Type of Document	Master's Thesis
Author	Hagmann, Christopher
URN	etd-08222008-063748
Title	Vibration of a nonlinear shear deformable beam by numerical simulation
Degree	Master of Science
Department	Engineering Mechanics
Advisory Committee	Advisor Name Title Heller, Robert A. Committee Member Kraige, Luther Glenn Committee Member Thangjitham, Surot Committee Member
Keywords	beam vibration nonlinear shear-deformable simulation
Date of Defense	1996-06-05
Availability	restricted
Abstract The vibration of a uniform geometrically nonlinear shear deformable beam subjected to a transverse harmonic excitation is investigated by the method of numerical simulation. Rotatory and axial inertia are included in the model. The beam is simply supported with supports a fixed distance apart. The nonlinear partial differential equations of motion are discretized in space by the Rayleigh-Ritz method, resulting in a set of nonlinear ordinary differential equations in time. The ordinary differential equations are integrated numerically to produce a time history of the solution of the equations. Transverse displacement, axial displacement, and cross sectional rotation are approximated by series of the corresponding linear natural mode shapes of the beam. Solutions of the equations of motion are compared to corresponding solutions where shear deformation and rotatory inertia are neglected. The effect of slenderness on the difference between the shear deformable case and the non shear deformable case is investigated by considering two beam configurations. In the simulations considered, the difference between the shear deformable model and the non shear deformable model increases as excitation frequency is increased and the length to thickness ratio of the beam is decreased.
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