Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode

Lei, Wu; Wang, Qishen; Elishakoff, Isaac

doi:10.1016/j.jsv.2004.08.038

Cited by 74 publications

(28 citation statements)

References 8 publications

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“…Due to varying cross-sectional area, modulus of elasticity and mass density along the beam axis, the governing differential equations of axially FG tapered beams for transverse and longitudinal vibrations and buckling are differential equations with variable coefficients for which closed-form solutions could be hardly found or even impossible to obtain; hence application of numerical techniques is essential. Development of the technical literature on axially FG beams could be mostly tracked in the works written by Elishakoff and his co-workers [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]26,29,32,33] who used semi-inverse method for solution of the governing differential equations. Assuming a uniform beam with constant mass density, Aydogdu [27] used semi-inverse method to study the free transverse vibration and stability of axially FG simply supported beams.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams

Shahba

Attarnejad

Hajilar

2011

Shock and Vibration

103

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Structural analysis of axially functionally graded tapered Euler-Bernoulli beams is studied using finite element method. A beam element is proposed which takes advantage of the shape functions of homogeneous uniform beam elements. The effects of varying cross-sectional dimensions and mechanical properties of the functionally graded material are included in the evaluation of structural matrices. This method could be used for beam elements with any distributions of mass density and modulus of elasticity with arbitrarily varying cross-sectional area. Assuming polynomial distributions of modulus of elasticity and mass density, the competency of the element is examined in stability analysis, free longitudinal vibration and free transverse vibration of double tapered beams with different boundary conditions and the convergence rate of the element is then investigated.

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Section: Introductionmentioning

confidence: 99%

Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams

Shahba

Attarnejad

Hajilar

2011

Shock and Vibration

103

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“…For example, Wu et al (2005) applied the semi-inverse method to find solutions to the dynamic equation of axially functionally graded simply supported beams. Huang and Li (2010) studied free vibration of axially functionally graded beams by using the Fredholm integral equations.…”

Section: Introductionmentioning

confidence: 99%

An approach for free vibration analysis of axially graded beams

Kukla¹,

Rychlewska²

2016

jtam

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In this study, the solution to the free vibration problem of axially graded beams with a non-uniform cross-section has been presented. The proposed approach relies on replacing functions characterizing functionally graded beams by piecewise exponential functions. The frequency equation has been derived for axially graded beams divided into an arbitrary number of subintervals. Numerical examples show the influence of the parameters of the functionally graded beams on the free vibration frequencies for different boundary conditions.

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“…Less researchers have treated this kind of structures. Sarkar and Ganguli (2014), Shahba and Rajasekaran (2012) and Wu et al (2005) found the natural frequencies of axially FGM beams which stiffness and material density are polynomials functions. Li et al (2013) proposed exact frequency equations of free vibration of exponentially axially FG beams.…”

Section: Introductionmentioning

confidence: 99%

Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

Bruant

Proslier

2015

Int J Mech Mater Des

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Up to now, optimal location for active control studies concern principally multilayers or homogeneous structures. In the case of functionally graded materials, very few papers exist and they only concern cross section variations. In this way, this paper deals with the optimization of piezoelectric actuators locations on axially functionally graded beams for active vibration control. For this kind of structures, the free vibration problem is more complicated as the governing equations have variable coefficients. Here, the eigenproblem is solved using Fredholm integral equations. The optimal locations of actuators are determined using an optimization criterion, ensuring good controllability of each eigenmode of the structure. The linear quadratic regulator, including a state observer, is used for active control simulations. Two numerical examples are presented for two kinds of boundary conditions.

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Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode

Cited by 74 publications

References 8 publications

Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams

Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams

An approach for free vibration analysis of axially graded beams

Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

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