On the isospectral beams
The free undamped infinitesimal transverse vibrations of a thin straight beam are modelled by a forth-order differential equation. This paper investigates the families of fourth-order systems which have one spectrum in common, and correspond to four different sets of end-conditions. The analysis is...
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| Format: | Article |
| Language: | English |
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Texas State University
2005-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/conf-proc/12/g1/abstr.html |
| _version_ | 1818956723272024064 |
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| author | Kazem Ghanbari |
| author_facet | Kazem Ghanbari |
| author_sort | Kazem Ghanbari |
| collection | DOAJ |
| description | The free undamped infinitesimal transverse vibrations of a thin straight beam are modelled by a forth-order differential equation. This paper investigates the families of fourth-order systems which have one spectrum in common, and correspond to four different sets of end-conditions. The analysis is based on the transformation of the beam operator into a fourth-order self-adjoint linear differential operator. This operator is factorized as a product $L=H^{*}H$, where $H$ is a second-order differential operator of the form $H=D^2+rD+s$, and $H^{*}$ is its adjoint operator. |
| first_indexed | 2024-12-20T10:58:29Z |
| format | Article |
| id | doaj.art-a37b7a1548aa4cdc9445e48373cfd808 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-20T10:58:29Z |
| publishDate | 2005-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-a37b7a1548aa4cdc9445e48373cfd8082022-12-21T19:43:06ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912005-04-01Conference125764On the isospectral beamsKazem GhanbariThe free undamped infinitesimal transverse vibrations of a thin straight beam are modelled by a forth-order differential equation. This paper investigates the families of fourth-order systems which have one spectrum in common, and correspond to four different sets of end-conditions. The analysis is based on the transformation of the beam operator into a fourth-order self-adjoint linear differential operator. This operator is factorized as a product $L=H^{*}H$, where $H$ is a second-order differential operator of the form $H=D^2+rD+s$, and $H^{*}$ is its adjoint operator.http://ejde.math.txstate.edu/conf-proc/12/g1/abstr.htmlIsospectral, Euler-Bernoulli equation for the vibrating beam, beam operator |
| spellingShingle | Kazem Ghanbari On the isospectral beams Electronic Journal of Differential Equations Isospectral, Euler-Bernoulli equation for the vibrating beam, beam operator |
| title | On the isospectral beams |
| title_full | On the isospectral beams |
| title_fullStr | On the isospectral beams |
| title_full_unstemmed | On the isospectral beams |
| title_short | On the isospectral beams |
| title_sort | on the isospectral beams |
| topic | Isospectral, Euler-Bernoulli equation for the vibrating beam, beam operator |
| url | http://ejde.math.txstate.edu/conf-proc/12/g1/abstr.html |
| work_keys_str_mv | AT kazemghanbari ontheisospectralbeams |