An Efficient Dynamic Analysis of Planar Arches

Abstract

The aim of this study is to investigate the curved rods subjected to dynamic loads with variable geometric properties along the axis theoretically. The transient analysis of the planar rods under the various in-plane dynamic loads has been analyzed in the Laplace domain. The obtained canonical form of the first order ordinary differential equations has been solved by Complementary Functions Method (CFM) in the transformed domain. The fifth-order Runge–Kutta method has been applied to the solution of the obtained equations.  The materials of the structural elements are assumed to be homogeneous, isotropic, and elastic. The solutions obtained are transformed to the time domain using the modified Durbin's inverse numerical Laplace transformed method. For the suggested models, a computer program is coded in Fortran for the dynamic analysis of the planar curved structural elements. Verification of the computer program is performed by comparing the results of the present methods with the other numerical methods available in the literature. The procedures have been proved to be highly accurate and efficient compared to various other numerical methods. 

Keywords

• Two-Point Boundary Value Problems,Complementary Functions Method (CFM),Inverse Laplace Transforms,Planar Arches

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