Asymptotically Exact Solution of the Problem of Harmonic Vibrations of an Elastic Parallelepiped
An asymptotically exact solution of the classical problem of elasticity about the steadystate forced vibrations of an elastic rectangular parallelepiped is constructed. The general solution of the vibration equations is constructed in the form of double Fourier series with undetermined coefficients,...
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| Veröffentlicht in: | Mechanics of solids 2017-11, Vol.52 (6), p.686-699 |
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| container_title | Mechanics of solids |
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| creator | Papkov, S. O. |
| description | An asymptotically exact solution of the classical problem of elasticity about the steadystate forced vibrations of an elastic rectangular parallelepiped is constructed. The general solution of the vibration equations is constructed in the form of double Fourier series with undetermined coefficients, and an infinite system of linear algebraic equations is obtained for determining these coefficients. An analysis of the infinite system permits determining the asymptotics of the unknowns which are used to convolve the double series in both equations of the infinite systems and the displacement and stress components. The efficiency of this approach is illustrated by numerical examples and comparison with known solutions. The spectrum of the parallelepiped symmetric vibrations is studied for various ratios of its sides. |
| doi_str_mv | 10.3103/S0025654417060085 |
| format | Article |
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O.</creator><creatorcontrib>Papkov, S. O.</creatorcontrib><description>An asymptotically exact solution of the classical problem of elasticity about the steadystate forced vibrations of an elastic rectangular parallelepiped is constructed. The general solution of the vibration equations is constructed in the form of double Fourier series with undetermined coefficients, and an infinite system of linear algebraic equations is obtained for determining these coefficients. An analysis of the infinite system permits determining the asymptotics of the unknowns which are used to convolve the double series in both equations of the infinite systems and the displacement and stress components. The efficiency of this approach is illustrated by numerical examples and comparison with known solutions. 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O.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20171101</creationdate><title>Asymptotically Exact Solution of the Problem of Harmonic Vibrations of an Elastic Parallelepiped</title><author>Papkov, S. O.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-2add6478944721c062e8fbc45f6a363dbd10cfdaca1c9cbe135ab9d467bd70f13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Asymptotic properties</topic><topic>Classical Mechanics</topic><topic>Elasticity</topic><topic>Forced vibration</topic><topic>Fourier series</topic><topic>Linear algebra</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Papkov, S. 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The general solution of the vibration equations is constructed in the form of double Fourier series with undetermined coefficients, and an infinite system of linear algebraic equations is obtained for determining these coefficients. An analysis of the infinite system permits determining the asymptotics of the unknowns which are used to convolve the double series in both equations of the infinite systems and the displacement and stress components. The efficiency of this approach is illustrated by numerical examples and comparison with known solutions. The spectrum of the parallelepiped symmetric vibrations is studied for various ratios of its sides.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.3103/S0025654417060085</doi><tpages>14</tpages></addata></record> |
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| ispartof | Mechanics of solids, 2017-11, Vol.52 (6), p.686-699 |
| issn | 0025-6544 1934-7936 |
| language | eng |
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| source | SpringerNature Journals |
| subjects | Asymptotic properties Classical Mechanics Elasticity Forced vibration Fourier series Linear algebra Physics Physics and Astronomy |
| title | Asymptotically Exact Solution of the Problem of Harmonic Vibrations of an Elastic Parallelepiped |
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