Transverse Vibration of a Class of Orthotropic Plates

1972 ◽  
Vol 39 (2) ◽  
pp. 613-615 ◽  
Author(s):  
N. J. DeCapua ◽  
B. C. Sun
Keyword(s):  
Transverse Vibration ◽  
Orthotropic Plates

scholarly journals Free Transverse Vibration of Rectangular Orthotropic Plates with Two Opposite Edges Rotationally Restrained and Remaining Others Free

2018 ◽  
Vol 9 (1) ◽  
pp. 22 ◽  
Author(s):  
Yuan Zhang ◽  
Sigong Zhang
Keyword(s):  
Boundary Conditions ◽  
Transverse Vibration ◽  
Integral Transforms ◽  
Mode Shapes ◽  
Alternative Formulation ◽  
Orthotropic Plates ◽  
Engineering Structures ◽  
Current Design ◽  
Classical Boundary ◽  
Finite Integral

Many types of engineering structures can be effectively modelled as orthotropic plates with opposite free edges such as bridge decks. The other two edges, however, are usually treated as simply supported or fully clamped in current design practice, although the practical boundary conditions are intermediate between these two limiting cases. Frequent applications of orthotropic plates in structures have generated the need for a better understanding of the dynamic behaviour of orthotropic plates with non-classical boundary conditions. In the present study, the transverse vibration of rectangular orthotropic plates with two opposite edges rotationally restrained with the remaining others free was studied by applying the method of finite integral transforms. A new alternative formulation was developed for vibration analysis, which provides much easier solutions. Exact series solutions were derived, and the excellent accuracy and efficiency of the method are demonstrated through considerable numerical studies and comparisons with existing results. Some new results have been presented. In addition, the effect of different degrees of rotational restraints on the mode shapes was also demonstrated. The present analytical method is straightforward and systematic, and the derived characteristic equation for eigenvalues can be easily adapted for broad applications.

scholarly journals Transverse vibration of orthotropic rectangular plates under moving bodies

2009 ◽  
Vol 31 (1) ◽  
pp. 47-56
Author(s):  
Nguyen Van Khang ◽  
Nguyen Minh Phuong
Keyword(s):  
Rectangular Plate ◽  
Transverse Vibration ◽  
Structural Engineering ◽  
Integration Method ◽  
Ritz Method ◽  
Rectangular Plates ◽  
Numerical Integration Method ◽  
Orthotropic Plates ◽  
Orthotropic Rectangular Plate ◽  
Moving Bodies

The use of orthotropic plates is common in all the fields of structural engineering: civil, traffic, aerospace and naval. In this paper the transverse vibration of orthotropic rectangular plates under moving bodies is investigated. The method of substructures is used to derive transverse vibration equations of an orthotropic rectangular plate under the action of moving bodies. For the calculation of dynamic response of orthotropic rectangular plate we use Ritz method and numerical integration method.

ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE UNIFORM VISCOELASTIC PLATE

2020 ◽  
Vol 7 (3) ◽  
pp. 52-56
Author(s):  
MMATMATISA JALILOV ◽  
◽  
RUSTAM RAKHIMOV ◽  
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Three Dimensional ◽  
Viscoelastic Plate ◽  
Constant Thickness ◽  
Regional Problem ◽  
Rigid Contact ◽  
Under Construction ◽  
Derivatives Of ◽  
Theoretical Results

This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of inlayer plates of constant thickness” [1]. In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations. The general equations of fluctuations of piecewise homogeneous viscoelastic plates of the constant thickness, described in work [1], are difficult on structure and contain derivatives of any order on coordinates x, y and time t and consequently are not suitable for the decision of applied problems and carrying out of engineering calculations. For the decision of applied problems instead of the general equations it is expedient to use confidants who include this or that final order on derivatives. The classical equations of cross-section fluctuation of a plate contain derivatives not above 4th order, and for piecewise homogeneous or two-layer plates the elementary approached equation of fluctuation is the equation of the sixth order. On the basis of the analytical decision of a problem the general and approached decisions of a problem are under construction, are deduced the equation of fluctuation of piecewise homogeneous two-layer plates taking into account rigid contact on border between layers, and also taking into account mechanical and rheological properties of a material of a plate. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.

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