Nonlinear Dynamics of FGM Conical Panel With Initial Imperfection in Thermal Environment

2017 ◽  
Author(s):  
Ming Hui Yao ◽  
Yan Niu ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Initial Imperfection ◽  
Harmonic Excitation ◽  
Functionally Graded ◽  
Phase Portraits ◽  
Power Law Distribution ◽  
Geometric Imperfection

In this paper, the nonlinear dynamics of a simply supported functionally graded materials (FGM) conical panel with different forms of initial imperfections is investigated. The conical panel is subjected to the simple harmonic excitation along the radial direction and the parametric excitation in the meridian direction. The small initial geometric imperfection of the conical panel is expressed by the form of the Cosine functions. According to a power-law distribution, the effective material properties are assumed to be graded along the thickness direction. Based on the first-order shear deformation theory and von Karman type nonlinear geometric relationship, the nonlinear equations of motion are established by using the Hamilton principle. The nonlinear partial differential governing equations are truncated by Galerkin’s method to obtain the ordinary differential equations along the radial displacement. The effects of imperfection types, half-wave numbers and amplitudes on the dynamic behaviors are studied by numerical simulation. Maximum Lyapunov exponents, bifurcation diagrams, time histories and phase portraits are obtained to show the dynamic response.

scholarly journals Nonlinear Dynamics of Imperfect FGM Conical Panel

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Yan Niu ◽  
Yuxin Hao ◽  
Minghui Yao ◽  
Wei Zhang ◽  
Shaowu Yang
Keyword(s):  
Nonlinear Dynamics ◽  
Equations Of Motion ◽  
Engineering Application ◽  
Shear Deformation Theory ◽  
Harmonic Excitation ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Phase Portraits ◽  
Power Law Distribution ◽  
Geometric Imperfection

Structures composed of functionally graded materials (FGM) can satisfy many rigorous requisitions in engineering application. In this paper, the nonlinear dynamics of a simply supported FGM conical panel with different forms of initial imperfections are investigated. The conical panel is subjected to the simple harmonic excitation along the radial direction and the parametric excitation in the meridian direction. The small initial geometric imperfection of the conical panel is expressed by the form of the Cosine functions. According to a power-law distribution, the effective material properties are assumed to be graded along the thickness direction. Based on the first-order shear deformation theory and von Karman type nonlinear geometric relationship, the nonlinear equations of motion are established by using the Hamilton principle. The nonlinear partial differential governing equations are truncated by Galerkin method to obtain the ordinary differential equations along the radial displacement. The effects of imperfection types, half-wave numbers of the imperfection, amplitudes of the imperfection, and damping on the dynamic behaviors are studied by numerical simulation. Maximum Lyapunov exponents, bifurcation diagrams, time histories, phase portraits, and Poincare maps are obtained to show the dynamic responses of the system.

Effect of carbon nanotube-reinforced magneto-electro-elastic facings on the pyrocoupled nonlinear deflection of viscoelastic sandwich skew plates in thermal environment

2021 ◽  
pp. 146442072110440
Author(s):  
Vinyas Mahesh
Keyword(s):  
Carbon Nanotube ◽  
Complex Modulus ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Energy Principle ◽  
Design Engineers ◽  
Total Potential ◽  
Viscoelastic Core

This work presents a finite-element-based numerical formulation to evaluate the nonlinear deflections of magneto-electro-elastic sandwich skew plates with a viscoelastic core and functionally graded carbon nanotube-reinforced magneto-electro-elastic face sheets. Meanwhile, the proposed formulation accommodates the geometrical skewness as well. The magneto-electro-elastic sandwich skew plate is operated in the thermal environment and subjected to various multiphysics loads, including electric and magnetic loads. The viscoelastic core is modelled via the complex modulus approach. Two different forms of viscoelastic cores, such as Dyad 606 and EC 2216, are considered in this study. Also, different thickness configurations of core and facing arrangements are taken into account. The plate kinematics is presumed through higher-order shear deformation theory, and von Karman's nonlinear strain displacement relations are incorporated. The global equations of motion are arrived at through the total potential energy principle and solved via the direct iterative method. Special attention is paid to assessing the influence of pyroeffects, coupling fields and electromagnetic boundary conditions on the nonlinear deflections of magneto-electro-elastic sandwich plates working in the thermal environment and subjected to electromagnetic loads, which is the first of its kind. Also, parametric studies dealing with the skew angles, carbon nanotube distributions and volume fractions, thickness ratio, and aspect ratio have been discussed. The results of this work are believed to be unique and serve as a guide for the design engineers towards developing sophisticated smart structures for various engineering applications.

scholarly journals Response of Functionally Graded Material Plate under Thermomechanical Load Subjected to Various Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Manish Bhandari ◽  
Kamlesh Purohit
Keyword(s):  
High Temperature ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Light Metal ◽  
Functionally Graded ◽  
Numerical Results ◽  
Element Formulation ◽  
Power Law Distribution

Functionally graded materials (FGMs) are one of the advanced materials capable of withstanding the high temperature environments. The FGMs consist of the continuously varying composition of two different materials. One is an engineering ceramic to resist the thermal loading from the high-temperature environment, and the other is a light metal to maintain the structural rigidity. In the present study, the properties of the FGM plate are assumed to vary along the thickness direction according to the power law distribution, sigmoid distribution, and exponential distribution. The fundamental equations are obtained using the first order shear deformation theory and the finite element formulation is done using minimum potential energy approach. The numerical results are obtained for different distributions of FGM, volume fractions, and boundary conditions. The FGM plate is subjected to thermal environment and transverse UDL under thermal environment and the response is analysed. Numerical results are provided in nondimensional form.

Effect of In-Plane Load and Thermal Environment on Buckling and Vibration Behavior of Two-Dimensional Functionally Graded Tapered Timoshenko Nanobeam

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Roshan Lal ◽  
Chinika Dangi
Keyword(s):  
Thermal Environment ◽  
Slenderness Ratio ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Power Law Distribution ◽  
Energy Principle

Abstract In this work, buckling and vibration characteristics of two-dimensional functionally graded (FG) nanobeam of nonuniform thickness subjected to in-plane and thermal loads have been analyzed within the frame work of Timoshenko beam theory. The beam is tapered by linear variation in thickness along the length. The temperature-dependent material properties of the beam are varying along thickness and length as per a power-law distribution and exponential function, respectively. The analysis has been presented using Eringen’s nonlocal theory to incorporate the size effect. Hamilton’s energy principle has been used to formulate the governing equations of motion. These resulting equations have been solved via generalized differential quadrature method (GDQM) for three combinations of clamped and simply supported boundary conditions. The effect of in-plane load together with temperature variation, nonuniformity parameter, gradient indices, nonlocal parameter, and slenderness ratio on the natural frequencies is illustrated for the first three modes of vibration. The critical buckling loads in compression have been computed by putting the frequencies equal to zero. A significant contribution of in-plane load on mechanical behavior of two-directional functionally graded nanobeam with nonuniform cross section has been noticed. Results are in good accordance.

Nonlinear Dynamic Behavior of Functionally Graded Truncated Conical Shell Under Complex Loads

2015 ◽  
Vol 25 (02) ◽  
pp. 1550025 ◽  
Author(s):  
S. W. Yang ◽  
Y. X. Hao ◽  
W. Zhang ◽  
S. B. Li
Keyword(s):  
Nonlinear Dynamics ◽  
Conical Shell ◽  
Nonlinear Dynamic ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Phase Portraits ◽  
Vertex Angle ◽  
First Order ◽  
Aerodynamic Pressure ◽  
Truncated Conical Shell

Nonlinear dynamic behaviors of ceramic-metal graded truncated conical shell subjected to complex loads are investigated. The shell is modeled by first-order shear deformation theory. The nonlinear partial differential governing equation in terms of transverse displacements of the FGM truncated conical shell is derived from the Hamilton's principle. Galerkin's method is then utilized to discretize the partial governing equations to a two-degree-of-freedom nonlinear ordinary differential equation. The temperature-dependent materials properties of the constituents are graded in the radial direction in accordance with a power-law distribution. The aerodynamic pressure can be calculated by using the first-order piston theory. The temperature field is assumed to be a steady-state constant-temperature distribution. Bifurcation diagrams, the maximum Lyapunov exponents, wave forms and phase portraits are obtained by numerical simulation to demonstrate the complex nonlinear dynamics response of the FGM truncated conical shell. The influences of the semi-vertex angle, the material gradient index, in-plane and aerodynamic load on the nonlinear dynamics are studied.

Supersonic Flutter of Functionally Graded Plates in a Thermal Environment

2006 ◽  
Author(s):  
H. M. Navazi ◽  
H. Haddadpour
Keyword(s):  
Differential Equations ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Time Integration ◽  
Analytical Investigation ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Numerical Time Integration ◽  
Flutter Margin

In this paper, an analytical investigation intended to determine the flutter margin of supersonic functionally graded panels is carried out. For this purpose, piston theory aerodynamics has been employed to model quasi-steady aerodynamic loading. The material properties of the plate are assumed to be graded continuously across the panel thickness. The variation of temperature-dependent thermoelastic properties follows a simple power-law distribution in terms of the volume fraction of the constituent materials. The effects of compressive in-plane loads and static pressure differential are studied. Both uniform and through the thickness nonlinear temperature distributions are also considered. Hamilton’s principle is used to determine the coupled partial differential equations of motion. Using Galerkin’s method, the derived equations are transformed into a set of coupled ordinary differential equations, and then solved by numerical time integration. Some examples comparing the flutter margin of FG panels with that of plates made of pure metals and pure ceramics are presented. The results of the present study are compared with those of the previous works, where finite element method was used. It is shown that the use of functionally graded materials can yield an increase or decrease of the aeroelastic stability in the supersonic flow for different regions.

Combination resonance analysis of imperfect functionally graded conical shell resting on nonlinear viscoelastic foundation in thermal environment under multi-excitation

2021 ◽  
pp. 107754632110065
Author(s):  
Hamid Aris ◽  
Habib Ahmadi
Keyword(s):  
Power Law ◽  
Material Properties ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Initial Imperfection ◽  
Functionally Graded ◽  
Harmonic Load ◽  
Combination Resonance ◽  
Conical Shells ◽  
Nonlinear Viscoelastic

In this work, nonlinear forced vibrations of truncated conical shells are presented using a semi-analytical method. The material properties are varied along the thickness direction as a power law distribution. The functionally graded truncated conical shells are exposed to external harmonic load and placed in the thermal environment and have an initial imperfection. Furthermore, the functionally graded truncated conical shells rests on generalized nonlinear viscoelastic foundations which consisted of a Winkler and Pasternak foundation parameters augmented by a Kelvin–Voigt viscoelastic model and a nonlinear cubic stiffness. The fundamental equations are extracted using first-order shear deformation theory in conjunction with nonlinear von Kármán relationships. The partial differential equations of truncated conical shells are reduced through Galerkin’s method, and the result is extracted using the multiple scales method. To analyze the resonance analyses, a two-term external excitation is considered. In this regard, various secondary resonances are investigated, and finally, the analyses about combination resonances are represented. To investigate the presented approach, a comparison study is performed with those addressed by other researchers. To analyze the nonlinear combination resonance behavior of truncated conical shells, the effect of geometrical characteristics, material properties, power law index, thermal effects, external load amplitude, and initial imperfection are examined. Finally, the steady-state responses of the nonlinear system are analyzed. As one of the most interesting results, the softening behavior of truncated conical shells with inverse quadratic distribution is the most, and for the quadratic distribution is the least.

Free Vibration Analysis of Functionally Graded Skew Plate in Thermal Environment Using Higher Order Theory

2018 ◽  
Vol 10 (01) ◽  
pp. 1850007 ◽  
Author(s):  
Smita Parida ◽  
Sukesh Chandra Mohanty
Keyword(s):  
Free Vibration ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Shear Strain ◽  
Power Law Distribution ◽  
Skew Angle

This paper deals with the free vibration of a skew functionally graded material (FGM) plate in the thermal environment. A higher-order shear deformation theory (HOSDT) is employed to develop a finite element model of the plate. The material properties are assumed to be temperature-dependent and are graded along the thickness direction as per simple power law distribution in terms of volume fraction of metal and ceramic constituent phases. The model is based on an eight-noded isoparametric element with seven degrees of freedom (DOFs) per node. The general displacement equation provides C[Formula: see text] continuity. The transverse shear strain undergoes parabolic variation through the thickness of the plate. The governing equations are derived using the Hamilton’s principle. The obtained results are compared with the published results to determine the accuracy of the method. The effects of various parameters like aspect ratio, side-thickness ratio, volume fraction index, boundary conditions and skew angle on the natural frequencies are investigated.

scholarly journals Free vibration of functionally graded sandwich plates with stiffeners based on the third-order shear deformation theory

2016 ◽  
Vol 38 (2) ◽  
pp. 103-122 ◽  
Author(s):  
Pham Tien Dat ◽  
Do Van Thom ◽  
Doan Trac Luat
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Power Law Distribution ◽  
Third Order ◽  
The Third

In this paper, the free vibration of functionally  sandwich grades plates with stiffeners is investigated by using the finite  element method. The material properties are assumed to be graded in the  thickness direction by a power-law distribution. Based on the third-order  shear deformation theory, the governing equations of motion are derived from  the Hamilton's principle. A parametric study is carried out to highlight the  effect of material distribution, stiffener parameters on the free  vibration characteristics of the plates.

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.

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