Closed-form dynamic response of damped mass-spring cascades

摘要

Closed-form responses due to step forces of finite and semi-infinite damped mass-spring cascades with variable boundary mass are derived. By convolution arbitrary responses may be obtained. Eigenfrequencies, eigenmodes and critical damping of nonuniform and uniform finite cascades are found, showing a decreasing critical damping with increasing eigenfrequency. Further the frequency-response functions of the cascades are given for three cases.