Nonlinear Free Vibration of Piezoelectric Functionally Graded Beams in Thermal Environment

2015 ◽  
Author(s):  
Ali Fallah ◽  
Mohammad Taghi Ahmadian ◽  
Ahmad Barari
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Nonlinear Behavior ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Functionally Graded ◽  
Nonlinear Free Vibration ◽  
Simple Analytical Expression

Nonlinear free vibration analysis of piezoelectric functionally graded (PFG) beams in thermal environment with any boundary conditions are investigated. The nonlinear governing Equation of motion is derived based on the Euler-Bernoulli beam theory and Von Karman’s strain-displacement relation. Simple analytical expression is presented for the nonlinear natural frequency using energy balanced method (EBM). Results are validated and compared with available results in the literature. Effects of different parameters such as vibration amplitude, boundary conditions, material inhomogenity, electrical and thermal loading on the nonlinear behavior of PFG beams are presented.

Free Vibration Analysis of Functionally Graded Beams Resting on Elastic Foundation in Thermal Environment

2016 ◽  
Vol 16 (07) ◽  
pp. 1550029 ◽  
Author(s):  
P. Zahedinejad
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Various Boundary Conditions

The free vibration of functionally graded (FG) beams with various boundary conditions resting on a two-parameter elastic foundation in the thermal environment is studied using the third-order shear deformation beam theory. The material properties are temperature-dependent and vary continuously through the thickness direction of the beam, based on a power-law distribution in terms of the volume fraction of the material constituents. In order to discretize the governing equations, the differential quadrature method (DQM) in conjunction with the Hamilton’s principle is adopted. The convergence of the method is demonstrated. In order to validate the results, comparisons are made with solutions available for the isotropic and FG beams. Through a comprehensive parametric study, the effect of various parameters involved on the FG beam was studied. It is concluded that the uniform temperature rise has more significant effect on the frequency parameters than the nonuniform case.

Stochastic Nonlinear Free Vibration Analysis of Functionally Graded Beam Subjected to Thermal Loading with Random Material Properties

2013 ◽  
Vol 747 ◽  
pp. 551-554
Author(s):  
Niranjan L. Shegokar ◽  
Achchhe Lal
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Perturbation Technique ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Nonlinear Free Vibration ◽  
Functionally Graded Beam

This paper deals with the stochastic nonlinear free vibration response of functionally graded materials (FGMs) beam subjected to thermal loadings with uncertain material properties subjected to uniform and nonuniform temperature changes with temperature independent (TID) and dependent (TD) material properties. System properties such as material properties of each constituents material and volume fraction index are taken as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strains using modified C0 continuity. A direct iterative based nonlinear finite element method in conjunction with first order perturbation technique (FOPT) is used for FGMs beam to compute the second order statistics (mean and coefficient of variation) of the nonlinear fundamental frequency. The present outlined approach has been validated with the results available in literatures and independent Monte Carlo simulation (MCS).

scholarly journals Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Dongyan Shi ◽  
Shuai Zha ◽  
Hong Zhang ◽  
Qingshan Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Shallow Shell ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
General Boundary ◽  
Volume Distribution ◽  
General Boundary Conditions

The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and Rayleigh-Ritz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

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.

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