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Symbolic Boundary Integral Equation Formulation for Coupled Vibrations of Asymmetric Beams

M. Tanaka
A. Bercin
Journal / Anthology

Communications in Numerical Methods in Engineering
Year: 1998
Volume: 14
Page range: 763-772

Symbolic computer algebra systems relieve one from the tedious task of different mathematical operations which are essential to obtain solutions. Due to their highly advanced features they have come to be used widely in computational mechanics. This paper describes an application of the modern computer algebra system Mathematica to the derivation of fundamental solutions necessary for the application of the boundary integral equation method. The problem treated is an asymmetric cross-section Timoshenko beam in free vibration. For this problem, the derivation of fundamental solutions involves lengthy mathematical operations which are very tedious if performed explicitly by hand. Therefore, using Mathematica we derive the fundamental solutions and generate the influence matrices from which the natural frequencies can be found.

*Engineering > Mechanical and Structural Engineering