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  1. 2 Acta Physica Polonica A

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  1. 1 2014

  2. 1 2012

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  1. 2 Kasprzyk S.

  2. 2 Marczuk R.

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Construction of Equivalent Models of Continuous and Discrete-Continuous Systems

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Kasprzyk S., Marczuk R.
Acta Physica Polonica A
|
2012
|
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.
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The Influence of Local Increase of Stress on Eigenvalues for a Simply Supported Beam

100%
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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