Free vibration of rectangular plates with attached discrete masses

Ding Zhou, Tianjian Ji

Research output: Contribution to journalArticlepeer-review


A direct approach is used to derive the exact solution for the free vibration of thin rectangular plates with discrete sprung masses attached. The plate is simply supported along two opposite edges and elastically supported along the two other edges. The elastic support can represent a range of boundary conditions from free to clamped supports. Considering only the compatibility of the internal forces between the plate and the sprung masses, the equations of the coupled vibration of the platespringmass system are derived. The exact expressions for mode and frequency equations of the coupled vibration of the plate and sprung masses are determined. The solutions converge steadily and monotonically to exact values. The correctness and accuracy of the solutions are demonstrated through comparison with published results. A parametric study is undertaken focusing on the plate with one or two sprung masses. The results can be used as a benchmark for further investigation. The solution provided in the paper is general and includes several special cases, such as the plate with classical boundary conditions, the plate attached with discrete rigid masses, the plate supported by discrete springs and the plate restricted by rigid vertical pointsupports
Original languageEnglish
Pages (from-to)101-118
Number of pages17
JournalShock and Vibration: shock and vibration control - crashworthiness - structural dynamics - impact engineering - sound
Issue number1
Publication statusPublished - Jan 2012


  • Coupled vibration, eigenfrequency, plate, sprung mass, exact solution


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