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

Abstract

Chain structured vibration systems with N degrees of freedom with masses mj and stiffnesses kj have been discussed in detail [1]. Some of them can be solved explicitly, others only numerically. Here, an inverse problem is considered: How mj, kj, 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)