Calculating the right-eigenvectors of a special vibration chain by means of modified Laguerre polynomials

zbMath1330.15011MaRDI QIDQ2634423

Wolfgang Weber, Bernd Anders, Bernd W. Zastrau

Publication date: 9 February 2016

Published in: Journal of Theoretical and Applied Mechanics (Sofia) (Search for Journal in Brave)

zbMATH Keywords

eigenvalueeigenvectorLaguerre polynomialmode shapevibration systemnatural value

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Eigenvalues, singular values, and eigenvectors (15A18) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Uniqueness of solutions of dynamical problems in solid mechanics (74H25) Linear vibration theory (70J99) Explicit solutions of dynamical problems in solid mechanics (74H05)

Cites Work

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• Analytical methods in rotor dynamics
• On natural frequencies and eigenmodes of a linear vibration system
• Asymptotics of eigenfrequencies in the dynamic response of elongated multi-structures

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