CC series solution for bending of rectangular plates on elastic foundations

1995 ◽  
Vol 16 (6) ◽  
pp. 593-601 ◽  
Author(s):  
Zhu Jiaming
Keyword(s):  
Series Solution ◽  
Rectangular Plates ◽  
Elastic Foundations

Natural Frequencies of Plate Systems using the Edge Effect Method

1967 ◽  
Vol 9 (4) ◽  
pp. 318-324 ◽  
Author(s):  
S. M. Dickinson ◽  
G. B. Warburton
Keyword(s):  
Natural Frequency ◽  
Edge Effect ◽  
Series Solution ◽  
Natural Frequencies ◽  
Rectangular Plates ◽  
Form Part ◽  
Approximate Frequency ◽  
Flexural Vibrations ◽  
Effect Method ◽  
Partial Success

In this paper the Bolotin edge effect method is used to consider the free flexural vibrations of systems built up from rectangular plates. The constituent plates of the systems are considered either to lie in the same plane and form part of a plate continuous over line supports or to lie in planes at right angles to each other, as in box constructions. The application of the edge effect method to single-and multi-plate systems is described and the approximate frequency equations for two two-plate systems are given. The first 10 natural frequency parameters for these two systems for particular side ratios are compared with those obtained using a series solution and agreement is shown to be good. A few frequency parameters for a closed box computed using the edge effect method and the series solution are also compared. The range of plate systems to which the edge effect method may be applied with complete success and the range to which it may be applied with only partial success are indicated. The sources of errors in the edge effect solutions are indicated.

An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges

2013 ◽  
Vol 572 ◽  
pp. 489-493 ◽  
Author(s):  
Kai Xue ◽  
Jiu Fa Wang ◽  
Qiu Hong Li ◽  
Wei Yuan Wang ◽  
Ping Wang
Keyword(s):  
Series Solution ◽  
Rectangular Plates ◽  
Analysis Method ◽  
Original Function ◽  
Cross Sectional ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fourier Cosine Series ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

An analysis method has been proposed for the vibration analysis of the Mindlin rectangular plates with general elastically boundary supports, in which the vibration displacements and the cross-sectional rotations of the mid-plane are sought as the linear combination of a double Fourier cosine series and auxiliary series functions. The use of these supplementary functions is to solve the potential discontinuity associated with the x-derivative and y-derivative of the original function along the four edges, so this method can be applied to get the exact solution. Finally the numerical results are presented to validate the correct of the method.

Sign in / Sign up

Export Citation Format

Share Document