained from the superposition of the modes, In superposition analysis, DuhamePs integral equation is used to evaluate the response of the system to any form of dynamic loading. Impulsive loads and step loads are examples of dynamic loads which produce transient waves. Analytical and numerical solutions to transient wave problems in elastic materials can be obtained by integral transform methods, particularly Fourier and Laplace transforms. The transient response of an axially-loaded bar was studied by performing the formulation in the Laplace transform space. The solution in the time domain was obtained by an appropriate numerical inverse Laplace transformation method. The results are compared with those of superposition analysis and ANSYS, and the efficiency of the Laplace transform method is demonstrated.Keywords: Dynamic loads, Laplace transform, Duhamel's integral, Wave propagation