Dynamic Analysis of Planar Flexible Beams with Finite Rotations by Using Inertial and Rotating Frames

An efficient formulation for dynamic analysis of planar Timoshenko’s beam with finite rotations is presented. Both an inertial frame and a rotating frame are introduced to simplify computational manipulation. The kinetic energy of the system is obtained by using the inertial frame so that it takes a quadratic uncoupled form. The rotating frame together with the small strain assumption is employed to derive the strain energy of the system. Since the exact solutions for linear static theory of Timoshenko’s beam are used to obtain the strain energy, the present stiffness operator is free from the locking problem without using any special technique. The resulting equations of motion of the system are defined in terms of a fixed global coordinates system. Nonlinear effects appear only in the transformation of displacement components between global and local coordinates. This results in a drastic simplification of nonlinear dynamic analysis of flexible beams. Numerical examples demonstrate the accuracy and efficiency of the present formulation.