The free and forced linear response of a constrained string translating across an elastic foundation is examined in this paper. The transfer function method is used in the analysis. For the general problem, three subsystems are identified. The subsystems are coupled by physical constraints imposed at the subsystem interfaces. Free vibration analysis shows that eigenvalue loci exhibit veering characteristics and vibration modes are localized. These phenomena are due to the coupling of the subsystems. A third-order perturbation solution is also derived to examine the local characteristics of regions of curve veering. Studies on the wave propagation aspects show that the string/foundation medium can have propagating and amplitude-attenuating free vibration waves depending on the stiffness, location, and size of the elastic foundation. Moreover, the amount of shape distortion of a propagating wave at the constraint discontinuity depends also on the foundation stiffness.

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