Application of Differential Transform Method to Free Vibration of Gabled Frames with Rotational Springs

Rezaiee‐Pajand, Mohammad; Sani, Ali Mohamadi; Hozhabrossadati, Seyed Mojtaba

doi:10.1142/s0219455417500122

Cited by 12 publications

(5 citation statements)

References 35 publications

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“…Reference [39] applied the differential transform method and Fourier transform to solve for the natural frequencies when analyzing the free vibrations of a portal frame that was assumed to be a special case gabled frame. The method was verified by comparing the results obtained, to those of portal frames from existing literature, as well as FEM.…”

Section: B Differential Transform Methodsmentioning

confidence: 99%

A Review of the Vibration Analysis Methods for Frame Structures

2022

BSETN-22 &Amp; L2hs2-22 Sept. 12-14, 2022 Budapest (Hungary)

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Frames are basic structural components that appear in civil engineering applications, as well as chemical, mechanical and aerospace fields. With the size and complexity of modern-day structures and machinery increasing, frames are now required to withstand much larger cyclic loads. This article attempts to review some of the literature from the past twenty-one years, on how researchers analysed the vibrations in structural frames. This review also places emphasis on the methods used to analyse frames with semi-rigid connections, due to their impact on structural response. The theories used by authors to model beam and column elements, along with the methods used to solve the equations of motion are covered. Sections outlining the vibration and damage monitoring methods are also presented in this article. Other sections cover the research into soil structure interactions, the use of shape memory alloys (SMAs) and piezoelectric devices, as well as physical experiments that were conducted.

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Section: B Differential Transform Methodsmentioning

confidence: 99%

A Review of the Vibration Analysis Methods for Frame Structures

2022

BSETN-22 &Amp; L2hs2-22 Sept. 12-14, 2022 Budapest (Hungary)

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“…Note that, in Table 3, the frequency coefficients obtained in [21] under the assumption of ignored effect of axial deformations are also shown. Based on the determined frequency coefficients and using the truncation at the fifth term in the displacement series (124) and (125), the transverse and axial displacements at the middle of the beam segment (BS 4) are shown in Fig.…”

Section: Example 4: Planar Gabled Frame With Four Membersmentioning

confidence: 99%

Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments

Tomović

Šalinić

Obradović

et al. 2020

Applied Mathematical Modelling

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“…Solution of the algebraic equations in the usual way leads to accurate results with fast convergence rate and small computational effort. Several problems in vibration analysis of the continuous system are studied by employing the DTM [38][39][40][41][42]. More information about this method could be found in [43,44].…”

Section: Semi-analytical Solution Using Dtmmentioning

confidence: 99%

Explicit formula to estimate natural frequencies of a double-beam system with crack

Mirzabeigy

Madoliat

Surace

2019

J Braz. Soc. Mech. Sci. Eng.

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In the present study, an analytical formula to estimate natural frequencies of a simply supported double-beam system in the presence of open crack is derived. Euler-Bernoulli hypothesis was applied to beams, and Winkler model was used for inner layer. Material properties and cross section geometry of beams could be arbitrary and different from each other. To obtain natural frequencies, Eigenvalue problem solving finally yields an algebraic equation which must be solved numerically and does not show effects of different damage parameters in the explicit form. In this regard, Rayleigh method was applied to derive explicit formulation for natural frequencies. In the case of crack occurrence, the mode shapes of intact beam were modified by adding cubic polynomial functions to represent crack effect. The unknown coefficients of polynomial functions were calculated by using boundary conditions of the system and compatibility conditions at the crack section. Using the obtained admissible functions and Rayleigh method, an explicit formulation was achieved for natural frequencies. The problem one more time was solved using the differential transform method to approve the accuracy of the analytical formulation for the cracked double-beam system. Comparison of analytical and numerical results indicates good accuracy of derived formulation for natural frequencies of the cracked double-beam system.

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Application of Differential Transform Method to Free Vibration of Gabled Frames with Rotational Springs

Cited by 12 publications

References 35 publications

A Review of the Vibration Analysis Methods for Frame Structures

A Review of the Vibration Analysis Methods for Frame Structures

Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments

Explicit formula to estimate natural frequencies of a double-beam system with crack

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