Affiliations: College of Civil Engineering, Nanjing University of
Technology, Nanjing 210009, People's Republic of China | School of Mechanical, Aerospace and Civil Engineering,
The University of Manchester, Manchester, UK
Note: [] Corresponding author: Dr. Ding Zhou, Professor, College of Civil
Engineering, Nanjing University of Technology, Nanjing 210009, People's
Republic of China. Tel.: +86 25 84316695; E-mail: [email protected]
Abstract: 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 plate-spring-mass 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
point-supports.
