Non-rotating beams isospectral to rotating Rayleigh beams

K, Srivatsa Bhat; Ganguli, Ranjan

doi:10.1016/j.ijmecsci.2018.04.049

Cited by 8 publications

(2 citation statements)

References 41 publications

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“…The Rayleigh beam theory has been relatively overshadowed by the Timoshenko beam theory [15][16][17][18][19][20], which can analyze the effect of shear deformation and rotatory inertia via vibration analysis of the structures. However, the Rayleigh beam theory is apparently superior to the Bernoulli-Euler beam theory in practical application, and research on vibration analysis using the Rayleigh beam theory is increasing [21][22][23][24][25][26][27][28]. In addition, the transfer matrix method such as the method developed in this study has not been studied yet.…”

Section: Introductionmentioning

confidence: 95%

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Free vibration analysis of tapered Rayleigh beams using the transfer matrix method

Lee

2020

J Braz. Soc. Mech. Sci. Eng.

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In this study, an exact transfer matrix method is developed to analyze the effect of rotatory inertia and tapering on the free vibration characteristics of tapered Rayleigh beams. The beam model developed addresses practical cross sections, including single-tapered and double-tapered beams. The governing differential equation is solved using the Frobenius method for power series solutions, and then, the transfer matrix is formulated to transform the state vectors defined from the displacements, bending moment, and shear force at the start and end points. To investigate the effect of rotatory inertia and taper ratio on the natural frequencies and mode shapes of beam structures, the length-to-height ratios of tapered beams with four classical boundary conditions and various taper ratios are examined. The accuracy of the developed method is demonstrated using the comparative results predicted in previous studies. Through a parametric study, the numerical results that are useful in practical applications are offered, and relevant conclusions not discussed in previous studies are proposed. Furthermore, the results discussed can serve as a benchmark solution.

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Section: Introductionmentioning

confidence: 95%

“…As shown in Fig. 1, the nondimensional length parameter x of a beam element is x = 0 and x = 1 at the start and end (24)…”

Section: Transfer Matrixmentioning

confidence: 99%

Free vibration analysis of tapered Rayleigh beams using the transfer matrix method

Lee

2020

J Braz. Soc. Mech. Sci. Eng.

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Free vibration analysis of a rotating double-tapered beam using the transfer matrix method

Lee

2020

J Mech Sci Technol

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Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam

Wang

Chen

2020

Chaos, Solitons & Fractals

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In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin-Voigt and fractional derivative element constitutive models, the two governing equations of fractional visco-elastic rotating beams are established. According to the approximation technique of shifted Chebyshev polynomials, the integer and fractional differential operator matrices of polynomials are derived. By means of the collocation method and matrix technique, the operator matrices of governing equations can be transformed into the algebraic equations. In addition, the convergence analysis is performed. In particular, unlike the existing results, we can get the displacement and the stress numerical solution of the governing equation directly in the time domain. Finally, the sensitivity of the algorithm is verified by numerical examples.

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Non-rotating beams isospectral to rotating Rayleigh beams

Cited by 8 publications

References 41 publications

Free vibration analysis of tapered Rayleigh beams using the transfer matrix method

Free vibration analysis of tapered Rayleigh beams using the transfer matrix method

Free vibration analysis of a rotating double-tapered beam using the transfer matrix method

Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam

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