Nonlinear Vibration of Thin Elastic Plates, Part 2: Internal Resonance by Amplitude-Incremental Finite Element

1984 ◽  
Vol 51 (4) ◽  
pp. 845-851 ◽  
Author(s):  
S. L. Lau ◽  
Y. K. Cheung ◽  
S. Y. Wu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Internal Resonance ◽  
Harmonic Excitation ◽  
Plate Element ◽  
Elastic Plates ◽  
Simply Supported ◽  
Speed Up ◽  
Numerical Process ◽  
Thin Elastic Plates

The simple amplitude-incremental triangular plate element derived in Part 1 of this paper is applied to treat the large-amplitude periodic vibrations of thin elastic plates with existence of internal resonance. A simply supported rectangular plate with immovable edges (b/a = 1.5) and having linear frequencies ω13 = 3.45 ω11 is selected as a typical example. The frequency response of free vibration as well as forced vibration under harmonic excitation are computed. To the best knowledge of the authors, these very interesting results for such plate problems have not appeared in literature previously. Some special considerations to simplify and to speed up the numerical process are also discussed.

Buckling analysis of plates of arbitrary shape

1984 ◽  
Vol 26 (1) ◽  
pp. 77-91 ◽  
Author(s):  
D. Bucco ◽  
J. Mazumdar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Arbitrary Shape ◽  
Numerical Technique ◽  
Buckling Analysis ◽  
Contour Method ◽  
Elastic Plates ◽  
Standard Finite Element Method ◽  
Thin Elastic Plates ◽  
Element Method

AbstractA simple and efficient numerical technique for the buckling analysis of thin elastic plates of arbitrary shape is proposed. The approach is based upon the combination of the standard Finite Element Method with the constant deflection contour method. Several representative plate problems of irregular boundaries are treated and where possible, the obtained results are validated against corresponding results in the literature.

scholarly journals A new finite element for free vibration analysis of stiffened composite plates

2007 ◽  
Vol 29 (4) ◽  
pp. 529-538 ◽  
Author(s):  
Tran Ich Thinh ◽  
Ngo Nhu Khoa
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Laminated Plates ◽  
Triangular Element ◽  
Plate Element ◽  
Stiffened Plate

A new 6-noded stiffened triangular plate element for the analysis of stiffened composite plates based on Mindlins deformation plate theory has been developed. The stiffened plate element is a combination of basic triangular element and bar component. The element can accommodate any number of arbitrarily oriented stiffeners and obviates the use of mesh lines along the stiffeners. Free vibration analyses of stiffened laminated plates have been carried out with this element and the results are compared with those published. The finite element results show very good matching with the experimental ones.

Free Vibration Analysis of Circular FGM Plate Having Variable Thickness Under Axisymmetric Condition by Finite Element Method

2005 ◽  
Author(s):  
M. Nikkhah-Bahrami ◽  
Abazar Shamekhi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Thickness Variation ◽  
Simply Supported ◽  
Element Method

This study presents the free vibration analysis of circular plate having variable thickness made of functionally-graded material. The boundary conditions of the plate is either simply supported or clamped. Dynamic equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander’s non-linear strain-displacement relation for thin plates. The finite element method is used to determine the natural frequencies. The results obtained show good agreement with known analytical data. The effects of thickness variation and Poisson’s ratio are investigated by calculating the natural frequencies. These effects are found not to be the same for simply supported and clamped plates.

Transverse bending of infinite and semi-infinite thin elastic plates. I

1957 ◽  
Vol 53 (1) ◽  
pp. 248-255 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Boundary Condition ◽  
Complex Variable ◽  
Practical Importance ◽  
Complex Potentials ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Simply Supported ◽  
Physical Conditions ◽  
Transverse Bending ◽  
Thin Elastic Plates

In recent years several authors have treated the fundamental problems of two-dimensional statical elasticity for isotropic and aeolotropic materials by the use of functions of a complex variable; references are given at the end of (7). In this paper Stevenson's notation (8,9) is adopted. Dawoud (2) has expressed the continuity conditions across a curve between two differently loaded regions in terms of the complex potentials and particular integrals for the two regions. A form of the boundary condition defining certain types of boundary constraint, including the rigidly clamped and hinged boundaries, has been introduced by the author and Dawoud (1). The introduction of this boundary condition is of practical importance, since neither rigidly clamped nor simply supported conditions can be realized fully under actual physical conditions and thus any case met in practice must lie somewhere between these two limiting cases.

Flexure by a Concentrated Force of the Infinite Plate on a Circular Support

1963 ◽  
Vol 30 (2) ◽  
pp. 225-231 ◽  
Author(s):  
J. Dundurs ◽  
Tung-Ming Lee
Keyword(s):  
Elastic Properties ◽  
Classical Theory ◽  
Infinite Plate ◽  
Arbitrary Point ◽  
Convergent Series ◽  
Elastic Plates ◽  
Concentrated Force ◽  
Simply Supported ◽  
Uniformly Convergent ◽  
Thin Elastic Plates

Treated is the flexure of an infinite plate which is simply supported on a circle and subjected to a concentrated force at an arbitrary point. The portion of the plate inside the circular support is allowed to have elastic properties that are different from those of the outside part. The solution is exact within the framework of the classical theory of thin elastic plates and is in the form of a uniformly convergent series. Several previously known solutions appear as limiting cases of the results given here.

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