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Natural frequencies of a multi‐degree‐of‐freedom vibration system
Author(s) -
Müller Peter C.,
Gürgöze Metin
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610141
Subject(s) - eigenvalues and eigenvectors , spring (device) , conjecture , vibration , natural frequency , degrees of freedom (physics and chemistry) , physics , chain (unit) , mathematics , mathematical physics , pure mathematics , mathematical analysis , thermodynamics , quantum mechanics
A chain structured mass‐spring vibration system with N degrees of freedom is considered where masses M j = m j m = m/j and spring stiffnesses k j = c j k = ( N + 1 ‐ j ) k , j = 1, …, N , have been applied. The conjecture of Mikota [1] on the natural frequencies is discussed showing how difficult it is to find an explicit solution of the related eigenvalue problem. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)