## Inverse Problems in Vibration |

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### Contents

ELEMENTARY MATRIX ANALYSIS | 1 |

1 | 7 |

Vibration of some simple systems | 19 |

Copyright | |

17 other sections not shown

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### Common terms and phrases

analysis applied assume beam called Chapter coefficients column combination completely completely non-negative compute consider construct continuous Corollary corresponding defined derivative described determinant differential discrete eigenfunctions eigenvalues eigenvectors elements end conditions equal equation Examples expressed Figure finite fixed follows force frequencies function given gives governing Green's function hand hence holds identically implies increasing independent inequalities integral interval introduce inverse problem Jacobian kernel linearly mass means minors modes natural necessary and sufficient nodes non-zero obtain orthogonal oscillatory oscillatory matrix particular polynomials positive definite principal procedure Proof properties prove reconstruction relation result rows satisfy Section sequence shows sign-oscillatory solution spectra stiffnesses string sufficient conditions Suppose symmetric symmetric matrix Theorem tion unique values vector vibration write written yields zero