Fourier-type integral transforms in modeling of transversal oscillation

Abstract

The model of transversal oscillation for an elastic piecewise-homogeneous rod is constructed. In order to find a solution of this model   a   Fourier-type integral transforms method for the fourth-order differential equations is developed. The decomposition theorem is proved by Cauchy contour integration method. The conditions of existence for fundamental solutions of the initial - boundary value problem are established and explicit expressions of these fundamental solutions are found. 

Keywords

• eigenfunction, fourth-order differential equation, fundamental solution, Green's function.

Original Research Paper

Öz

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