scholarly journals Nonlinear vibrations of thin plates with variable thickness: Application to sound synthesis of cymbals

2019 ◽  
Vol 145 (2) ◽  
pp. 977-988
Author(s):  
Quoc Bao Nguyen ◽  
Cyril Touzé
Keyword(s):  
Variable Thickness ◽  
Nonlinear Vibrations ◽  
Sound Synthesis ◽  
Thin Plates

Buckling Analysis of Circular FGM Plate Having Variable Thickness Under Uniform Compression by Finite Element Method

2005 ◽  
Author(s):  
Abazar Shamekhi ◽  
Mohammad H. Naei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variable Thickness ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Thin Plates ◽  
Thickness Variation ◽  
Simply Supported ◽  
Element Method

This study presents the buckling analysis of radially-loaded circular plate with variable thickness made of functionally-graded material. The boundary conditions of the plate is either simply supported or clamped. The stability 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 critical buckling load. The results obtained show good agreement with known analytical and numerical data. The effects of thickness variation and Poisson’s ratio are investigated by calculating the buckling load. These effects are found not to be the same for simply supported and clamped plates.

Nonlinear Bending of Rectangular Magnetoelectroelastic Thin Plates with Linearly Varying Thickness

2018 ◽  
Vol 19 (3-4) ◽  
pp. 351-356
Author(s):  
Feng Wang ◽  
Yu-fang Zheng ◽  
Chang-ping Chen
Keyword(s):  
Differential Equations ◽  
Variable Thickness ◽  
Plate Theory ◽  
Nonlinear Differential Equations ◽  
Thin Plates ◽  
Thickness Variation ◽  
Algebraic Equations ◽  
Nonlinear Bending ◽  
Nonlinear Load ◽  
Magnetic Potentials

AbstractWith employing the von Karman plate theory, and considering the linearly thickness variation in one direction, the bending problem of a rectangular magnetoelectroelastic plates with linear variable thickness is investigated. According to the Maxwell’s equations, when applying the magnetoelectric load on the plate’s surfaces and neglecting the in-plane electric and magnetic fields in thin plates, the electric and magnetic potentials varying along the thickness direction for the magnetoelectroelastic plates are determined. The nonlinear differential equations for magnetoelectroelastic plates with linear variable thickness are established based on the Hamilton’s principle. The Galerkin procedure is taken to translate a set of differential equations into algebraic equations. The numerical examples are presented to discuss the influences of the aspect ratio and span–thickness ratio on the nonlinear load–deflection curves for magnetoelectroelastic plates with linear variable thickness. In addition, the induced electric and magnetic potentials are also presented with the various values of the taper constants.

Nonlinear vibrations of rectangular laminated thin plates

AIAA Journal ◽  
1992 ◽  
Vol 30 (1) ◽  
pp. 180-188 ◽  
Author(s):  
Jongsik Woo ◽  
Sudhakar Nair
Keyword(s):  
Nonlinear Vibrations ◽  
Thin Plates

scholarly journals Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Pham Van Vinh
Keyword(s):  
Functionally Graded Material ◽  
Variable Thickness ◽  
Mixed Finite Element ◽  
Plate Thickness ◽  
Functionally Graded ◽  
Thin Plates ◽  
Quadrilateral Element ◽  
Graded Material ◽  
Element Technique ◽  
Power Law Index

A new mixed four-node quadrilateral element (MiQ4) is established in this paper to investigate functionally graded material (FGM) plates with variable thickness. The proposed element is developed based on the first-order shear deformation and mixed finite element technique, so the new element does not need any selective or reduced numerical integration. Numerous basic tests have been carried out to demonstrate the accuracy and convergence of the proposed element. Besides, the numerical examples show that the present element is free of shear locking and is insensitive to the mesh distortion, especially for the case of very thin plates. The present element can be applied to analyze plates with arbitrary geometries; it leads to reducing the computation cost. Several parameter studies are performed to show the roles of some parameters such as the power-law index, side-to-thickness ratio, boundary conditions (BCs), and variation of the plate thickness on the static bending behavior of the FGM plates.

Nonlinear Vibrations of Beams, Strings, Plates, and Membranes Without Initial Tension

2004 ◽  
Vol 71 (4) ◽  
pp. 551-559 ◽  
Author(s):  
Zhongping Bao ◽  
Subrata Mukherjee ◽  
Max Roman ◽  
Nadine Aubry
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Cross Sections ◽  
Nonlinear Vibrations ◽  
Young's Modulus ◽  
Thin Plates ◽  
Radius Of Gyration ◽  
Initial Tension ◽  
Various Boundary Conditions ◽  
Analytical Expressions

The subject of this paper is nonlinear vibrations of beams, strings (defined as beams with very thin uniform cross sections), plates and membranes (defined as very thin plates) without initial tension. Such problems are of great current interest in minute structures with some dimensions in the range of nanometers (nm) to micrometers (μm). A general discussion of these problems is followed by finite element method (FEM) analyses of beams and square plates with different boundary conditions. It is shown that the common practice of neglecting the bending stiffness of strings and membranes, while permissible in the presence of significant initial tension, is not appropriate in the case of nonlinear vibrations of such objects, with no initial tension, and with moderately large amplitude (of the order of the diameter of a string or the thickness of a plate). Approximate, but accurate analytical expressions are presented in this paper for the ratio of the nonlinear to the linear natural fundamental frequency of beams and plates, as functions of the ratio of amplitude to radius of gyration for beams, or the ratio of amplitude to thickness for square plates, for various boundary conditions. These expressions are independent of system parameters—the Young’s modulus, density, length, and radius of gyration for beams; the Young’s modulus, density, length of side, and thickness for square plates. (The plate formula exhibits explicit dependence on the Poisson’s ratio.) It is expected that these results will prove to be useful for the design of macro as well as micro and nano structures.

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