An Analytical Approach to Vibration Analysis of Beams with Variable Properties

Mohammadnejad, M.; Saffari, Hamed; Bagheripour, Mohammad Hossein

doi:10.1007/s13369-013-0898-1

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…Also, Yayli et al [52] investigated the free vibration of EBB rested on the elastic foundation using Stoke's transformation method (2014). Mohammadnejad et al [37] exhibited mode shape functions of the non-prismatic Timoshenko and of EBBs using power series. The proposed method is formulated for beams with various boundary conditions and is applied to obtain the buckling load of the nonprismatic EBB.…”

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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“…Zalka presented the closed‐form formulae for the torsional analysis of asymmetrical multistory buildings, braced by moment‐resisting frames, shear walls, and cores. Mohammadnejad et al and Saffari et al presented an analytical approach for determination of the vibration frequencies of nonprismatic Bernoulli and Timoshenko beams by converting the governing differential equation to its weak‐form integral equations. Lee developed an approximate solution procedure for free vibration analysis of tube‐in‐tube tall buildings using the power‐series solution method.…”

Section: Introductionmentioning

confidence: 99%

A new approach for free vibration analysis of nonuniform tall building structures with axial force effects

Ramezani

Mohammadizadeh

Shojaee

2019

Structural Design Tall Build

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Dynamic analysis of beam-like structures is significantly important in modeling actual cases such as tall buildings and several other related applications as well. This article studies free vibration analysis of tall buildings with nonuniform cross-section structures. A novel and simple approach is presented to solve natural frequencies of free vibration of cantilevered tall structures with variable flexural rigidity and mass densities. These systems could be replaced by a cantilever Timoshenko beam with varying cross-sections. The governing partial differential equation for vibration of a nonuniform Timoshenko beam under variable axial loads is transformed with varying coefficients to its weak form of integral equations. Natural frequencies can be determined by requiring the resulting integral equation, which has a nontrivial solution. The presented method in this study has fast convergence. Including high accuracy for the obtained numerical results as well. Numerical examples including framed tube as well as tube-in-tube structures are carried out in the study and compared with available results in the literature, and also with the results obtained from finite element analysis in order to show the accuracy of the proposed method in the study. Obtained results indicate that the presented method in this study is powerful enough for the free vibration analysis of tall buildings. KEYWORDS axial force, free vibration, nonuniform, tall building, Timoshenko beam, weak form integral equation 1 | INTRODUCTIONFree vibration analysis plays an important role in the structural design of tall buildings, especially for the first mode because the first mode shape is a dominant component in wind and earthquake-induced vibrations of tall buildings. Therefore, it is important to investigate the calculating methods of natural frequencies and mode shapes for tall buildings. Many researchers in structural engineering have devoted to obtain accurate theoretical results for the free vibration of tall buildings in the past decades. In free vibrations analysis of cantilevered tall structures, it is possible to regard them as beams with variable cross-section. [1,2] Wang [3] derived the closed-form solutions for the free flexural vibration of a beam with variably distributed stiffness, but uniform mass. Li et al. [1] and Li [4] studied the free flexural vibration of tall buildings as well as high-rise structures, which have variably distributed stiffness and mass. However, the effect of axial forces acting on the cantilevered structures with variable cross-section on natural frequencies and mode shapes was not considered. The subject of free vibration of nonuniform beams has been paid attention by many researchers. However, few of them have considered the effects of axial forces on beam vibration frequencies. Most of these studies include simplifications in calculation process such that the governing differential equation becomes manageable to solve. Li et al. [5] investigated free vibration of cantilevered tall structures under various ...

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Frequency and Deflection Responses of Shear Deformable Skew Sandwich Curved Shell Panel: A Finite Element Approach

Katariya

Panda

2018

Arab J Sci Eng

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An Analytical Approach to Vibration Analysis of Beams with Variable Properties

Cited by 6 publications

References 14 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

A new approach for free vibration analysis of nonuniform tall building structures with axial force effects

Frequency and Deflection Responses of Shear Deformable Skew Sandwich Curved Shell Panel: A Finite Element Approach

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