In this study a comprehensive approach for modeling flexibility for a beam with tip mass is presented. The method utilizes a Timoshenko beam with geometric stiffening. The element matrices are reported as the integral of the product of shape functions. This enhances their utility due to their generic form. They are utilized in a symbolic-based algorithm for the automatic generation of the element matrices. The time-dependent terms are factored after assembly for better computational implementation. The effect of speed and tip mass on cross coupling between the elastic and rigid body motions represented by Coriolis, normal and tangential accelerations is investigated. The nonlinear term (geometric stiffening) is modeled by introducing a tensor which plays the same role as element matrices for the linear terms. This led to formulation of the exact tangent matrix needed to solve the nonlinear differential equation.

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