scholarly journals Nonlinear Dynamic Analysis for Rectangular FGM Plates with Variable Thickness Subjected to Mechanical Load

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Khuc Van Phu ◽  
Le Xuan Doan ◽  
Nguyen Van Thanh
Keyword(s):  
Variable Thickness ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Rectangular Plates ◽  
Classical Plate Theory

 In this paper, the governing equations of rectangular plates with variable thickness subjected to mechanical load are established by using the classical plate theory, the geometrical nonlinearity in von Karman-Donnell sense. Solutions of the problem are derived according to Galerkin method. Nonlinear dynamic responses, critical dynamic loads are obtained by using Runge-Kutta method and the Budiansky–Roth criterion. Effect of volume-fraction index k and some geometric factors are considered and presented in numerical results.

Vibration Reduction of Laminated Plates With Various Piezoelectric Functionally Graded Actuators

2008 ◽  
Author(s):  
Marek Pietrzakowski
Keyword(s):  
Numerical Simulations ◽  
Volume Fraction ◽  
Effective Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Dynamic Responses ◽  
Electromechanical Properties ◽  
Classical Plate Theory ◽  
Fraction Distribution

The aim of the present study is to develop models of active laminated plates containing monolithic piezopolymer sensor layers and a new type of actuator layers made of Piezoelectric Functionally Graded (PFG) material, which is a mixture of piezoceramics and polymer or epoxy matrix. The electromechanical properties of the PFG layers can be tailored varying continuously the piezoceramic volume fraction across the thickness during the manufacturing process. The analysis and numerical simulations are focused on the relationship between the material compositional gradient and electromechanical properties and also dynamic responses of the structure obtained. Three types of functions, which describe the volume fraction distribution of constituents, are considered: exponential, parabolic and sigmoid. The effective properties of the PFG material, i.e. the Young’s modulus and piezoelectric coefficient gradations, are determined using to the rule of mixtures. A constant velocity feedback algorithm is used for the active damping of transverse plate vibration. The dynamic analysis concerns steady-state behavior of rectangular symmetrically laminated plates and is based on hypothesis of the classical plate theory. The numerical simulations are performed to recognize the influence of the applied pattern of the piezoceramic fraction distribution and its parameters on the gradient of elastic and piezoelectric properties within the PFG actuators and, as the final result, the active plate structural response presented in terms of amplitude-frequency characteristics. The changes in both the natural frequencies and resonant amplitudes are compared and the influence of the piezoceramic gradation on the control system operational effectiveness is also indicated and discussed.

Nonlinear dynamic buckling of full-filled fluid sandwich FGM circular cylinder shells

2019 ◽  
Author(s):  
Doan Xuan Le ◽  
Phu Van Khuc
Keyword(s):  
Circular Cylinder ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Geometrical Nonlinearity ◽  
Dynamic Buckling ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Method Effects ◽  
Classical Shell Theory

This paper is presented to solve the nonlinear dynamic buckling of sandwich functionally graded circular cylinder shells filled with fluid. Governing equations are derived using the classical shell theory and the geometrical nonlinearity in von Karman-Donnell sense is taken into account. Solutions of the problem are established by using Galerkin’s method and Rung-Kutta method. Effects of thermal environment, parameters of geometric, volume fraction index k and fluid on dynamic responses of shells are investigated.

scholarly journals Nonlinear Dynamic Response and Vibration of 2D Penta-graphene Composite Plates Resting on Elastic Foundation in Thermal Environments

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Nguyen Dinh Duc ◽  
Pham Tien Lam ◽  
Nguyen Van Quyen ◽  
Vu Dinh Quang
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Density Functional ◽  
Thermal Environment ◽  
Mechanical Load ◽  
Plate Theory ◽  
Composite Plates ◽  
Classical Plate Theory ◽  
Nonlinear Dynamic Response ◽  
Graphene Composite

This research demonstrates an analytical method for investigation vibration and dynamic response of plates structure which made from 2-Dimensional (2D) penta-graphene. The density functional theory is used to figure out the elastic modulus of single layer penta-graphene. The classical plate theory is applied to determine basic equations of 2D penta-graphene composite plates. The numerical results obtained using the Bubnov-Galerkin method and Rung-Kutta method. The results in this research showed high agreement when it is compared with the other study. The results demonstrate the effect of shape parameters, material properties, foundation parameters, the mechanical load on the nonlinear dynamic response of 2D penta-graphene plates. One of the highlights of this study was to investigate the effect of the thermal environment on the behavior of 2D penta-graphene plates.  

Nonlinear Dynamic Analysis for FGM Circular Plates

2012 ◽  
Vol 29 (2) ◽  
pp. 287-296 ◽  
Author(s):  
H.-L. Dai ◽  
X. Yan ◽  
L. Yang
Keyword(s):  
Dynamic Analysis ◽  
Shear Deformation ◽  
Circular Plate ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Nonlinear Dynamic Analysis ◽  
Functionally Graded ◽  
Transient Problem ◽  
Nonlinear Transient

AbstractIn the paper, nonlinear dynamic analysis of a circular plate composed of functionally graded material (FGM) is presented. Considering a transverse shear deformation and geometric nonlinearity, the von Karman geometric relation of the FGM circular plate is established. Based on the theory of the first-order shear deformation, a new set of equilibrium equations is developed by the principle of minimum total energy. Applying the finite difference method and Newmark scheme, the nonlinear transient problem is solved by the iterative method. To validate the presented method, the transient problem of the FGM circular plate is compared with those of the existed literature, and good agreement is observed. The effects of the volume fraction index, boundary conditions, mechanical load and the ratio of thickness to radius on the nonlinear transient problem of the FGM circular plate are investigated.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

Effect of Shear Deformations on the Bending of Rectangular Plates

1960 ◽  
Vol 27 (1) ◽  
pp. 54-58 ◽  
Author(s):  
V. L. Salerno ◽  
M. A. Goldberg
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Plate Theory ◽  
Order Partial Differential Equation ◽  
Rectangular Plates ◽  
Partial Differential ◽  
Classical Plate Theory ◽  
Simply Supported ◽  
Wide Range

The three partial differential equations derived by Dr. E. Reissner2, 3 have been reduced to a fourth-order partial differential equation resembling that of the classical plate theory and to a second-order differential equation for determining a stress function. The general solution for the two partial differential equations has been applied to a simply supported plate with a constant load p and to a plate with two opposite edges simply supported and the other two edges free. Numerical calculations have been made for the simply supported plate and the results compared with those of classical theory. The calculations for a wide range of parameters indicate that the deviation is small.

Experimental studies on the dynamic response of thin rectangular plates subjected to moving mass

2020 ◽  
pp. 107754632093313 ◽  
Author(s):  
Sajjad Seifoori ◽  
Ahmad Mahdian Parrany ◽  
Sajjad Darvishinia
Keyword(s):  
Dynamic Response ◽  
Rectangular Plate ◽  
Plate Theory ◽  
Experimental Studies ◽  
Time History ◽  
Moving Mass ◽  
Rectangular Plates ◽  
Classical Plate Theory ◽  
Thin Rectangular Plate ◽  
Expansion Technique

This article presents experimental studies on the dynamic response of a thin rectangular plate with clamped boundary conditions subjected to a moving mass. The designed experimental setup is described in detail, and the obtained experimental results are compared with theoretical solutions. In this regard, the governing motion equation of the thin rectangular plate excited by a moving mass is formulated based on the classical plate theory, and the eigenfunction expansion technique is used to solve the equation. Parametric studies are carried out to investigate the effect of some parameters, including the moving object mass and velocity, as well as the plate’s aspect ratio and thickness, on the dynamic response of the plate based on the time history of the plate’s central point deflection.

Maximization of Natural Frequencies for Functionally Graded Rectangular Plates

2021 ◽  
Vol 891 ◽  
pp. 116-121
Author(s):  
Aleksander Muc
Keyword(s):  
Analytical Methods ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Optimization Techniques ◽  
Point Of View ◽  
Rectangular Plates ◽  
Classical Plate Theory ◽  
Arbitrary Boundary

In this paper optimal design of free vibrations for functionally graded plates is studied using the analytical methods. The analytical methods can be employed for the solution of six of 21 arbitrary boundary conditions (the combinations of clamped, simply supported and free). The influence of various models of porosity and forms of different reinforcements with nanoplatelets and carbon nanotubes are investigated, including variations of stiffness/density along the thickness of a plate. The analysis is carried out for the classical plate theory. Parametric studies illustrate the possibility of increasing natural frequencies and the necessity of implementing the optimization techniques to find the best solutions from the engineering point of view.

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