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Finite Element Model Of A Timoshenko Beam With Structural Damping, Louis Ablen Roussos

Mechanical & Aerospace Engineering Theses & Dissertations

A numerical integration technique, a modified version of the Newmark method, is applied to transient motion problems of systems with mass, stiffness, and small nonlinear damping. The nonlinearity is cast as a pseudo-force to avoid repeated recalculation and decomposition of the effective stiffness matrix; thus, the solution technique is dubbed the "pseudo-force Newmark method." Comparisons with exact and perturbation solutions in single-degree-of-freedom problems and with a Gear-method numerical solution in a cantilevered Timoshenko beam finite element problem show the solution technique to be efficient, accurate, and, thus, feasible provided the nonlinear damping is small. As a preliminary step into the …