A new analytical approach for determination of flexural, axial and torsional natural frequencies of beams

Mohammadnejad, M.

doi:10.12989/sem.2015.55.3.655

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…The proposed method is formulated for beams with various boundary conditions and is applied to obtain the buckling load of the nonprismatic EBB. Mohammadnejad [36] applied the power series to approximate the natural frequencies of the nonuniform Rayleigh beam. The integral equations changed to a system of linear algebraic equations using the power series.…”

Section: Introductionmentioning

confidence: 99%

Free vibrations of non-uniform beams on a non-uniform Winkler foundation using the Laguerre collocation method

Ghannadiasl

Zamiri

Borhanifar

2020

J Braz. Soc. Mech. Sci. Eng.

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Natural frequencies and free vibration are important characteristics of beams with non-uniform cross section. Hence, the solution for free vibrations of non-uniform beams is presented using a Laguerre collocation method. The elastically restrained beam model is based on the Euler-Bernoulli theory. Also, the non-uniform beam is rested on a non-uniform foundation (Winkler type). The Laguerre collocation method is introduced for solving the differential equation. This approach reduces the governing differential equation to a system of algebraic equations, and finally, the problem is greatly simplified. Properties of Laguerre polynomials and the operational matrix of derivation are first presented. Eventually, the proposed method is applied for solving the governing differential equation subject to initial conditions, and the results are compared with other results from the literature.

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Section: Introductionmentioning

confidence: 99%

Free vibrations of non-uniform beams on a non-uniform Winkler foundation using the Laguerre collocation method

Ghannadiasl

Zamiri

Borhanifar

2020

J Braz. Soc. Mech. Sci. Eng.

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“…In this case, the stress distribution and displacement will be appreciably reduced. Other methods for analyzing framed-tube are presented by researchers such as Paulino (2010), Mahjub et al 2011, Kamgar and Rahgozar (2013), Rahgozar et al (2014), Malekinejad and Rahgozar (2014), Mohammadnejad (2015), Rahgozar et al (2015), Khajuai Rad et al (2017. A parametric dimensionless formula has been developed for flexural stiffness of high-rise buildings with the objective of optimization problem by Alavi et al (2017).…”

Section: Introductionmentioning

confidence: 99%

Static analysis of tall buildings based on Timoshenko beam theory

Davari

Malekinejad

Rahgozar

2019

Int J Adv Struct Eng

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In this paper, the continuum model, which is known as Kwan model, has been presented for the analysis of tall buildings that have been as an appropriate approximation of the overall behavior of the structure. Tall building was modeled as a cantilever beam and analyzed with the assumption of flexural behavior based on Euler-Bernoulli Beam Theory, then the displacement of floors was calculated. o consider the shear lag effects in the overall displacement of the structure, Timoshenko's beam model has been considered and related relations were extracted. The lateral displacement formulas obtained and calculated for the framed tube system modeled by Kwan's method. To verify the results, numerical models were created in software (ETABS) and statically were analyzed for lateral loading. Finally the results were compared with those obtained by computer analysis and the corresponding diagrams were presented. At the end, the shape factor formula has been developed to improve the results of the Timoshenko's theory.

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Free vibration analysis of axially functionally graded beams using Fredholm integral equations

Mohammadnejad

2022

Arch Appl Mech

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A new analytical approach for determination of flexural, axial and torsional natural frequencies of beams

Cited by 3 publications

References 18 publications

Free vibrations of non-uniform beams on a non-uniform Winkler foundation using the Laguerre collocation method

Free vibrations of non-uniform beams on a non-uniform Winkler foundation using the Laguerre collocation method

Static analysis of tall buildings based on Timoshenko beam theory

Free vibration analysis of axially functionally graded beams using Fredholm integral equations

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