Free Vibration Analysis of Beams Considering Different Geometric Characteristics and Boundary Conditions

Avcar, Mehmet

doi:10.5923/j.mechanics.20140403.03

Cited by 30 publications

(35 citation statements)

References 18 publications

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“…Because of the various difficulties in experimental studies, the researchers have tended to continuum mechanics approaches. However, the classical continuum models which are successful for modelling of macro-sized structural elements [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] fail to predict the mechanical behavior characteristics of small-sized structures. Consequently, several non-classical continuum theories have been developed such as couple stress theory [23][24][25], micropolar theory [26], nonlocal elasticity theory [27,28] and strain gradient theories [29][30][31][32] to determine the mechanical responses of such structures.…”

Section: Introductionmentioning

confidence: 99%

Effect of Rotary Inertia on Vibrational Response of Embedded Graphene Sheets

Akgöz¹

2016

International Journal of Engineering &Amp; Applied Sciences

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In the present study, influence of rotary inertia on the size-dependent free vibration analysis of embedded singlelayered graphene sheets is examined based on modified couple stress theory. Governing differential equations and corresponding boundary conditions in motion are derived by implementing Hamilton's principle on the basis of Kirchhoff thin plate theory. Also, effect of elastic foundation is taken into consideration by using a twoparameter elastic foundation model. Influences of additional material length scale parameter, mode number, elastic foundation and rotary inertia on the natural frequencies are investigated in detail.

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Section: Introductionmentioning

confidence: 99%

Effect of Rotary Inertia on Vibrational Response of Embedded Graphene Sheets

Akgöz¹

2016

International Journal of Engineering &Amp; Applied Sciences

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“…Substituting boundary conditions given in Eqs (11)(12)(13)(14) into Eq. (8) separately; and then after some mathematical operations, the frequency parameters of the beam, L    , are www.ijacsa.thesai.org obtained for the first ten modes.…”

Section: Mathematical Modelling Of the Problemmentioning

confidence: 99%

“…Vibration analyses of structural systems have been performed with the aid of different methods [6][7][8][9][10][11][12][13][14][15]. However, the complex shaped structures may be analyzed with soft computing techniques more easily.…”

Section: Introductionmentioning

confidence: 99%

An Artificial Neural Network Application for Estimation of Natural Frequencies of Beams

Avcar¹,

Saplioğlu²

2015

ijacsa

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Abstract-In this study, natural frequencies of the prismatical steel beams with various geometrical characteristics under the four different boundary conditions are determined using Artificial Neural Network (ANN) technique. In that way, an alternative efficient method is aimed to develop for the solution of the present problem, which provides avoiding loss of time for computing some necessary parameters. In this context, initially, first ten frequency parameters of the beam are found, where Bernoulli-Euler beam theory was adopted, and then natural frequencies are computed theoretically. With the aid of theoretically obtained results, the data sets are formed and ANN models are constructed. Here, 36 models are developed using primary 3 models. The results are found from these models by changing the number and properties of the neurons and input data. The handiness of the present models is examined by comparing the results of these models with theoretically obtained results. The effects of the number of neurons, input data and training function on the models are investigated. In addition, multiple regression models are developed with the data, and adjusted R-square is examined for determining the inefficient input parameters

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“…(2), the workpiece displacement can be expanded as [3] X w ðt; SÞ ¼ X n i¼1 X i ðtÞ sinhðk i LÞ À sinðk i LÞ cosðk i LÞ À coshðk i LÞ…”

Section: Dde Modelmentioning

confidence: 99%

Regenerative chatter in self-interrupted plunge grinding

Yan

Wiercigroch

2016

Meccanica

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This paper investigates dynamics of regenerative chatter in self-interrupted plunge grinding with delayed differential equations (DDEs) and partial differential equations (PDEs). The DDEBIF-TOOL, a numerical simulation tool and the method of multiple scales are used to analyse stability and construct bifurcation diagrams. It was found out that in majority of cases, chatter is accompanied by a loss of contact. The loss of contact leaves uncut surface during the pass of grinding wheels, and thus the regeneration mechanism does not play a role. In that case, the delay used to represent the time span between two successive cuts should be multiple (double, triple, quadruple or higher). As a consequence, the chatter with losing contact cannot be accurately described by the DDEs with a fixed time delay. To address this problem, the PDEs are introduced to record the variation of workpiece profile. The PDEs are transformed into the ODEs by a Galerkin projection, and then the grinding dynamics is studied numerically. Solutions obtained from the DDEs and the PDEs are in a good agreement for a continuous grinding but there is a discrepancy for a self-interrupted cutting.

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Free Vibration Analysis of Beams Considering Different Geometric Characteristics and Boundary Conditions

Cited by 30 publications

References 18 publications

Effect of Rotary Inertia on Vibrational Response of Embedded Graphene Sheets

Effect of Rotary Inertia on Vibrational Response of Embedded Graphene Sheets

An Artificial Neural Network Application for Estimation of Natural Frequencies of Beams

Regenerative chatter in self-interrupted plunge grinding

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