Dynamic analysis of axially loaded cantilever shear‐beam under large deflections with small rotations

The modal analysis and seismic response of a vibrating cantilever, with or without tip mass rotary inertia, are investigated in this study using shear deformable beam model including the effect vertical load. Based on existing approaches, an original method is proposed that does not use fourth-order uncoupled equations to determine deflection rotation. In fact, approach presented herein transforms second-order coupled system into first-order which can be solved more easily matrix algebra Laplace transform. Furthermore, form allows straightforward demonstration orthogonality conditions, is, problem self-adjoint, solution case forced superposition. addition, even if applicable only cantilever scope general, applied beams other boundary conditions. Finally, by superposition shown, some examples discussed for uniform continuously varying cross-sectional properties.