scholarly journals Statistical Identification of Parameters for Damaged FGM Structures with Material Uncertainties in Thermal Environment

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-21
Author(s):  
Yalan Xu ◽  
Yu Qian ◽  
Kongming Guo
Keyword(s):  
Stochastic Model ◽  
Material Properties ◽  
Damage Identification ◽  
Model Updating ◽  
Thermal Environment ◽  
Iteration Process ◽  
Functionally Graded ◽  
Computational Method ◽  
Modal Parameters ◽  
Material Uncertainties

Considering that the statistic numerical characteristics are often required in the probability-based damage identification and safety assessment of functionally graded material (FGM) structures, an stochastic model updating-based inverse computational method to identify the second-order statistics (means and variances) of material properties as well as distribution of constituents for damaged FGM structures with material uncertainties is presented by using measurable modal parameters of structures. The region truncation-based optimization method is employed to simplify the computational process in stochastic model updating. In order to implement the forward propagation of uncertainties required in the stochastic model updating and avoid large error resulting in the nonconvergence of the iteration process, an algorithm is proposed to compute the covariance between the modal parameters and the identified parameters for damaged FGM structures. The proposed method is illustrated by a numerically simulated damaged FGM beam with continuous spatial variation of material properties and verified by comparing with the Monte-Carlo simulation (MCS) method. The influences of the levels and sources of measured data uncertainties as well as the boundary conditions on the identification results are investigated. The numerical simulation results show the efficiency and effectiveness of the presented method for the identification of material parameter variability by using the measurable modal parameters of damaged FGM structures.

Free vibration analysis of functionally graded double-tapered beam rotating in thermal environment considering geometric nonlinearity, shear deformability, and Coriolis effect

2017 ◽  
Vol 232 (12) ◽  
pp. 2244-2262 ◽  
Author(s):  
Suman Pal ◽  
Debabrata Das
Keyword(s):  
Mathematical Model ◽  
Free Vibration ◽  
Material Properties ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Coriolis Effect ◽  
Governing Equations

The present work investigates the free vibration behavior of double-tapered functionally graded beams rotating in thermal environment, using an improved mathematical model. The functional gradation for ceramic–metal compositions, following power-law, is considered to be symmetric with respect to the mid-plane, leading to metal-rich core and ceramic-rich outer surfaces of the beam. The temperature dependence of the material properties are considered using Touloukian model. The nonlinearity in strain–displacement relationships for both the axial and transverse shear strains are considered. Firstly, the governing equations for deformed beam configuration under time-independent centrifugal loading are obtained using minimum total potential energy principle, and the solution is obtained following Ritz method. Then the free vibration problem of the centrifugally deformed beam is formulated employing Lagrange’s principle and considering tangent stiffness of the deformed beam configuration. Coriolis effect is considered in the mathematical model, and the governing equations are transformed to the state-space for obtaining an eigenvalue problem. The results for the first two modes of both chord-wise and flap-wise vibrations are presented in nondimensional plane to show the effects of taperness parameter, root-offset parameter, volume fraction exponent, operating temperature, and functionally graded material composition. The results in comparative form are presented for both temperature-dependent and temperature-independent material properties.

Nonlinear thermo-mechanical dynamic analysis and vibration of higher order shear deformable piezoelectric functionally graded material sandwich plates resting on elastic foundations

2016 ◽  
Vol 20 (2) ◽  
pp. 191-218 ◽  
Author(s):  
Nguyen Dinh Duc ◽  
Pham Hong Cong
Keyword(s):  
Dynamic Analysis ◽  
Material Properties ◽  
Nonlinear Dynamic ◽  
Thermal Environment ◽  
Nonlinear Dynamic Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Sandwich Plates ◽  
Elastic Foundations

Used the Reddy's higher-order shear deformation plate theory, the nonlinear dynamic analysis and vibration of imperfect functionally graded sandwich plates in thermal environment with piezoelectric actuators (PFGM) on elastic foundations subjected to a combination of electrical, damping loadings and temperature are investigated in this article. One of the salient features of this work is the consideration of temperature on the piezoelectric layer, and the material properties of the PFGM sandwich plates are assumed to be temperature-dependent. The governing equations are established based on the stress function, the Galerkin method, and the Runge–Kutta method. In the numerical results, the effects of geometrical parameters; material properties; imperfections; elastic foundations; electrical, thermal, and damping loads on the vibration and nonlinear dynamic response of the PFGM sandwich plates are discussed. The obtained natural frequencies are verified with the known results in the literature.

scholarly journals Vibration Analysis of Non-Uniform Imperfect Functionally Graded Beams with Porosities in Thermal Environment

2017 ◽  
Vol 33 (6) ◽  
pp. 739-757 ◽  
Author(s):  
F. Ebrahimi ◽  
M. Hashemi
Keyword(s):  
Material Properties ◽  
Vibration Analysis ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Mechanical Vibration ◽  
Beam Theory ◽  
Transformation Method ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Linear Temperature

AbstractIn the present study, thermo-mechanical vibration behavior of non-uniform beams made of functionally graded (FG) porous material are investigated under different thermal loadings for the first time. It is observed that during the fabrication of functionally graded materials (FGMs) porosities and micro-voids can be occured inside the material, thus in this study vibration analysis of FG beams by considering the effect of these imperfections is performed. Material properties of the FG beam are assumed to be temperature-dependent and vary continuously through thickness direction according to a power-law scheme which is modified to approximate material properties for both even and uneven distributions of the porosities. Different thermal environmental conditions, including uniform, linear and non-linear temperature changes through the thickness direction are considered. The motion equations are derived based on the Euler-Bernoulli beam theory through Hamilton's principle and they are solved applying the differential transformation method (DTM). In order to show the accuracy of the present analysis, comparisons are made with previous researches and an excellent agreement is observed. The obtained results are presented for the thermo-mechanical vibration characteristics of the FG beams such as the influences of various temperature rises, gradient index, porosity volume fraction, taper ratio and the boundary conditions in detail.

Interaction Between Thermal Field and Two-Dimensional Functionally Graded Materials: A Structural Mechanical Example

2019 ◽  
Vol 11 (10) ◽  
pp. 1950099 ◽  
Author(s):  
Ye Tang ◽  
Shun Zhong ◽  
Tianzhi Yang ◽  
Qian Ding
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Materials ◽  
Material Properties ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Graded Materials ◽  
Promising Strategy ◽  
Generalized Differential ◽  
Euler Bernoulli Beam

The buckling and free vibration of a Euler–Bernoulli beam composed of two-directional functionally graded materials (FGMs) in thermal environment are analyzed. The material properties and temperature distributions are considered to be continuously varied along both axial and thickness directions. Such two-directional FGMs provide the basis of a promising strategy to tune the dynamic behavior of a structure in a controlled fashion, achieving tunable response as desired. The dynamic equation of the beam and relevant boundary conditions are derived based on Hamilton’s principle. The generalized differential quadrature method is used for determining the exact buckling configuration and the natural frequencies of the beam with different boundary conditions. Numerical results are presented to examine the effects of material gradations on the critical buckling temperature. It is concluded that both temperature change and material properties have significant influences on the natural frequency, which suggests that it is possible to tailor or tune the dynamic behaviors of a beam by using man-made FGMs in a complex environment.

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.

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

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