Axisymmetric Vibration, Buckling and Bending of Laminated Plates with Transversely Isotropic Layers

2003 ◽  
pp. 99-126
Author(s):  
Jianqiao Ye
Keyword(s):  
Transversely Isotropic ◽  
Laminated Plates ◽  
Axisymmetric Vibration

Mixed State Hamiltonian Element for Plane Transversely Isotropic Magnetoelectroelastic Solids

2013 ◽  
Vol 275-277 ◽  
pp. 1978-1983
Author(s):  
Xiao Chuan Li ◽  
Jin Shuang Zhang
Keyword(s):  
Mixed State ◽  
Hamiltonian Formulation ◽  
Transversely Isotropic ◽  
Laminated Plates ◽  
Governing Equations ◽  
Time Coordinate ◽  
First Order ◽  
Linear Elements ◽  
Propagation Matrix ◽  
Magnetoelectroelastic Solids

Hamiltonian dual equation of plane transversely isotropic magnetoelectroelastic solids is derived from variational principle and mixed state Hamiltonian elementary equations are established. Similar to the Hamiltonian formulation in classic dynamics, the z coordinate is treated analogous to the time coordinate. Then the x-direction is discreted with the linear elements to obtain the state-vector governing equations, which are a set of first order differential equations in z and are solved by the analytical approach. Because present approach is analytic in z direction, there is no restriction on the thickness of plate through the use of the present element. Using the propagation matrix method, the approach can be extended to analyze the problems of magnetoelectroelastic laminated plates. Present semi-analytical method of mixed Hamiltonian element has wide application area.

Vibrations of Transversely Isotropic Finite Circular Cylinders

1994 ◽  
Vol 61 (4) ◽  
pp. 964-970 ◽  
Author(s):  
K. T. Chau
Keyword(s):  
Hyperbolic Equations ◽  
Longitudinal Vibration ◽  
Transversely Isotropic ◽  
Frequency Equation ◽  
Circular Cylinders ◽  
Finite Cylinder ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Vibration Frequencies ◽  
Axisymmetric Mode

This paper investigates the exact frequency equations for all the possible natural vibrations in a transversely isotropic cylinder of finite length. Two wave potentials are used to uncouple the equations of motion; the resulting hyperbolic equations are solved analytically for the vibration frequencies of a finite cylinder with zero shear tractions and zero axial displacement on the end surfaces and with zero tractions on the curved surfaces. In general, the mode shapes and the frequency equations of vibrations depend on both the range of the frequency and the elastic properties of the material. The vibration frequencies for sapphire cylinders are studied as an example. Two limiting cases are also considered: the long bar limit equals the frequency equation for the longitudinal vibration of bars obtained by Morse (1954) and by Lord Rayleigh (1945); and the frequency equation for thin disks (small length/radius ratio) is also obtained. The frequency for the first axisymmetric mode agrees with the experimental observation by Lusher and Hardy (1988) to within one percent. Natural frequencies for the first three longitudinal and circumferential modes are plotted for all cylinder geometries. The lowest frequency always corresponds to the first nonsymmetric mode regardless of the dimension of the cylinder. For axisymmetric vibration modes, numerical plots show that double roots exist in the frequency equations; such doublets were observed experimentally by Booker and Sagar (1971).

Free axisymmetric vibration of transversely isotropic piezoelectric circular plates

1999 ◽  
Vol 36 (30) ◽  
pp. 4629-4652 ◽  
Author(s):  
Ding Haojiang ◽  
Xu Rongqiao ◽  
Chi Yuwei ◽  
Chen Weiqui
Keyword(s):  
Transversely Isotropic ◽  
Axisymmetric Vibration ◽  
Circular Plates

EFFECT OF THE ROTATION ON PLANE VIBRATIONS IN A TRANSVERSELY ISOTROPIC INFINITE HOLLOW CYLINDER

2011 ◽  
Vol 25 (26) ◽  
pp. 3513-3528 ◽  
Author(s):  
S. R. MAHMOUD ◽  
A. M. ABD-ALLA ◽  
N. A. AL-SHEHRI
Keyword(s):  
Natural Frequency ◽  
Hollow Cylinder ◽  
Isotropic Material ◽  
Natural Frequencies ◽  
Transversely Isotropic ◽  
Axisymmetric Vibration ◽  
Harmonic Waves ◽  
Harmonic Vibrations ◽  
Transversely Isotropic Materials ◽  
Effects Of Rotation

In the present paper, a technique is presented for obtaining estimates for the natural frequencies of axisymmetric vibration for transversely isotropic material. The wave propagation of harmonic waves in hollow cylinder of transversely isotropic materials subjected to certain boundary conditions is studied. The two-dimensional equations of elastodynamic are solved in terms of displacement by using the technique of variables separation. The natural frequency of the plane vibrations in the case of harmonic vibrations has been obtained. The natural frequencies are calculated numerically and the effects of rotation is discussed. The numerical results obtained have been illustrated graphically to understand the behavior of natural frequency versus the ratio h. Comparisons are made with the result in the absence of rotation.

On the buckling analysis of isotropic, transversely isotropic, and laminated rectangular plates via Reddy plate theory: an exact closed-form procedure

2011 ◽  
Vol 226 (5) ◽  
pp. 1210-1224 ◽  
Author(s):  
Sh Hosseini-Hashemi ◽  
S R Atashipour ◽  
M Fadaee
Keyword(s):  
Closed Form ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Transversely Isotropic ◽  
Form Solution ◽  
Laminated Plates ◽  
Rectangular Plates ◽  
Third Order ◽  
Solution Methods

Based on Reddy's third-order shear deformation theory, an exact closed-form solution is proposed to describe linear buckling of transversely isotropic laminated rectangular plates under either mono- or bi-axial compressive in-plane loads. To this end, the coupled governing equations are exactly converted to two sets of uncoupled equations for in-plane and transverse deformations of symmetric laminated plates. The new uncoupled equations are analytically solved by applying both Navier and Lévy-type solution methods. The validity and high accuracy of the current exact solution are evaluated by comparing the present results with their counterparts reported in literature.

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