Integral equation formulation and flutter analysis of damped non-conservative Timoshenko beams

This paper presents a mathematical modeling and a numerical methodological approach based on integral equation formulation and radial basis functions (RBF) for the dynamic behaviour damped Timoshenko beams under follower forces. Using the fundamental solution of the main operator and the RBF, the governing non-self-adjoint partial differential equation is transformed into an integral equation. Based on the harmonic assumption and internal concatenation points an eigenvalue problem is obtained and numerically solved. The flutter analysis, complex modes and the frequency load responses are investigated for beams under various subtangential follower loads, aspect ratios, internal and viscous damping.