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Eigenfrequencies and Simplified Models of Semi‐Infinite Cascades with Variable Boundary Mass
Author(s) -
Dieterman H. A.,
Metrikine A.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970770318
Subject(s) - cascade , boundary (topology) , variable (mathematics) , boundary value problem , mathematical analysis , physics , mathematics , mechanics , chemistry , chromatography
The eigenfrequencies of a semi‐infinite cascade of mass‐spring systems with variable boundary mass are studied. The investigation shows that real eigenfrequencies only occur for a boundary mass equal to or smaller than half the mass of the bodies in the cascade. For values of the boundary mass between a half mass and a full mass the cascade shows to have no eigenfrequencies. For a boundary mass larger than the internal masses only imaginary eigenfrequencies are present. Frequency‐response functions for the different cases are derived. Some simplified models for the semi‐infinite system are given and a comparison is made with the dynamic behaviour of continuous systems.