Nonlinear vibration and active control of functionally graded beams with piezoelectric sensors and actuators

2011 ◽  
Vol 22 (18) ◽  
pp. 2093-2102 ◽  
Author(s):  
Yiming Fu ◽  
Jianzhe Wang ◽  
Yiqi Mao
Keyword(s):  
Active Control ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Sensors And Actuators ◽  
Nonlinear Dynamic Equations ◽  
Piezoelectric Layers

Employing higher order shear deformation theory, geometric nonlinear theory, and Hamilton’s principle, a set of nonlinear governing equations for the functionally graded beams with surface-bonded piezoelectric layers is derived. Then, the negative velocity feedback algorithm coupling the direct and inverse piezoelectric effect is used to control the piezoelectric functionally graded beams actively. Using the finite difference method and Newmark method synthetically, the numerical solutions for the nonlinear dynamic equations of functionally graded beams with piezoelectric patches are obtained iteratively. In the numerical examples, the effects of the volume fraction exponent on the nonlinear dynamic responses and amplitude–frequency curves are investigated, and the active control responses of the functionally graded beams with piezoelectric layers under different control gains and volume fraction exponents are analyzed. Some meaningful solutions have been presented.

On the Dynamic Response of Imperfection Sensitive Higher Order Functionally Graded Plates with Random System Parameters

2019 ◽  
Vol 11 (03) ◽  
pp. 1950025 ◽  
Author(s):  
Mohammed Shakir ◽  
Mohammad Talha
Keyword(s):  
Volume Fraction ◽  
Perturbation Technique ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Integration Scheme ◽  
Power Law Distribution ◽  
Random System ◽  
System Parameters

This paper presents the influence of various random system parameters on dynamics response of imperfection sensitive higher order shear deformable functionally graded material (FGM) plates. Young’s moduli, Poisson’s ratio and volume fraction index are considered as random system parameters. The material properties of the FGM plates are assumed to vary along the thickness direction using simple power-law distribution in terms of the volume fraction of the constituents. The plate kinematics is based on Reddy’s higher order shear deformation theory. Finite element method (FEM) is employed in conjunction with first-order perturbation technique (FOPT) and Newmark integration scheme to explore the influence of different system parameters, like volume fraction indices, aspect ratio, material uncertainties, and imperfection amplitude on the dynamic responses of the FGM plates.

Active Control of Plates Made of Functionally Graded Piezoelectric Material Subjected to Thermo-Electro-Mechanical Loads

2019 ◽  
Vol 19 (09) ◽  
pp. 1950107 ◽  
Author(s):  
Yu Xue ◽  
Jinqiang Li ◽  
Fengming Li ◽  
Zhiguang Song
Keyword(s):  
Dynamic Response ◽  
Piezoelectric Material ◽  
Active Control ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Load Parameter ◽  
Mechanical Loads ◽  
Functionally Graded Piezoelectric Material ◽  
Functionally Graded Piezoelectric

The present paper concentrates on the active control of the static bending and dynamic response of a functionally graded piezoelectric material (FGPM) plate subjected to thermo-electro-mechanical loads. Using the first-order shear deformation theory and Hamilton’s principle, the equation of motion for the FGPM plate is deduced. Based on the smart properties of piezoelectric ceramic, the active control of the static bending and vibration of the FGPM plate is studied by the mechanical load feedback, velocity feedback and LQR control methods in thermal environment. The effects of load parameter, temperature, volume fraction index and feedback control gain on the static bending and dynamic response of the FGPM plate are examined in detail. The simulation results show that the present control method can largely improve both the static and dynamic stability of the FGPM plate.

MECHANICAL VIBRATION AND BUCKLING ANALYSIS OF FGM PLATES AND SHELLS USING A FOUR-NODE QUASI-CONFORMING SHELL ELEMENT

2008 ◽  
Vol 08 (02) ◽  
pp. 203-229 ◽  
Author(s):  
SUNG-CHEON HAN ◽  
GILSON RESCOBER LOMBOY ◽  
KI-DU KIM
Keyword(s):  
Numerical Solutions ◽  
Volume Fraction ◽  
Mechanical Vibration ◽  
Shear Deformation Theory ◽  
Homogeneous Element ◽  
Shell Element ◽  
Functionally Graded ◽  
Sigmoid Function ◽  
Rectangular Plates ◽  
Plates And Shells

In this paper, we investigate the natural frequencies and buckling loads of functionally graded material (FGM) plates and shells, using a quasi-conforming shell element that accounts for the transverse shear strains and rotary inertia. The eigenvalues of the FGM plates and shells are calculated by varying the volume fraction of the ceramic and metallic constituents using a sigmoid function, but the Poisson ratios of the FGM plates and shells are assumed to be constant. The expressions for the membrane, bending and shear stiffness of FGM shell elements are more a complicated combination of material properties than a homogeneous element. In order to validate the finite element numerical solutions, the Navier solutions for rectangular plates based on the first order shear deformation theory are also presented. The present numerical solutions for composite and sigmoid FGM (S-FGM) plates and shells are verified by the Navier solutions and various examples of composite and FGM structures. The present results are in good agreement with the Navier theoretical solutions.

scholarly journals Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method

2013 ◽  
Vol 2013 ◽  
pp. 1-33 ◽  
Author(s):  
Francesco Tornabene ◽  
Alessandro Ceruti
Keyword(s):  
Dynamic Optimization ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Search Space ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Static Deflection ◽  
Power Law Distribution ◽  
Graded Material ◽  
Doubly Curved

This study deals with a mixed static and dynamic optimization of four-parameter functionally graded material (FGM) doubly curved shells and panels. The two constituent functionally graded shell consists of ceramic and metal, and the volume fraction profile of each lamina varies through the thickness of the shell according to a generalized power-law distribution. The Generalized Differential Quadrature (GDQ) method is applied to determine the static and dynamic responses for various FGM shell and panel structures. The mechanical model is based on the so-called First-order Shear Deformation Theory (FSDT). Three different optimization schemes and methodologies are implemented. The Particle Swarm Optimization, Monte Carlo and Genetic Algorithm approaches have been applied to define the optimum volume fraction profile for optimizing the first natural frequency and the maximum static deflection of the considered shell structure. The optimization aim is in fact to reach the frequency and the static deflection targets defined by the designer of the structure: the complete four-dimensional search space is considered for the optimization process. The optimized material profile obtained with the three methodologies is presented as a result of the optimization problem solved for each shell or panel structure.

Functionally Graded Plates under Thermal and Moisture Effects

2012 ◽  
Vol 535-537 ◽  
pp. 1382-1385
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Numerical Solutions ◽  
Volume Fraction ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Postbuckling Behavior ◽  
Moisture Effects ◽  
Graded Material ◽  
Thermal Postbuckling ◽  
Hygrothermal Environments

The postbucking behaviors of Functionally Graded Material (FGM) plate in hygrothermal environments are investigated. The material properties of FGM change continuously in the thickness direction according to the volume fractions of the materials. The formulations are based on the First-order Shear Deformation Theory (FSDT) and von Karman strain-displacement relations are applied. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. Newton-Raphson technique is adopted to analyze the thermal postbuckling behavior of the model. Furthermore, moisture effects on the model are significantly appeared due to the increase of the volume fraction index of the materials.

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 Buckling Behavior of FG-CNT Reinforced Composite Conical Shells Subjected to a Combined Loading

Nanomaterials ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 419 ◽  
Author(s):  
Abdullah H. Sofiyev ◽  
Francesco Tornabene ◽  
Rossana Dimitri ◽  
Nuri Kuruoglu
Keyword(s):  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Structural Response ◽  
Systematic Investigation ◽  
Functionally Graded ◽  
Combined Loading ◽  
Proportional Loading ◽  
Conical Shells ◽  
Reinforced Composite ◽  
Buckling Behavior

The buckling behavior of functionally graded carbon nanotube reinforced composite conical shells (FG-CNTRC-CSs) is here investigated by means of the first order shear deformation theory (FSDT), under a combined axial/lateral or axial/hydrostatic loading condition. Two types of CNTRC-CSs are considered herein, namely, a uniform distribution or a functionally graded (FG) distribution of reinforcement, with a linear variation of the mechanical properties throughout the thickness. The basic equations of the problem are here derived and solved in a closed form, using the Galerkin procedure, to determine the critical combined loading for the selected structure. First, we check for the reliability of the proposed formulation and the accuracy of results with respect to the available literature. It follows a systematic investigation aimed at checking the sensitivity of the structural response to the geometry, the proportional loading parameter, the type of distribution, and volume fraction of CNTs.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

TSDT theory for free vibration of functionally graded plates with various material properties

2021 ◽  
Vol 8 (4) ◽  
pp. 691-704
Author(s):  
M. Janane Allah ◽  
◽  
Y. Belaasilia ◽  
A. Timesli ◽  
A. El Haouzi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Implicit Algorithm ◽  
Proposed Model ◽  
Graded Material ◽  
Composite Modeling

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

Sign in / Sign up

Export Citation Format

Share Document