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

• Authors: S. Kasprzyk
• Languages of publication: EN

Abstracts

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.

Keywords

EN

46.70.De; 46.40.-f

Discipline

• 46.40.-f: Vibrations and mechanical waves(see also 43.40.+s Structural acoustics and vibration; 62.30.+d Mechanical and elastic waves; vibrations in mechanical properties of solids)
• 46.70.De: Beams, plates, and shells

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2011
• Volume: 119
• Issue: 6A
• Pages: 981-985

Dates

published

2011-06

Contributors

author

S. Kasprzyk

• Katedra Mechaniki i Wibroakustyki, AGH - UST, al. A. Mickiewicza 30, 30-059 Kraków, Poland

References

• 1. P. Antosik, J. Mikulski, R. Sikorski, Theory of Distributions; the Sequential Approach, Elsevier Sci. Publ., New York 1973
• 2. F.P. Beer, E.R. Johnson, (Jr.), Mechanics for Engineers, Cliffs, New Yersey 1977
• 3. S. Kasprzyk, S. Sędziwy, Bull. Acad. Sci. Math. 31, 329 (1983)
• 4. S. Kasprzyk, S. Sędziwy, Bull. Acad. Sci. Tech. Sci. 43, 413 (1995)
• 5. L. Schwartz, Mathematics for Physical Sciences, Dover Books on Mathematics, Dover Publ., Dover 2008

Identifiers

DOI

10.12693/APhysPolA.119.981