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.
|Number of pages||4|
|Journal||ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik|
|Publication status||Published - 1 Dec 1997|