Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions

Shahba, Ahmad; Attarnejad, Reza; Marvi, Morteza Tavanaie; Hajilar, Shahin

doi:10.1016/j.compositesb.2011.01.017

Cited by 254 publications

(124 citation statements)

References 28 publications

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“…The system of nonlinear equations (19) can be solved by an incremental/iterative procedure based on the Newton-Raphson method (Crisfield, 1991). In order to deal with complex situations, in which the structure tangent stiffness matrix ceases to be positive definite, the spherical arc-length constraint method proposed by Crisfield (1991) is adopted.…”

Section: Equilibrium Equationsmentioning

confidence: 99%

“…Fallah and Aghdam (2011) derived the nonlinear governing differential equation for geometrically nonlinear vibration and post-buckling analysis of FG beams resting on a nonlinear elastic foundation. Shahba et al (2011) employed the exact shape functions of a uniformed homogeneous Timoshenko beam segment to formulate a finite element formulation for computing natural frequencies and buckling loads of tapered Timoshenko beams made of axially FGM. Piovan et al (2012) developed a finite element model for the dynamic and buckling analyses of FG circular curved beams.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Large Deflection Analysis of Functionally Graded Beams Resting on a Two-Parameter Elastic Foundation

Gan

Kien

2014

Journal of Asian Architecture and Building Engineering

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This paper presents a finite element procedure for the large deflection analysis of functionally graded (FG) beams resting on a two-parameter elastic foundation. The material properties of the FG beams are assumed to vary continuously in the thickness direction by a power-law distribution. Based on the strain energy expression, a shear deformable beam element, taking the effect of the material non-homogeneity and the foundation support into account, is formulated and employed in the analysis. An incremental/iterative procedure in combination with the arc-length control method is used for solving nonlinear equilibrium equations. The numerical results show that the convergence of the formulated element is fast, and the large displacements of the beams can be accurately assessed by using a few numbers of the elements. A parametric study is carried out to highlight the effect of the material non-homogeneity and the foundation support on the large deflection behavior of the beams. The influence of the aspect ratio on the large deflection response of the beam is also examined and highlighted.

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Section: Equilibrium Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Large Deflection Analysis of Functionally Graded Beams Resting on a Two-Parameter Elastic Foundation

Gan

Kien

2014

Journal of Asian Architecture and Building Engineering

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“…Based on the modified couple-stress theory introduced by Yang et al (2002), Kong et al (2008) analytically calculated the size-dependent natural frequencies of Euler-Bernoulli beams. Shahba et al (2011) studied the free vibration and stability analysis of axially FG tapered Timoshenko beams using a finite element approach. There are also several numerical investigations about different aspects of vibration of tapered beams (see e.g., Cheng et al (2011);Saffari et al (2008); Bazoune et al (2001) among others).…”

Section: Introductionmentioning

confidence: 99%

Analytical Couple-stress Solution for Size-dependent Large-amplitude Vibrations of FG Tapered-nanobeams

Baghani

Mohammadsalehi

Dabaghian

2016

Lat. Am. j. solids struct.

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In this paper, analytical couple-stress solution for size-dependent large-amplitude vibrations of FG (functionally-graded) taperednanobeams is presented. Using the modified couple-stress theory, the small scale effects are accounted for. Employing the Homotopy-Pade Analysis Method, efficient and accurate analytical expressions for the deflection and non-linear frequencies of the both single and double tapered nanobeam are presented. Very good agreement is observed between the present work results and some available results reported in the literature. This study may be helpful to investigate the size-dependent mechanical properties of MEMS\NEMS. Therefore, the proposed analytical solution can be used as an efficient tool for the material or geometrical parametric studies of small scale devices consisting of beams for their design and optimization which involves a large number of simulations.

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“…Akgöz and Civalek [16] investigated vibration response of non-homogenous and non-uniform microbeams in conjunction with Bernoulli-Euler beam and modified couple stress theory. Shahba et al [17] carried out free vibration and stability analysis of axially functionally graded tapered Timoshenko beams. The authors employed finite element technique to analyze the effects of taper ratio, elastic constraint, attached mass and the material nonhomogeneity on the natural frequencies and critical buckling load.…”

Section: Introductionmentioning

confidence: 99%

Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

Lohar¹,

Mitra

Sahoo³

2016

IFSL

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Abstract.A displacement based semi-analytical method is utilized to study non-linear free vibration and mode shapes of an exponential tapered axially functionally graded (AFG) beam resting on an elastic foundation. In the present study geometric nonlinearity induced through large displacement is taken care of by non-linear strain-displacement relations. The beam is considered to be slender to neglect the rotary inertia and shear deformation effects. In the present paper at first the static problem is solved through an iterative scheme using a relaxation parameter and later on the subsequent dynamic analysis is carried out as a standard eigen value problem. Energy principles are used for the formulation of both the problems. The static problem is solved by using minimum potential energy principle whereas in case of dynamic problem Hamilton's principle is employed. The free vibrational frequencies are tabulated for exponential taper profile subject to various boundary conditions and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane and in some particular case the mode shape results are furnished.

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Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions

Cited by 254 publications

References 28 publications

Large Deflection Analysis of Functionally Graded Beams Resting on a Two-Parameter Elastic Foundation

Large Deflection Analysis of Functionally Graded Beams Resting on a Two-Parameter Elastic Foundation

Analytical Couple-stress Solution for Size-dependent Large-amplitude Vibrations of FG Tapered-nanobeams

Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

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