Some Solutions of the Timoshenko Beam Equation for Short Pulse-Type Loading

1958 ◽  
Vol 25 (3) ◽  
pp. 379-385
Author(s):  
H. J. Plass
Keyword(s):  
Timoshenko Beam ◽  
Short Pulse ◽  
Sine Wave ◽  
Beam Equation ◽  
Transform Method ◽  
The Laplace Transform ◽  
Support Conditions ◽  
Time Required ◽  
The Impact ◽  
Timoshenko Beam Equation

Abstract A collection of solutions to the Timoshenko beam equation is presented. Various types of support conditions and impact conditions are included. In every case the impact is assumed to be a pulse in the form of a half-sine wave. The results were found numerically, using the method of characteristics, except for one case, which was done in addition by the Laplace transform method, for check purposes. Agreement with experiment is good except for a pulse of duration comparable to the time required for the bending-type wave to travel a distance of one diameter. Discussion is included of the differences among the various cases studied.

Dynamic Rate Effects on Timoshenko Beam Response

1985 ◽  
Vol 52 (2) ◽  
pp. 439-445 ◽  
Author(s):  
T. J. Ross
Keyword(s):  
Timoshenko Beam ◽  
Bending Moment ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Rate Effects ◽  
The Laplace Transform ◽  
Step Loading ◽  
Fixed End ◽  
Constitutive Formulation ◽  
Viscoelastic Timoshenko Beam

The problem of a viscoelastic Timoshenko beam subjected to a transversely applied step-loading is solved using the Laplace transform method. It is established that the support shear force is amplified more than the support bending moment for a fixed-end beam when strain rate influences are accounted for implicitly in the viscoelastic constitutive formulation.

Response of a Simply Supported Timoshenko Beam to a Purely Random Gaussian Process

1958 ◽  
Vol 25 (4) ◽  
pp. 496-500
Author(s):  
J. C. Samuels ◽  
A. C. Eringen
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Beam Equation ◽  
Mean Square ◽  
Bending Stress ◽  
Random Loading ◽  
Simply Supported ◽  
The Mean ◽  
Timoshenko Beam Equation ◽  
Classical Beam Theory

Abstract The generalized Fourier analysis is applied to the damped Timoshenko beam equation to calculate the mean-square values of displacements and bending stress, resulting from purely random loading. Compared with the calculations, based on the classical beam theory, it was found that the displacement correlations of both theories were in excellent agreement. Moreover, the mean square of the bending stress, contrary to the results of the classical beam theory, was found to be convergent. Computations carried out with a digital computer are plotted for both theories.

Multiparameter Perturbation Solution of Algebraic Equations

1966 ◽  
Vol 33 (1) ◽  
pp. 218-219 ◽  
Author(s):  
W. F. Ames ◽  
J. F. Sontowski
Keyword(s):  
Power Series ◽  
Perturbation Method ◽  
Algebraic Equation ◽  
Timoshenko Beam ◽  
Perturbation Solution ◽  
Beam Equation ◽  
Algebraic Equations ◽  
Timoshenko Beam Equation

The classical perturbation method—the expansion of a solution of an algebraic equation as a power series in a parameter—is extended to an expansion in several parameters. An example concerning the Timoshenko beam equation is used to illustrate the ideas. Advantages of the procedure are discussed in the light of this example.

Timoshenko Beam Dynamics

1971 ◽  
Vol 38 (3) ◽  
pp. 591-594 ◽  
Author(s):  
G. M. Anderson
Keyword(s):  
Laplace Transform ◽  
Timoshenko Beam ◽  
General Problem ◽  
Beam Dynamics ◽  
Time Dependent ◽  
Residue Theorem ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Beam Analysis ◽  
The Laplace Transform

The general problem of Timoshenko beam analysis is solved using the Laplace transform method. Time-dependent boundary and normal loads are considered. It is established that the integrands of the inversion integrals are always single-valued for beams of finite length and modal solutions can always be obtained using the residue theorem.

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