Transfer Matrices for Beams Loaded Axially and Laid on an Elastic Foundation

1969 ◽  
Vol 20 (3) ◽  
pp. 281-306 ◽  
Author(s):  
B. A. Djodjo
Keyword(s):  
Elastic Foundation ◽  
Timoshenko Beam ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Transfer Matrices ◽  
Homogeneous Case ◽  
Simultaneous Treatment ◽  
Modified Model ◽  
Continuous Beams ◽  
Axially Loaded

SummaryUsing a modified model of the axially-loaded Timoshenko beam, nine field transfer matrices for the homogeneous case and three field matrices for the non-homogeneous case have been derived, covering thus all the “cases of state” of continuous beams loaded axially and laid on an elastic foundation. The loads and restraints (translatory and rotatory) may be both concentrated and distributed. The matrices make possible a simultaneous treatment of free vibrations, forced vibrations, statics and buckling.

Vibration of an Infinitely Extending Plate Resting on an Elastic Foundation

1963 ◽  
Vol 30 (3) ◽  
pp. 355-362 ◽  
Author(s):  
Kazuyosi Ono
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Infinite Number ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
The Other ◽  
Damped Oscillation

Free vibrations and forced vibrations of an infinitely extending plate resting on an elastic foundation and carrying a mass are solved. Then the amplitudes of the free vibrations produced by an impulse applied to the mass on the plate are determined, and it is found that two kinds of vibration are produced in the plate: One is a free vibration and the other is a special vibration, which consists of an infinite number of free vibrations and resembles a damped oscillation.

scholarly journals Vibrations of a Timoshenko beam on an inertial foundation under a moving load

2018 ◽  
Vol 196 ◽  
pp. 01056
Author(s):  
Magdalena Ataman
Keyword(s):  
Timoshenko Beam ◽  
Moving Load ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Governing Equations ◽  
Concentrated Load ◽  
Numerical Example ◽  
Moving Force ◽  
Speed Response

In the paper vibrations of the Timoshenko beam on an inertial foundation subjected to a moving force are discussed. Considered model of the inertial foundation is described by three parameters. They take into account elasticity, shear and inertia of the subgrade. In the literature such model of the subgrade is called Vlasov or Vlasov-Leontiev model. The Timoshenko beam is traversed by a concentrated load, moving with uniform speed. Response of the beam is found from the governing equations of motion of the problem. Problem of forced vibrations and problem of free vibrations of the beam are solved. Damping of the system is taken into consideration. Solution of the problem is illustrated by numerical example.

FREE VIBRATIONS OF A STEPPED, SPINNING TIMOSHENKO BEAM

1997 ◽  
Vol 203 (4) ◽  
pp. 717-722 ◽  
Author(s):  
N. Popplewell ◽  
D. Chang
Keyword(s):  
Timoshenko Beam ◽  
Free Vibrations
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