The Analyses for Natural Frequency of Laminated Plate Using an Improved Higher-Order Theory

2011 ◽  
Vol 138-139 ◽  
pp. 793-798
Author(s):  
Jin Wu Wu ◽  
Ling Zhi Huang
Keyword(s):  
Natural Frequency ◽  
Laminated Composite ◽  
Order Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Laminated Composite Plate ◽  
Random Form ◽  
Higher Order Method ◽  
Higher Order Theory

An improved higher order method was used in calculating the natural frequency of laminated composite plate. The function of equation of free vibration of laminated plate was established using Hamilton's principle and calculated the natural frequencies of plates. The influence of the laying-angle and thickness ratio and cross-elastic modulus ratio to the frequency of the plate were analyzed. It is shown that the natural frequency of antisymmetric angle-ply laminated plates and antisymmetric cross-ply laminated plate can be calculated by using this paper theory; in addition, it is feasible to calculate the natural frequency of the random form of laying laminate.

A Consistent Higher-Order Theory of Laminated Plates with Nonlinear Impact Modal Analysis

1994 ◽  
Vol 116 (3) ◽  
pp. 371-378 ◽  
Author(s):  
C. C. Chao ◽  
T. P. Tung ◽  
C. C. Sheu ◽  
J. H. Tseng
Keyword(s):  
Modal Analysis ◽  
Double Fourier Series ◽  
Order Theory ◽  
Higher Order ◽  
Small Time ◽  
Laminated Plates ◽  
Surface And Interface ◽  
Higher Order Theory ◽  
Patch Loading ◽  
The Impact

A consistent higher-order theory is developed for cross-ply laminated thick plates under transverse normal impact via an energy variational approach, in which the 3-D surface/edge boundary conditions and interlaminar displacement/stress continuities are satisfied, in an attempt to find the dynamic deformation and all six stress components throughout the plate during the impact process. The dynamic displacement field is expressed in a mixed form of in-plane double Fourier series and cubic polynomials through thickness as 12 variables for each layer. A system of modified Lagrange’s equations is derived with all surface and interface constraints included. The nonlinear impact modal analysis is performed using the Hertz contact law in a patch loading simulation and Green’s function for small time-steps linearization. The 3-D displacements are found with thickness shrinking and stresses generally unsymmetric with respect to the mid-surface. Tensile cracks are predicted at the unimpacted side.

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