Free vibration analysis of Timoshenko beams by DSC method

Cívalek, Ömer; Kiracioglu, Okyay

doi:10.1002/cnm.1279

Cited by 86 publications

(56 citation statements)

References 69 publications

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“…With regard to numerical simulation, various methods have been proposed for the simulation of the Timoshenko beam equations. These range from the finite element methods mentioned above [7,8,9,10,11,12,13,14,15], to reduced-order methods (Galerkin [16] and modal methods [17]), to pseudospectral methods [18] and specialised methods such as Discrete Singular Convolution [19]. Most of the work cited above deals with the problem of calculating the first few eigenfrequencies of the Timoshenko system, for engineering purposes.…”

Section: Introductionmentioning

confidence: 99%

Conservative finite difference time domain schemes for the prestressed Timoshenko, shear and Euler–Bernoulli beam equations

Ducceschi

Bilbao

2019

Wave Motion

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This paper presents a number of finite difference time domain (FDTD) schemes to simulate the vibration of prestressed beams to various degrees of accuracy. The Timoshenko, shear and Euler-Bernoulli models are investigated, with a focus on the numerical modelling for the Timoshenko system. The conservation of a discrete Hamiltonian to machine accuracy ensures stability and convergence of the numerical schemes. The difference equations are in the form of theta schemes, which depend on a number of free parameters that can be tuned in order to reduce numerical dispersion. Although the schemes are built by means of second-order accurate finite difference operators only, fully fourth-order accurate schemes may be designed through modified equation techniques, and wideband-accurate schemes are also possible. The latter are schemes designed to maximise the resolving power at all wavelengths. Investigation of beams of cross section varying from from slender to thick allows a thorough comparison between the various schemes, for the three beam models.

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Section: Introductionmentioning

confidence: 99%

Conservative finite difference time domain schemes for the prestressed Timoshenko, shear and Euler–Bernoulli beam equations

Ducceschi

Bilbao

2019

Wave Motion

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“…However, the convenient methods of symmetric and anti-symmetric extension, successfully used for the treatment of simply supported, clamped and sliding boundary conditions in beams and plates [12,13], cannot be directly employed for the free boundary conditions in Timoshenko beams. This is the reason why the free boundary was not considered in a very recent paper on free vibration of Timoshenko beams [26]. To overcome this difficulty, a slight modification, proposed earlier by present authors [27], is made on the existing method of the symmetric extension to eliminate the degrees of freedom ðmÞ at fictitious points outside the left and right boundary for the case of a free-free Timoshenko beam, namely, …”

Section: The Dsc and Solution Proceduresmentioning

confidence: 96%

“…(26) and (27) are necessary only for the displacement v by considerations of the first free boundary condition of Eq. (8), i.e., u 0 À v 0…”

Section: The Dsc and Solution Proceduresmentioning

confidence: 99%

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The discrete singular convolution for analyses of elastic wave propagations in one-dimensional structures

Wang

2010

Applied Mathematical Modelling

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a b s t r a c tIn this paper, the problem of wave propagations in one-dimensional (1D) structures is investigated for the first time by using the discrete singular convolution (DSC), a relatively new and promising numerical approach. For simplicity, the non-regularized Lagrange's delta sequence kernel is adopted in the DSC for most cases. For comparisons, the Regularized Shannon's delta kernel is also adopted in the DSC for two cases. Methods for applying the free boundary conditions, concentrated loads and concentrated masses are proposed and validated. Detailed formulations and solution procedures are given. Travelling waves in an isotropic aluminum bar and Timoshenko beam are studied. A high degree of accuracy in simulations by the DSC is observed. Numerical results are compared to those obtained from the spectral finite element (SFE) approach, proved a very efficient method in modeling elastic wave propagations. The comparison highlights the efficiency of the DSC in modeling elastic wave propagations. The present research extends the application range of the discrete singular convolution to problems of elastic wave propagations.

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“…Therefore, researchers have been focused on the vibration analysis of beam structures using different theories and several solution methods [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Functionally Graded Rayleigh Beam

Avcar¹,

Alwan²

2017

International Journal of Engineering &Amp; Applied Sciences

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In the present study, free vibration of Rayleigh beam composed of functionally graded materials (FGMs) is investigated. For this purpose, the equation of the motion of functionally graded (FG) beam derived according to Rayleigh beam theory. The material properties are assumed to vary continuously through the thickness of the beam according to the power-law form. Resulting equations are solved for simply supported boundary conditions. In order to validate the results, a comparison is carried out with available results for homogeneous beam. The effects of varying material properties on the dimensionless free vibration frequency parameters are examined. It is seen that varying material properties have significant effects on dimensionless free vibration frequency parameters of FG Rayleigh beam

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Free vibration analysis of Timoshenko beams by DSC method

Cited by 86 publications

References 69 publications

Conservative finite difference time domain schemes for the prestressed Timoshenko, shear and Euler–Bernoulli beam equations

Conservative finite difference time domain schemes for the prestressed Timoshenko, shear and Euler–Bernoulli beam equations

The discrete singular convolution for analyses of elastic wave propagations in one-dimensional structures

Free Vibration of Functionally Graded Rayleigh Beam

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