Year of Publication


Document Type





Mechanical Engineering

First Advisor

John R. Baker


Nonlinear parametric response of a flexible cantilever beam is simulated. In the simulations, lateral response of the beam due to an imposed axial harmonic base displacement excitation is calculated. The response frequency is approximately half the input frequency. The transient simulations include the assumption of damping proportional to the square of the velocity along the beam. Velocity-squared damping is realistic for situations in which fluid forces resisting the structural motion are significant. The commercial finite element software, ANSYS, is used to perform the simulations. A flexible method is developed and implemented in this work, based on the ANSYS Parametric Design Language, for including the quadratic damping assumption in the analysis. Variation of steady state response amplitude is examined for a range of quadratic damping coefficients over a range of axial base excitation frequencies. Further, a definition of phase angle of the response with the respect to the input is proposed for these nonlinear cases in which the input frequency is an integer multiple of the response frequency. The response phase with respect to excitation is studied over a range of damping coefficients and excitation frequencies. In addition, numerical solutions of nonlinear dynamic systems obtained from the implicit finite element method and the explicit dynamics finite element method are compared. The nonlinear dynamic systems considered are a flexible beam subjected to axial base excitation and also lateral excitations. The studies comparing explicit and implicit method results include cases of stress-stiffening and large deflections.