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Integral equation formulation and analysis of utter instabilities of Timoshenko beams under non conservative loads

N. Ouakkasse, L. Azrar


The aim of this paper is to elaborate a mathematical modeling and a numerical methodological approach based on radial basis functions and integral equation formulation for numerical solution of the non self adjoint partial differential system governing the dynamic behavior of Timoshenko beams. The fundamental solution of the basic operator is explicitly given and used to transform the PDE to an integral equation. Using the radial basis functions for the resulting body integral, the governing equation is reduced to an algebro-differential system. Based on the harmonic assumption and internal concatenation points an eigenvalue problem is obtained and numerically solved for various follower loads.

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