Unified Green's functions of forced vibration of axially loaded Timoshenko beam: Transition parameter

2016 ◽  
Vol 113 ◽  
pp. 211-220 ◽  
Author(s):  
T. Chen ◽  
G.Y. Su ◽  
Y.S. Shen ◽  
B. Gao ◽  
X.Y. Li ◽  
...  
Keyword(s):  
Timoshenko Beam ◽  
Forced Vibration ◽  
Green's Functions ◽  
Green’S Functions ◽  
Transition Parameter ◽  
Axially Loaded

Forced Vibration of a Damped Combined Linear System

1985 ◽  
Vol 107 (3) ◽  
pp. 275-281 ◽  
Author(s):  
L. A. Bergman ◽  
J. W. Nicholson
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Forced Vibration ◽  
Green's Functions ◽  
Natural Frequencies ◽  
Green’S Functions ◽  
Orthogonality Relation ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
General Method

A new and general method for determining the exact undamped natural frequencies and natural modes of vibration, the orthogonality relation for the natural modes, and the response to arbitrary excitation for both damped and undamped combined linear systems is given. The method, based upon Green’s functions of the vibrating distributed subsystems, is demonstrated for a multiplicity of linear oscillators connected to a simple beam.

Green’s Functions for Timoshenko Beam Problems

1997 ◽  
Author(s):  
C. M. Wang ◽  
K. Y. Lam ◽  
X. Q. He
Keyword(s):  
Numerical Methods ◽  
Exact Solutions ◽  
Elastic Foundation ◽  
Timoshenko Beam ◽  
Green's Functions ◽  
Green’S Functions ◽  
Vibration Problems

In this paper, a unified formulation is given for the bending, buckling and vibration problems of uniform Timoshenko and Euler-Bernoulli beams resting on various models of elastic foundation. Canonical Green’s functions have been derived for these beams which can be readily used to furnish exact solutions. In addition to elucidating the behaviour of the beams, the exact solutions serve as important benchmark results for checking the convergence and accuracy of various solutions obtained from numerical methods.

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