Development of Normal Mode Theory for Multi-Degree-of-Freedom Systems Using an Energy Inner Product

Linear vibrations of a multi-degree-of-freedom system are considered using an energy inner product. It is shown how standard theorems for selfadjoint operators can then be used to easily derive orthogonality conditions with respect to the energy inner product.

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Bibliographische Detailangaben
Veröffentlicht in:	SIAM review 1988-06, Vol.30 (2), p.302-304
1. Verfasser:	Kelly, S. Graham
Format:	Artikel
Sprache:	eng
Schlagworte:	Classroom Notes Coordinate systems Eigenvalues Eigenvectors Energy Inner products Mathematical theorems Matrices Modal response Natural frequencies Ordinary differential equations Orthogonality Product standards Vibration
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Beschreibung
Zusammenfassung:	Linear vibrations of a multi-degree-of-freedom system are considered using an energy inner product. It is shown how standard theorems for selfadjoint operators can then be used to easily derive orthogonality conditions with respect to the energy inner product.
ISSN:	0036-1445 1095-7200
DOI:	10.1137/1030051