A numerical method for free vibration analysis of beams

Prokić, Aleksandar; Bešević, Miroslav; Lukić, Dragan

doi:10.1590/s1679-78252014000800009

Cited by 13 publications

(8 citation statements)

References 23 publications

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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%

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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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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

View full text Add to dashboard Cite

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“…The effect of the axial load on the natural frequencies is investigated as the rotational speed increases. At the same time, the numerical method for solution of the free vibration of Timoshenko beams with arbitrary boundary conditions is presented by Prokić et al (Prokić et al, 2014). Basically, the numerical method is based on numerical integration rather than the numerical differentiation.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Solution for Free Vibration of Elastically Restrained Timoshenko Beam on an Arbitrary Variable Winkler Foundation and Under Axial Load

Ghannadiasl

Mofid

2015

Lat. Am. j. solids struct.

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Natural frequencies are important dynamic characteristics of a structure where they are required for the forced vibration analysis and solution of resonant response. Therefore, the exact solution to free vibration of elastically restrained Timoshenko beam on an arbitrary variable elastic foundation using Green Function is presented in this paper. An accurate and direct modeling technique is introduced for modeling uniform Timoshenko beam with arbitrary boundary conditions. The applied method is based on the Green Function. Thus, the effect of the translational along with rotational support flexibilities, as well as, the elastic coefficient of Winkler foundation and other parameters are assessed. Finally, some numerical examples are shown to present the efficiency and simplicity of the Green Function in the new formulation.

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“…Fazelzadeh and Kazemi-Lari (2013) studied the stability of a cantilever beam resting on an elastic foundation under the action of a uniformly distributed tangential load. Prokic et al (2014) presented a numerical method for solution of the free vibration of beams governed by a set of second order ordinary differential equations. Sinir et al (2014) studied the exact solution of buckling and vibration response of post-buckling configurations of beams with non-classical boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Control of a Support Excitation Smart Beam Subjected to a Follower Force with Piezoelectric Sensors/Actuators

Azadi

Fazelzadeh

2015

Lat. Am. j. solids struct.

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In this paper, an active control is used to suppress the flutter vibration of a support excitation beam subjected to a follower force, using piezoelectric sensors/actuators. The beam is fixed to a motion support from one end and the other end is subjected to a follower force. The governing equations of motion are derived based on the generalized function theory and Lagrange-RayleighRitz technique, considering the Euler-Bernoulli beam theory. A robust Lyapunov based control scheme is applied to the system to suppress the induced flutter vibrations of the beam. The mathematical modeling of the beam with control algorithm is derived. Finally the system is simulated and the effects of the type of excitation, the magnitude of the follower force, instrument disturbances, and parameter uncertainties are studied. The simulation results show the applicability and robustness of the controller algorithm.

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A numerical method for free vibration analysis of beams

Cited by 13 publications

References 23 publications

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

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

An Analytical Solution for Free Vibration of Elastically Restrained Timoshenko Beam on an Arbitrary Variable Winkler Foundation and Under Axial Load

Control of a Support Excitation Smart Beam Subjected to a Follower Force with Piezoelectric Sensors/Actuators

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