Abstract: In this paper, an analytical approach for free vibration
analysis of rectangular and circular membranes is presented. The
method is based on wave approach. From wave standpoint vibration
propagate, reflect and transmit in a structure. Firstly, the propagation
and reflection matrices for rectangular and circular membranes are
derived. Then, these matrices are combined to provide a concise and
systematic approach to free vibration analysis of membranes.
Subsequently, the eigenvalue problem for free vibration of membrane
is formulated and the equation of membrane natural frequencies is
constructed. Finally, the effectiveness of the approach is shown by
comparison of the results with existing classical solution.
Abstract: In this paper, an analytical approach for free vibration
analysis of four edges simply supported rectangular Kirchhoff plates
is presented. The method is based on wave approach. From wave
standpoint vibration propagate, reflect and transmit in a structure.
Firstly, the propagation and reflection matrices for plate with simply
supported boundary condition are derived. Then, these matrices are
combined to provide a concise and systematic approach to free
vibration analysis of a simply supported rectangular Kirchhoff plate.
Subsequently, the eigenvalue problem for free vibration of plates is
formulated and the equation of plate natural frequencies is
constructed. Finally, the effectiveness of the approach is shown by
comparison of the results with existing classical solution.