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.

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.

Traveling Force on a Timoshenko Beam

1965 ◽  
Vol 32 (2) ◽  
pp. 351-358 ◽  
Author(s):  
A. L. Florence
Keyword(s):  
Laplace Transform ◽  
Timoshenko Beam ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Concentrated Load ◽  
Infinite Beam ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Wave Solutions ◽  
The Laplace Transform

Wave solutions are obtained by the Laplace-transform method for a semi-infinite beam subjected to a concentrated load moving at a velocity which may be supersonic, intersonic, or subsonic with respect to the bending and shear-wave velocities of the beam. Curves are drawn showing the velocity distribution behind a load moving supersonically.

scholarly journals Mathematical modeling and algorithm for calculation of thermocatalytic process of producing nanomaterial

2021 ◽  
Vol 23 (3) ◽  
pp. 1590
Author(s):  
Bakhtiyar Ismailov ◽  
Zhanat Umarova ◽  
Khairulla Ismailov ◽  
Aibarsha Dosmakanbetova ◽  
Saule Meldebekova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Phase ◽  
Nonlinear Effects ◽  
Operating Characteristics ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Wide Range ◽  
The Laplace Transform ◽  
Complex Mathematical Model

<p>At present, when constructing a mathematical description of the pyrolysis reactor, partial differential equations for the components of the gas phase and the catalyst phase are used. In the well-known works on modeling pyrolysis, the obtained models are applicable only for a narrow range of changes in the process parameters, the geometric dimensions are considered constant. The article poses the task of creating a complex mathematical model with additional terms, taking into account nonlinear effects, where the geometric dimensions of the apparatus and operating characteristics vary over a wide range. An analytical method has been developed for the implementation of a mathematical model of catalytic pyrolysis of methane for the production of nanomaterials in a continuous mode. The differential equation for gaseous components with initial and boundary conditions of the third type is reduced to a dimensionless form with a small value of the peclet criterion with a form factor. It is shown that the laplace transform method is mainly suitable for this case, which is applicable both for differential equations for solid-phase components and calculation in a periodic mode. The adequacy of the model results with the known experimental data is checked.</p>

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