Bounds for the principal eigenvalue of a nonhomogeneous bar with a tip mass (Q2762966)
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scientific article; zbMATH DE number 1689816
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bounds for the principal eigenvalue of a nonhomogeneous bar with a tip mass |
scientific article; zbMATH DE number 1689816 |
Statements
16 January 2002
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bar
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tip mass
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eigenvalue problem
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boundary value problem
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0.82729363
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0.82437104
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0.82278365
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0.82020307
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0.8157692
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0.8149319
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0.81361085
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Bounds for the principal eigenvalue of a nonhomogeneous bar with a tip mass (English)
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The author considers a long, uniformly thin bar of finite length with an endpoint carrying a tip mass. The natural frequencies of that bar are determined by the eigenvalues of some class of fourth-order ordinary differential equations satisfying four boundary conditions. Upper and lower bounds on the first eigenvalue are found under several restrictions imposed on the density of the bar.
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