AI SearchFinite displacement theory for the vibration of Timoshenko's beams
Call Number: AIT Thesis no. 1326 Material type:
TextSeries: Asian Institute of Technology. Thesis ; no. 1326Publication details: Bangkok : Asian Institute of Technology, 1978Description: 23 pSubject(s): Online resources: Dissertation note: Thesis (M.Eng.) - Asian Institute of Technology, 1978 Summary: In this study, the undamped forced vibration of nonlinear Timoshenko's beams with axial force effects is analyzed by considering simply supported, homogeneous, isotropic beams. The basic equations have been formulated with the nonlinear terms in the expression for normal strain included. In order to uncouple the resulting nonlinear partial differential equations, the axial displacement function obtained from the small displacement theory and modified by satisfying the boundary conditions for the nonlinear case has been used. In the process of solving the basic equations the nonlinear terms are linearized by expanding them in a Fourier series in accordance with the technique used by CAUGHEY in his analysis of nonlinear systems. The results are plotted in the form of response curves of amplitude versus frequency ratio, for beams with different dimensional parameters. To exhibit the effect of axial force, response curves are also plotted for various values of the parameter corresponding to the axial force. In addition, a table is provided to show the trend of variation of the fundamental frequency with varying axial force.
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A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering of the Asian Institute of Technology, Bangkok, Thailand
Thesis (M.Eng.) - Asian Institute of Technology, 1978
In this study, the undamped forced vibration of nonlinear Timoshenko's beams with axial force effects is analyzed by considering simply supported, homogeneous, isotropic beams. The basic equations have been formulated with the nonlinear terms in the expression for normal strain included. In order to uncouple the resulting nonlinear partial differential equations, the axial displacement function obtained from the small displacement theory and modified by satisfying the boundary conditions for the nonlinear case has been used. In the process of solving the basic equations the nonlinear terms are linearized by expanding them in a Fourier series in accordance with the technique used by CAUGHEY in his analysis of nonlinear systems. The results are plotted in the form of response curves of amplitude versus frequency ratio, for beams with different dimensional parameters. To exhibit the effect of axial force, response curves are also plotted for various values of the parameter corresponding to the axial force. In addition, a table is provided to show the trend of variation of the fundamental frequency with varying axial force.
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