Determination of natural modes of linear mass‐spring vibration systems by Laguerre polynomials | Zendy

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Determination of natural modes of linear mass‐spring vibration systems by Laguerre polynomials

Author(s) -

C. Müller Peter

Publication year - 2009

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.200910118

Subject(s) - laguerre polynomials , eigenvalues and eigenvectors , spring (device) , inverse , vibration , laguerre's method , mathematics , chain (unit) , inverse problem , mathematical analysis , pure mathematics , orthogonal polynomials , physics , classical orthogonal polynomials , geometry , quantum mechanics , thermodynamics

Chain structured vibration systems with N degrees of freedom with masses m j and stiffnesses k j have been discussed in detail [1]. Some of them can be solved explicitly, others only numerically. Here, an inverse problem is considered: How m j , k j , j = 1, …, N, should be chosen such that the related eigenvalue/eigenvector‐problem can be solved by Laguerre polynomials? (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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