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.

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.

Vibration analysis of axially moving line supported functionally graded plates with temperature-dependent properties

2013 ◽  
Vol 228 (6) ◽  
pp. 953-969 ◽  
Author(s):  
Hamed Asadi ◽  
Mohammad M Aghdam ◽  
Mahmoud Shakeri
Keyword(s):  
Dynamic Analysis ◽  
Material Properties ◽  
Vibration Analysis ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Functionally Graded Plates ◽  
Temperature Dependent ◽  
Axially Moving ◽  
Temperature Dependent Properties

Vibration analysis of axially moving functionally graded plates with internal line supports and temperature-dependent properties is investigated using harmonic differential quadrature method. The plate is subjected to static in-plane forces while out-of-plane loading is dynamic. Stability of an axially moving plate, traveling at a constant velocity between different supports and experiencing small transverse vibrations are considered. The series of internal rigid line supports parallel to the plate edges are considered together with various arbitrary combinations of boundary conditions. Material properties of the plate are assumed temperature-dependent which is a non-linear function of temperature and differ continuously through thickness according to a power-law distribution of the volume fractions of the plate constituents. Two types of micromechanical models, namely, the Voigt and Mori–Tanaka models are considered. Based on the classical plate theory, the governing equations are obtained for functionally graded plate using the Hamilton’s principle. In the frame of a general dynamic analysis, it is shown that the onset of instability takes place in the form of divergence. The plate may experience divergence or flutter instability at a super critical velocity. Results for dynamic analysis of isotropic and laminated plates are validated with available data in the existing literature, which show excellent agreement. Furthermore, some new results are presented for vibration analysis of functionally graded material plates to study effects of the location of line supports, material properties, volume fraction, temperature, loading, aspect ratio and speed.

Thermo-Mechanical Vibration Analysis of Size-Dependent Functionally Graded Micro-Beams with General Boundary Conditions

2018 ◽  
Vol 10 (08) ◽  
pp. 1850088 ◽  
Author(s):  
Zhu Su ◽  
Guoyong Jin ◽  
Lifeng Wang ◽  
Dan Wang
Keyword(s):  
Vibration Analysis ◽  
Mechanical Vibration ◽  
Beam Theory ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Penalty Function Method ◽  
Cosine Series ◽  
Scale Parameters ◽  
Size Dependent

A unified formulation for thermo-mechanical vibration analysis of size-dependent Timoshenko micro-beams comprised of functionally graded materials (FGMs) with general restraints is presented. The size effect is considered by incorporating the modified strain gradient theory into Timoshenko beam theory. The thermal and mechanical properties of FGMs are related to temperature and are assumed as continuous variation along the thickness. The Mori–Tanaka estimate is used for calculation of the material properties of FGM micro-beam. The formulation is deduced on the basis of the variational principle combined with penalty function method. The displacements and rotation of the FGM micro-beam are uniformly expanded by a modified Fourier series composed of traditional cosine series and some appropriate supplementary functions. Several comparisons of the present solutions with those from existing literature confirm the validity of the current formulation. In addition, a parametric study is given to demonstrate the influence of length scale parameters, gradient indices, end restraints and temperature changes on vibration characteristic of functionally graded micro-beam.

Free vibration analysis of rotating functionally graded material plate under nonlinear thermal environment using higher order shear deformation theory

2018 ◽  
Vol 233 (6) ◽  
pp. 2056-2073 ◽  
Author(s):  
S Parida ◽  
SC Mohanty
Keyword(s):  
Free Vibration ◽  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Graded Material

In the present article, a higher order shear deformation theory is used to develop a finite element model for the free vibration analysis of a rotating functionally graded material plate in the thermal environment. The model is based on an eight-noded isoparametric element with seven degrees-of-freedom per node. The material properties are temperature dependent and graded along its thickness according to a simple power law distribution in terms of volume fraction of the constituents. The general displacement equation provides C0 continuity, and the transverse shear strain undergoes parabolic variation through the thickness of the plate. Therefore, the shear correction factor is not used in this theory. The obtained results are compared with the published results in the literature to determine the accuracy of the method. The effects of various parameters like hub radius, rotation speed, aspect ratio, thickness ratio, volume fraction index, and temperature on the frequency of rotating plate are investigated.

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.

scholarly journals Free vibration of piezoelectric FGM sandwich beam with porous core embedded in thermal environment and elastic foundation

2021 ◽  
Vol 15 (4) ◽  
pp. 15-28
Author(s):  
Tran Quang Hung ◽  
Tran Minh Tu ◽  
Do Minh Duc
Keyword(s):  
Temperature Distribution ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Thermal Environment ◽  
Ritz Method ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Lagrange Equations ◽  
Linear Temperature

This paper aims to present thermo-electrical free vibration characteristics of functionally graded material (FGM) sandwich beam placed on the two-parameter elastic foundation. The beam is constructed of a foam core, two middle FGM layers, and two outer piezoelectric layers. It is assumed that the beam is subjected to a constant voltage and a uniform/linear temperature distribution. Physical properties of the core and two middle layers vary smoothly through the thickness according to the cosine and power-law forms, respectively. Lagrange equations in conjunction with the Reddy third-order beam theory is employed to derive the governing equations of motion. A simple polynomial trial function-based Ritz method is adopted for the approximation of the displacement field to obtain the vibration response. The correctness of the study is verified by comparisons with other authors’ published results. Influences of geometry parameters, material property distribution, applied voltage, elastic foundation, temperature distribution, temperature change, porosity coefficient, span-to-height ratio, and boundary conditions are investigated through parametric studies.

Modified strain gradient theory for nonlinear vibration analysis of functionally graded piezoelectric doubly curved microshells

2021 ◽  
pp. 095440622110458
Author(s):  
Vahid Movahedfar ◽  
Mohammad M Kheirikhah ◽  
Younes Mohammadi ◽  
Farzad Ebrahimi
Keyword(s):  
Nonlinear Vibration ◽  
Material Properties ◽  
Vibration Analysis ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Scale Parameters ◽  
Functionally Graded Piezoelectric ◽  
Doubly Curved

Based on modified strain gradient theory, nonlinear vibration analysis of a functionally graded piezoelectric doubly curved microshell in thermal environment has been performed in this research. Three scale parameters have been included in the modeling of thin doubly curved microshell in order to capture micro-size effects. Graded material properties between the top and bottom surfaces of functionally graded piezoelectric doubly curved microshell have been considered via incorporating power-law model. It is also assumed that the microshell is exposed to a temperature field of uniform type and the material properties are temperature-dependent. By analytically solving the governing equations based on the harmonic balance method, the closed form of nonlinear vibration frequency has been achieved. Obtained results indicate the relevance of calculated frequencies to three scale parameters, material gradation, electrical voltage, curvature radius, and temperature changes.

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