The vibration of a highly flexible cantilever beam is investigated. The order three equations of motion, developed by Crespo da Silva and Glyn (1978), for the nonlinear flexural-flexural-torsional vibration of inextensional beams, are used to investigate the time response of the beam subjected to harmonic excitation at the base. The equation for the planar flexural vibration of the beam is solved using the finite element method. The finite element model developed in this work employs Galerkin's weighted residuals method, combined with the Newmark technique, and an iterative process. This finite element model is implemented in the program NLB1, which is used to calculate the steady state and transient responses of the beam. The steady state response obtained with NLB is compared to the experimental response obtained by Malatkar (2003). Some disagreement is observed between the numerical and experimental steady state responses, due to the presence of numerical error in the calculation of the nonlinear inertia term in the former. The transient response obtained with NLB reasonably agrees with the response calculated with ANSYS®.
Library of Congress Subject Headings
Girders--Vibration--Mathematical models; Vibration--Mathematical models; Torsion; Flexure
Delgado-Velázquez, Iván, "Nonlinear vibration of a cantilever beam" (2007). Thesis. Rochester Institute of Technology. Accessed from
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