The forced vibration of singly modified damped elastic surface systems

Abstract A technique is developed to predict the forced vibration of membranes, beams, plates or shells when they have attached to them at a single point a linear lumped parameter element or assembly of elements. The distributed parameter element is treated as viscously damped and the lumped parameter assembly may also contain viscous dampers. Solution is obtained in terms of generalized Fourier series in the unmodified eigenfunctions for the distributed portion of the system and the principle of superposition is used to handle the imposed forces and those generated at the attachment. The method is illustrated by investigating a uniformly forced simply supported rectangular plate with a lumped mass at its center and that of a point forced simple beam with a rigid pin support imposed at some arbitrary point.

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