 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 57, Issue 5 / 2022 | Next article >> |
| A.G. Petrov, "Existence of Normal Coordinates for Forced Oscillations of Linear Dissipative Systems," Mech. Solids. 57 (5), 1035-1043 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
5 |
Pages |
1035-1043 |
| DOI |
10.3103/S0025654422050223 |
| Title |
Existence of Normal Coordinates for Forced Oscillations of Linear Dissipative Systems |
| Author(s) |
A.G. Petrov (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, petrovipmech@gmail.com) |
| Abstract |
A linear dissipative mechanical system with a finite number of degrees of freedom is defined by three quadratic forms: the kinetic and potential energy of the system, as well as the dissipative Rayleigh function. It is known that one can always introduce normal coordinates in which the kinetic and potential energies are reduced to the sum of squares with some coefficients. The third quadratic form, in general, does not reduce to a sum of squares. This study discusses the conditions under which all three quadratic forms can be reduced to a sum of squares by a single transformation. For such systems, one can introduce normal coordinates, in which the system is split into independent systems of the second order, and their analysis is greatly simplified. Examples of the analysis of forced oscillations of linear dissipative systems for two and three degrees of freedom are given. |
| Keywords |
quadratic forms, canonical form, small vibrations, friction forces |
| Received |
18 August 2021 | Revised |
25 October 2021 | Accepted |
15 November 2021 |
| Link to Fulltext |
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