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Applicability of the Fourier Expansion Method of Separation of Variables in the Linear Discrete-Continuous Systems with Distributional Coefficients

100%
Kasprzyk S.
Acta Physica Polonica A
|
2011
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vol. 119
|
issue 6A
981-985
EN
The analytical examination of mechanical systems in the aspect of their vibro-isolation can be limited to the construction of a computational system. The analytical description of the adopted appropriate computational model may be executed with the help of a set of differential equations of the second order, differential equations with partial derivatives or of both types at the same time. The latest description is associated with the so-called discrete-continuous systems. It is the most convenient to analyze the vibrations of the linear discrete-continuous systems in the class of functions generalized with the Fourier method of separation of variables. Until now it was possible to execute only for a small set of parameters of the system's structure. In the work the author presents a computational model that covers all the structural parameters of the system.
2
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Construction of Equivalent Models of Continuous and Discrete-Continuous Systems

63%
Kasprzyk S., Marczuk R.
Acta Physica Polonica A
|
2012
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vol. 121
|
issue 1A
A-191-A-196
EN
New models have been constructed for three physical systems. These models are characterized by a uniform and transparent mathematical description. The mathematical description belongs to the class of generalized functions, which means that all equations as well as their solutions are understood in the sense of weak topology. The elements of the set of generalized functions need not be differentiable (in the classical sense) at each point domain of the function. Analyzing of actual systems in the class of generalized functions does not require a division into subsystems, which simplifies significantly execution of all mathematical operations. As compared with the classical methods, those presented in the study allow for a much faster achievement of the goal.
3
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New Concepts of the Study of an Infinite Beam on Elastic Foundation Based on the Distribution Theory

63%
Felis J., Kasprzyk S.
Acta Physica Polonica A
|
2014
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vol. 125
|
issue 4A
A-190-A-196
EN
The new approach to investigation the bending of the infinite length beam on the elastic foundation, applying the theory of distributions, is presented.
4
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The Influence of Local Increase of Stress on Eigenvalues for a Simply Supported Beam

63%
Kasprzyk S., Marczuk R.
Acta Physica Polonica A
|
2014
|
vol. 125
|
issue 4A
A-169-A-173
EN
Local increase of bending stress in a beam may be caused by a decrease of the cross-section (fracture) or a local increase of bending torque. The increase of stress issues from the well known interdependence between the stress, the bending torque and the sectional modulus. The work presents a derivation of differential equations for eigenfunctions in both cases. Knowing the eigenfunctions and boundary conditions we determine a system of algebraic equations for the eigenvalues that are different from the eigenvalues of the beam without local stress disturbances. Two computational models of local increase of stress were constructed: with fracture and with local increase of bending torque.
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