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.

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.

Thermally induced postbuckling of thin CNT-reinforced composite plates under nonuniform in-plane temperature distributions

2020 ◽  
pp. 089270572096217
Author(s):  
Le Thi Nhu Trang ◽  
Hoang Van Tung
Keyword(s):  
Thermal Load ◽  
Effective Properties ◽  
Plate Theory ◽  
Composite Plates ◽  
Functionally Graded ◽  
Postbuckling Behavior ◽  
Classical Plate Theory ◽  
Temperature Distributions ◽  
Basic Equations ◽  
Plane Temperature

This paper presents an analytical investigation on postbuckling behavior of thin plates reinforced by carbon nanotubes (CNTs) and subjected to nonuniform thermal loads. Unlike many previous works considered ideal case of thermal load is that uniform temperature rise, the present study considers more practical situations of thermal load are that sinusoidal and linear in-plane temperature distributions. CNTs are reinforced into matrix through functionally graded distributions and effective properties of nanocomposite are estimated according to extended rule of mixture. Basic equations are based on classical plate theory taking into account Von Karman nonlinearity, initial geometrical imperfection, interactive pressure from elastic foundations and elasticity of tangential constraints of simply supported boundary edges. Basic equations are solved by using analytical solutions and Galerkin method. From the obtained closed-form relations, thermal buckling and postbuckling behavior of nanocomposite plates are analyzed through numerical examples.

Geometrically Nonlinear Free Axisymmetric Vibrations Analysis of Thin Circular Functionally Graded Plates

2014 ◽  
Vol 971-973 ◽  
pp. 489-506
Author(s):  
El Kaak Rachid ◽  
El Bikri Khalid ◽  
Benamar Rhali
Keyword(s):  
Volume Fraction ◽  
Plate Theory ◽  
Mass Density ◽  
Functionally Graded ◽  
Algebraic Equations ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Linear Mode ◽  
Linear Algebraic Equations ◽  
Non Linear

This paper deals with nonlinear free axisymmetric vibrations of functionally graded thin circular plates whose properties vary through its thickness. The inhomogeneity of the plate is characterized by a power law variation of the Young’s modulus and mass density of the material along the thickness direction, whereas Poisson’s ratio is assumed to be constant. The theoretical model is based on Hamilton’s principle and spectral analysis using a basis of admissible Bessel’s functions to yield the frequencies of the circular plates under clamped boundary conditions on the basis of the classical plate theory. The large vibration amplitudes problem, reduced to a set of non-linear algebraic equations, is solved numerically. The non-linear to linear frequency ratios are presented for various values of the volume fraction index n showing hardening type non-linearity. The distribution of the radial bending stress associated to the non-linear mode shape is also given for various vibration amplitudes, and is compared with those predicted by the linear theory.

Axisymmetric Solutions of Functionally Graded Circular and Annular Plates Using Second-Order Shear Deformation Plate Theory

2006 ◽  
Author(s):  
Ali Reza Saidi ◽  
Shahab Sahraee
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Second Order ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Classical Plate Theory ◽  
Maximum Displacement ◽  
Shear Deformation Plate Theory ◽  
Axisymmetric Bending

In this paper, axisymmetric bending and stretching of functionally graded solid circular and annular plate is studied based on the second-order shear deformation plate theory (SST). The solutions for deflections, force and moment resultants of the second-order theory are presented in terms of the corresponding quantities of the isotropic plates based on the classical plate theory from which one can easily obtain the SST solutions for axisymmetric bending of functionally graded circular plates. It is assumed that the mechanical properties of the functionally graded plates vary continuously through the thickness of the plate and obey a power law distribution of the volume fraction of the constituents. Numerical results for maximum displacement are presented for various percentages of ceramic-metal volume-fractions and have been compared with those obtained from first-order shear deformation plate theory (FST).

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.

scholarly journals Optimum response of functionally graded piezoelectric plates in thermal environments

2017 ◽  
Vol 35 (3) ◽  
pp. 606-617 ◽  
Author(s):  
Hossein Nourmohammadi ◽  
Bashir Behjat
Keyword(s):  
Power Law ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Plate Theory ◽  
Poisson Ratio ◽  
Functionally Graded ◽  
Sensors And Actuators ◽  
Thermal Environments ◽  
Functionally Graded Piezoelectric ◽  
Power Law Index

AbstractIn this article, the static response of the functionally graded piezoelectric (FGP) plates with piezoelectric layers (sandwich FGPM) is studied based on the first order shear deformation plate theory. The plate is under mechanical, electrical and thermal loadings and finite element method is employed to obtain the solution of the equation. All mechanical, thermal and piezoelectric properties, except Poisson ratio, obey the power law distribution through the thickness. By solving the governing equation, optimum value of power law index is investigated in each type of loading. The effects of different volume fraction index, layer arrangements, various boundary conditions and different loading types, are studied on the deflection of FGPM plate. It is inferred that, the correlations between the deflection, power law index and layer arrangement are completely different in the mechanical and thermal loading and the optimum value of the power law index should be selected in each case separately. This optimum values can be used as a design criterion to build a reliable sensors and actuators in thermal environments.

A Study on Adhesively Bonded Aluminum Plates Under Shock-Wave Loading

2017 ◽  
Author(s):  
Salih Yildiz ◽  
Yiannis Andreopoulos ◽  
Robert E. Jensen ◽  
Daniel Shaffren ◽  
Doug Jahnke ◽  
...  
Keyword(s):  
Shock Wave ◽  
Plate Theory ◽  
Dissimilar Materials ◽  
Laminated Plates ◽  
Shock Wave Loading ◽  
Wave Loading ◽  
Classical Plate Theory ◽  
Film Adhesive ◽  
Aluminum Plates ◽  
Application Fields

Adhesive joint technology has been developed gradually, and the application fields of this type of joints have been expanded increasingly since they reduce the weight of the applications, provide uniform stress distribution across the joints, allow to bond similar, and dissimilar materials, and contribute to dampen the shock, and vibration. However, the performance of the adhesive joints under high loading rate such as blast or ballistic loading has been studied by few researchers. In this study, fully laminated plates consisting of 6061 aluminum plates (15” in diameter and 1/16” thick) and FM300K epoxy film adhesive were tested under shock wave loading. Full displacement field over the testing plates were obtained by TRC-SDIC technique, and the strain on the plates were computed by classical plate theory for large deflections. FEM model was analyzed and the results were compared with experimental results.

scholarly journals Higher-Order Thermo-Elastic Analysis of FG-CNTRC Cylindrical Vessels Surrounded by a Pasternak Foundation

Nanomaterials ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 79 ◽  
Author(s):  
Masoud Mohammadi ◽  
Mohammad Arefi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Deformation Theory ◽  
Volume Fraction ◽  
Effective Properties ◽  
Shear Deformation Theory ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Elastic Response ◽  
Governing Equations ◽  
Third Order ◽  
Reinforced Composite

This study analyses the two-dimensional thermo-elastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical pressure vessels, by applying the third-order shear deformation theory (TSDT). The effective properties of FG-CNTRC cylindrical pressure vessels are computed for different patterns of reinforcement, according to the rule of mixture. The governing equations of the problem are derived from the principle of virtual works and are solved as a classical eigenproblem under the assumption of clamped supported boundary conditions. A large parametric investigation aims at showing the influence of some meaningful parameters on the thermo-elastic response, such as the type of pattern, the volume fraction of CNTs, and the Pasternak coefficients related to the elastic foundation.

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