Out-of-plane free vibration of functionally graded circular curved beams in thermal environment

2010 ◽  
Vol 92 (2) ◽  
pp. 541-552 ◽  
Author(s):  
P. Malekzadeh ◽  
M.R. Golbahar Haghighi ◽  
M.M. Atashi
Keyword(s):  
Free Vibration ◽  
Thermal Environment ◽  
Functionally Graded ◽  
Curved Beams ◽  
Out Of Plane

OUT-OF-PLANE FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED CIRCULAR CURVED BEAMS SUPPORTED ON ELASTIC FOUNDATION

2010 ◽  
Vol 02 (03) ◽  
pp. 635-652 ◽  
Author(s):  
P. MALEKZADEH ◽  
M. R. GOLBAHAR HAGHIGHI ◽  
M. M. ATASHI
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Curved Beams ◽  
Out Of Plane ◽  
Benchmark Solutions

As a first endeavor, the out-of-plane free vibration analysis of thin-to-moderately thick functionally graded (FG) circular curved beams supported on two-parameter elastic foundation is presented. The formulation is derived based on the first-order shear deformation theory (FSDT), which includes the effects of shear deformation and rotary inertia due to both torsional and flexural vibrations. The material properties are assumed to be graded in the direction normal to the plane of the beam curvature. The differential quadrature method (DQM), as an efficient and accurate method, is employed to discretize the equations of motion and the related boundary conditions. In order to assure the accuracy of the formulation and the method of solution, convergence behavior of the nondimensional natural frequencies is examined for FG circular curved beams and comparison studies with those of isotropic curved beams, available in the literature, are performed. The effects of the elastic foundation coefficients, boundary conditions, the material graded index and different geometrical parameters on the natural frequency parameters of the FG circular curved beams are investigated. The new results can be used as benchmark solutions for future research works.

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.

Free vibration and buckling analysis of elastically supported transversely inhomogeneous functionally graded nanoplate in thermal environment using Rayleigh–Ritz method

2020 ◽  
pp. 107754632096693
Author(s):  
Piyush P Singh ◽  
Mohammad S Azam
Keyword(s):  
Free Vibration ◽  
Thermal Environment ◽  
Ritz Method ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Small Scale ◽  
Pasternak Foundation ◽  
Differential Model ◽  
Aspect Ratios ◽  
Elastically Supported

In this study, free vibration and buckling behaviors of a functionally graded nanoplate supported by the Winkler–Pasternak foundation using a nonlocal classical plate theory are investigated. Eringen’s nonlocal differential model has been used for considering the small-scale effect. The properties of the functionally graded nanoplate are considered to vary transversely following the power law. The governing vibration and buckling equations of an elastically supported functionally graded nanoplate have been derived using the principle of virtual work, and the solution is obtained using the Rayleigh–Ritz method and characteristic polynomials. The advantage of this method is that it disposes of all the drawbacks regarding edge constraints. The objective of the article is to see the effect of edge constraints, aspect ratios, material property exponent, nonlocal parameter, and foundation parameters on the nondimensionalized frequency and the buckling load of an embedded functionally graded nanoplate in a thermal environment. The study highlights that the nonlocal effect is pronounced for higher modes and/or higher aspect ratios and need to be considered for the analysis of the nanoplate. Further, it is observed that the effect of the Pasternak foundation is prominent on nondimensionalized frequencies and buckling of the functionally graded nanoplate.

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