Bending behavior of FGM-coated and FGM-undercoated plates with two simply supported opposite edges and two free edges

2007 ◽  
Vol 81 (2) ◽  
pp. 157-167 ◽  
Author(s):  
Yen-Ling Chung ◽  
Wei-Ting Chen
Keyword(s):  
Simply Supported ◽  
Bending Behavior ◽  
Free Edges

BENDING BEHAVIOR OF SIMPLY SUPPOTED METALLIC SANDWICH PLATES WITH DIMPLED CORES

2008 ◽  
Vol 22 (31n32) ◽  
pp. 6179-6184 ◽  
Author(s):  
DAE-YONG SEONG ◽  
CHANG GYUN JUNG ◽  
DONG-YOL YANG ◽  
DONG GYU AHN
Keyword(s):  
High Precision ◽  
Sandwich Plate ◽  
Sheet Thickness ◽  
Radius Of Curvature ◽  
Sandwich Plates ◽  
Collapse Load ◽  
Forming Process ◽  
Simply Supported ◽  
Bending Behavior ◽  
Sandwich Core

Metallic sandwich plates are lightweight structural materials with load-bearing and multi-functional characteristics. Previous analytic studies have shown that the bendability of these plates increases as the thickness decreases. Due to difficulty in the manufacture of thin sandwich plates, dimpled cores (structures called egg-box cores) are employed as a sandwich core. High-precision dimpled cores are easily fabricated in a sectional forming process. The cores are then bonded with skin sheets by multi-point resistance welding. The bending characteristics of simply supported plates were observed by the defining measure, including the radius ratio of the small dimple, the thickness of a sandwich plate, and the pattern angle (0°/90°, 45°). Experimental results revealed that sandwich plates with a thickness of 2.2 mm and a pattern angle of 0°/90° showed good bendability as the punch stroke under a collapse load was longer than other cases. In addition, the gap between attachment points was found to be an important parameter for the improvement of the bendability. Finally, sandwich plates with dimpled cores were bent with a radius of curvature of 330 mm for the sheet thickness of 2.2 mm using an incremental bending apparatus.

scholarly journals Frequency Equations and Modes of Free Vibrations of Rectangular Plates with Various Edge Conditions

1994 ◽  
Vol 208 (5) ◽  
pp. 307-319 ◽  
Author(s):  
C W Bert ◽  
M Malik
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Free Vibrations ◽  
Edge Condition ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Edge Conditions ◽  
Classical Boundary ◽  
Free Edges

This paper considers linear free vibrations of thin isotropic rectangular plates with combinations of the classical boundary conditions of simply supported, clamped and free edges and the mathematically possible condition of guided edges. The total number of plate configurations with the classical boundary conditions are known to be twenty-one. The inclusion of the guided edge condition gives rise to an additional thirty-four plate configurations. Of these additional cases, twenty-one cases have exact solutions for which frequency equations in explicit or transcendental form may be obtained. The frequency equations of these cases are given and, for each case, results of the first nine mode frequencies are tabulated for a range of the plate aspect ratios.

Vibration of Stiffened Rectangular Plates

1964 ◽  
Vol 68 (648) ◽  
pp. 850-851
Author(s):  
K. T. Sundara Raja Iyengar ◽  
K. S. Jagadish
Keyword(s):  
The Other ◽  
Spring Constant ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Rayleigh Method ◽  
Free Edges

The vibrations of stiffened plates have been considered by Kirk and Mahalingam. Kirk has treated plates with several stiffeners and also a plate with a single stiffener. For plates with several stiffeners he uses the Rayleigh Method as employed by Warburton. The calculated frequencies have been shown to compare favourably with the experimental frequencies when the stiffness has been taken as ef3/3 for a stiffener. While considering the plate with a single stiffener he has replaced the stiffener by a line of massless springs the spring constant of which is determined on the basis of certain approximations. The Rayleigh method has then been applied to solve the simplified problem. A plate with two opposite edges free and the other two simply supported with a central stiffener parallel to the free edges has also been considered by Kirk.

PERIODIC AND CHAOTIC MOTIONS OF FGM THIN PLATE WITH TWO SIMPLY SUPPORTED OPPOSITE AND TWO FREE EDGES

2011 ◽  
Vol 21 (06) ◽  
pp. 1737-1753 ◽  
Author(s):  
Y. X. HAO ◽  
W. ZHANG ◽  
J. YANG
Keyword(s):  
Material Properties ◽  
Volume Fraction ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Transverse Motion ◽  
Rectangular Plates ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Simply Supported ◽  
Free Edges

An analysis on the nonlinear forced vibration of thermally loaded FGM plate with two simply supported opposite and two free edges subjected to the in-plane and transversal excitations is presented. The material properties of the FGM plates are assumed to be temperature dependent and change continuously throughout the thickness of the plate, according to the volume fraction of the constituent materials based on the power law function. The temperature is assumed to be constant in the plane and varied only in the thickness direction of the plate. The plate is modeled by using the Von Karman hypothesis and the equations of motion are obtained by using an energy approach. It is our aim to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the FGM rectangular plates with two simply supported opposite and two free edges. The equations of motion can be reduced into a two-degree-of-freedom nonlinear system of transverse motion under combined thermal and external excitations by using the Galerkin's method. By the numerical method, the nonlinear dynamical equations are analyzed to find the nonlinear responses of the FGM plate with two simply supported opposite and two free edges. Under certain conditions the periodic motions and the chaotic motions of the FGM plate are found. The bifurcation diagram demonstrates that for a certain geometric and material properties the chaotic responses of the plate exist as the transverse excitation changes. Moreover, numerical simulations also illustrate that the deflections of the nonlinear dynamic of the FGM rectangular plate are larger than that of the periodic motions.

scholarly journals Experimental and Theoretical Research on Bending Behavior of Photovoltaic Panels with a Special Boundary Condition

Energies ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 3435 ◽  
Author(s):  
Tengyuan Zhang ◽  
Lingzhi Xie ◽  
Yongxue Li ◽  
Tapas Mallick ◽  
Qingzhu Wei ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Closed Form Solution ◽  
Form Solution ◽  
Theoretical Research ◽  
Systematic Research ◽  
Special Boundary ◽  
Governing Equations ◽  
Simply Supported ◽  
Special Boundary Condition ◽  
Bending Behavior

Currently, the photovoltaic (PV) panels widely manufactured on market are composed of stiff front and back layers and the solar cells embedded in a soft polymeric interlayer. The wind and snow pressure are the usual loads to which working PV panels need to face, and it needs the panels keep undamaged under those pressure when they generate electricity. Therefore, an accurate and systematic research on bending behavior of PV panels is important and necessary. In this paper, classical lamination theory (CLT) considering soft interlayer is applied to build governing equations of the solar panel. A Rayleigh–Rita method is modified to solve the governing equations and calculate the static deformation of the PV panel. Different from many previous researches only analyzing simply supported boundary condition for four edges, a special boundary condition which consists of two opposite edges simply supported and the others two free is studied in this paper. A closed form solution is derived out and used to do the numerical calculation. The corresponding bending experiments of PV panels are completed. Comparing the numerical results with experiment results, the accuracy of the analytical solutions are verified.

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