Dieterman H.A. and Metrikine A.V.

 

Eigenfrequencies and simplified models of semi-infinite cascades with variable boundary mass

 

ZAMM 77(3), 232-235, 1997

 

Summary. 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.