Nonlinear Dynamics of a Translational FGM Plate with Strong Mode Interaction

2018 ◽  
Vol 18 (03) ◽  
pp. 1850031 ◽  
Author(s):  
Yan Qing Wang ◽  
Jean W. Zu
Keyword(s):  
Nonlinear Dynamics ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Power Law ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Mode Interaction ◽  
Dynamical Response ◽  
Nonlinear Frequency ◽  
Power Law Distribution

This paper examines the nonlinear dynamics of a translational functionally graded material (FGM) plate. The plate is composed of nickel and stainless steel, and its property is graded in the thickness direction that obeys a power-law distribution. By adopting the Kármán nonlinear geometrical relations, the equation of motion is derived from the D’Alembert’s principle by considering the dynamic equilibrium relationships for the out-of-plane vibration of the plate. The equation of motion is discretized by using the Galerkin method and thus a series of ordinary differential equations with mode-coupling terms are obtained. These ordinary differential equations are then solved by utilizing the method of harmonic balance. The analytical results are verified by the adaptive step-size fourth-order Runge–Kutta technique. The stability analysis of analytical solutions is also carried out by introducing small perturbation for steady state solutions. Both natural frequency and nonlinear frequency-amplitude characteristics are presented. In the translational FGM plate, strong nonlinear mode interaction phenomenon has been detected. The nonlinear frequency response shows intensive hardening-spring characteristics. Moreover, various system parameters such as power-law distribution, translating speed of the plate, in-plane tension force, damping coefficient and external excitation amplitude are selected as the controlled variables to present parametric study. Their effects on the nonlinear dynamical response of the translational FGM plate are highlighted.

scholarly journals Geometrical Influence on Stability of FGM Beams under Vibration

2020 ◽  
Vol 9 (4) ◽  
pp. 2027-2033
Keyword(s):  
Power Law ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Finite Element Analyses ◽  
Power Law Distribution ◽  
Rotating Beam ◽  
Stability Boundaries ◽  
Exponential Law ◽  
Graded Material ◽  
The Stability

In this paper the influence of geometry on the stability of a functionally graded material rotating beam is reported. The equation of motion is formulated using Hamilton’s principle in association with finite element analyses. Floquet’s theory was used for establishing the stability boundaries. The properties of functionally graded ordinary (FGO) and functionally graded sandwich (FGSW) beams under consideration are assumed to be graded following either power law or exponential law across the thickness of the beam. The effect of geometry in terms of slenderness parameter on the dynamic stability of both FGO & FGSW beams have been investigated. The increase in slenderness parameter enhances the stability of both the FGO and FGSW beams. Further it has been observed that exponential distribution of properties ensures better stability compared to power law distribution of properties.

Nonlinear Vibration Analysis of Viscoelastic Smart Sandwich Plates Through the use of Fractional Derivative Zener Model

2021 ◽  
pp. 2150061
Author(s):  
Hamid Reza Talebi Amanieh ◽  
Seyed Alireza Seyed Roknizadeh ◽  
Arash Reza
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Nonlinear Vibration ◽  
Fractional Order ◽  
Sandwich Plate ◽  
Functionally Graded ◽  
Viscoelastic Layer ◽  
Sandwich Plates ◽  
Multiple Time ◽  
Nonlinear Frequency

In this paper, the nonlinear vibrational behavior of a sandwich plate with embedded viscoelastic material is studied through the use of constitutive equations with fractional derivatives. The studied sandwich structure is consisted of a viscoelastic core that is located between the faces of functionally graded magneto-electro-elastic (FG-MEE). In order to determine the frequency-dependent feature of the viscoelastic layer, four-parameter fractional derivative model is utilized. The material properties of FG-MEE face sheets have been distributed considering the power law scheme along the thickness. In addition, for derivation of the governing equations on the sandwich plate, first-order shear deformation plate theory along with von Karman-type of kinematic nonlinearity are implemented. The derived partial differential equations (PDEs) have been transformed to the ordinary differential equations (ODEs) through the Galerkin method. After that, the nonlinear vibration equations for the sandwich plate have been solved by multiple time scale perturbation technique. Moreover, for evaluating the effect of different parameters such as electric and magnetic fields, fractional order, the ratio of the core-to-face thickness and the power low index on the nonlinear vibration characteristics of sandwich plates with FG-MEE face sheets, the parametric analysis has been performed. The obtained results revealed the enhanced nonlinear natural frequency through an increment in the fractional order. Furthermore, the prominent influence of fractional order on the nonlinear frequency of sandwich plate was declared at the negative electric potential and positive magnetic potential.

Aerothermoelastic Stability of Functionally Graded Circular Cylindrical Shells

2010 ◽  
Author(s):  
Farhad Sabri ◽  
Aouni A. Lakis
Keyword(s):  
Finite Element ◽  
Power Law ◽  
Shell Thickness ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Element Formulation ◽  
Power Law Distribution ◽  
Aerodynamic Pressure ◽  
Circular Cylindrical Shells

In this work, a hybrid finite element formulation is presented to predict the flutter boundaries of circular cylindrical shells made of functionally graded materials. The development is based on the combination of linear Sanders thin shell theory and classic finite element method. Material properties are temperature dependent, and graded in the shell thickness direction according to a simple power law distribution in terms of volume fractions of constituents. The temperature field is assumed to be uniform over the shell surface and along the shell thickness. First order piston theory is applied to account for supersonic aerodynamic pressure. The effects of temperature rise and shell internal pressure on the flutter boundaries of FG circular cylindrical shell for different values of power law index are investigated. The present study shows efficient and reliable results that can be applied to the aeroelastic design and analysis of shells of revolution in aerospace vehicles.

BI-STABLE ANALYSES OF LAMINATED FGM SHELLS

2012 ◽  
Vol 12 (02) ◽  
pp. 311-335 ◽  
Author(s):  
X. Q. HE ◽  
L. LI ◽  
S. KITIPORNCHAI ◽  
C. M. WANG ◽  
H. P. ZHU
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Optimum Combination ◽  
Thickness Direction ◽  
Power Law Distribution ◽  
Deployable Structures ◽  
Graded Material ◽  
Two Parameter

Based on an inextensional two-parameter analytical model for cylindrical shells, bi-stable analyses were carried out on laminated functionally graded material (FGM) shells with various layups of fibers. Properties of FGM shells are functionally graded in the thickness direction according to a volume fraction power law distribution. The effects of constituent volume fractions of FGM matrix are examined on the curvature and twist of laminated FGM shells. The results reveal that the optimum combination of constituents of FGM matrix can be obtained for the maximum twist of FGM shells with antisymmetric layups, which helps the design of deployable structures. The effects of Young's modulus of fibers and the symmetry of layups on bi-stable behaviors are also discussed in detail.

scholarly journals A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Ali Jafari
Keyword(s):  
Differential Equations ◽  
Porous Material ◽  
Power Law ◽  
Material Properties ◽  
Solution Method ◽  
Equations Of Motion ◽  
Higher Order ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Temperature Dependent

In the present paper, thermomechanical vibration characteristics of functionally graded (FG) Reddy beams made of porous material subjected to various thermal loadings are investigated by utilizing a Navier solution method for the first time. Four types of thermal loadings, namely, uniform, linear, nonlinear, and sinusoidal temperature rises, through the thickness direction are considered. Thermomechanical material properties of FG beam are assumed to be temperature-dependent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of motion are derived based on higher order shear deformation beam theory. Hamilton’s principle is applied to obtain the governing differential equations of motion which are solved by employing an analytical technique called the Navier type solution method. Influences of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, thermal effects, and slenderness ratios on natural frequencies of the temperature-dependent FG beams with porosities are investigated and discussed in detail. It is concluded that these effects play significant role in the thermodynamic behavior of porous FG beams.

Investigation of Nonlinear Dynamics of Magnetoelastic Oscillations in Normal Magnetized Ferrite Plate

2015 ◽  
Vol 233-234 ◽  
pp. 471-475 ◽  
Author(s):  
D.A. Pleshev ◽  
Vladimir S. Vlasov ◽  
Leonid N. Kotov ◽  
F.F. Asadullin ◽  
S.M. Poleshikov ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Ferromagnetic Resonance ◽  
Magnetization Vector ◽  
Step Length ◽  
Interaction Constant ◽  
Magnetoelastic Interaction ◽  
Ferrite Plate ◽  
Dissipation Parameter

The present work deals with investigation of features of a magnetization vector of nonlinear precession and elastic displacements close to ferromagnetic resonance in normal magnetized ferrite plate. The system of ordinary differential equations was solved numerically by the Runge-Kutta 7-8 orders method with control of the integration at every step length. The possible excitation of magnetoelastic autooscillations was found out in the paper. Two mechanisms of autooscillations: reorientation and detuning were investigated. The boundaries between the regular and chaotic reorientation autooscillations depending on the magnetic dissipation parameter and magnetoelastic interaction constant were determined.

Vibrational behavior of beams made of functionally graded materials by using a mixed formulation

2020 ◽  
Vol 234 (18) ◽  
pp. 3650-3666 ◽  
Author(s):  
Souhir Zghal ◽  
Fakhreddine Dammak
Keyword(s):  
Functionally Graded Materials ◽  
Power Law ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Mixed Formulation ◽  
Shear Stresses ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Vibrational Behavior

This paper investigates the vibrational behavior of beams made of functionally graded materials using a mixed formulation. Unlike the other high order shear deformation theories (HSDTs), the proposed formulation is elaborated within a double field of displacements and stresses which offers the possibility of the development of low order linear elements with enhanced accuracy. As well as, the effect of the transverse shear strains and the zero condition of the transverse shear stresses on the top and bottom surfaces are verified. The material characteristics of the beams are described via a power law distribution in order to take into account the continuous variation of the volume fraction of its constituents along the thickness direction. Numerical simulations are conducted to show the influence of power law index, slenderness ratios, and boundary conditions on natural frequencies of functionally graded beams. Results demonstrate the efficiency and the applicability of the model based on a refined mixed formulation and its ability to predict the vibrational behavior of functionally graded beams with good accuracy.

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