Keywords: plate vibration, vibration suppression, passive control, Green's function.

The problem of achieving vibration suppression or confinement in a rectangular plate with two simply supported opposite edges and subjected to an external excitation force has been examined analytically and experimentally. This is achieved by adding combinations of the following: a concentrated mass; and, or grounded translational springs; and, or rotational springs at selected locations on the plate. Moreover, the analysis is extended to the case of using translational and, or rotational oscillators to remove plate vibration. For a plate with an external localized force that acts at any point, the displacement amplitude on a portion of the plate can be suppressed by adjusting the value of the added attachments. From the control point of view this is called a passive control method aimed to regulate the vibration displacement. Essentially the added attachments cause modal cancellation, which occurs when the dominant modes involved in the vibration appear out of phase on the part of the plate where the vibration is suppressed but in phase on the other part where the vibration amplitude becomes larger. This study may be of particular use if there is an interest in eliminating unwanted vibrations from certain parts of a plate structure more than another or preventing a localized excitation from propagating into certain parts. The analytical displacement response for the case of an SFSF plate is verified experimentally using a laser measuring system and yielded reasonable results. A key feature of the present work is that the problem is formulated in terms of the Green's functions. This method is exact and straightforward. It was chosen for its freedom from numerical inaccuracy when compared with the standard application of modal superposition technique. The boundary conditions are embedded in the Green's function of the corresponding plate and it is not necessary to solve the free vibration problem in order to obtain the eigenvalues and the corresponding eigenfunctions, which are required for modal superposition solution. Equally important, this procedure demonstrates appreciably greater computational efficiency when compared with other methods.

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