Vibration Analysis of a Symmetric Double-Beam with an Elastic Middle Layer at Arbitrary Boundary Conditions

Abdulsahib, Imad A.; Atiyah, Qasim A.

doi:10.18280/mmep.090433

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…An elastic layer between them having the elastic stiffness (Ke) connects these beams. The Bernoulli-Euler beam theory for vibrations is utilized to relate the equations of motion [12,13]:…”

Section: Theoretical Workmentioning

confidence: 99%

“…Vertical translation and rotation elastic restrictions were applied to the ends of the double-beam. Abdulsahib and Atiyah [12] studied the effect of non-linear elasticity on the frequency of sandwich beams under arbitrary boundary conditions. The impact of the inner layer's non-linearity stiffness on those frequencies was calculated using the energy balancing approach.…”

Section: Introductionmentioning

confidence: 99%

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The Behavior of the Synchronous and Asynchronous Natural Frequencies for Asymmetric Double Beams

Atiyah¹,

Abdulsahib²

2022

MMEP

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The effect of vibrations on asymmetric double beams is a common engineering problem in various engineering applications. In this paper, the synchronous (lower) and asynchronous (higher) natural frequencies of the asymmetric double beams are calculated using the Bernoulli-Euler method. Where the traditional methods are used to find the frequency equations at different boundary conditions, such as Pinned beam, clamped-Clamped beam, Clamped-Free beam, and Clamped-Pinned beam. The increase in the stiffness of the elastic connected layer leads to an increase in the values of the high frequencies of double beams. The greatest effect of changing the thickness of one of the upper or lower beams is for CF beams and the least effect is for CP beams. The length of the beam affects the higher and lower frequencies in high and close proportions for almost all types of beams, and the least effect is only on the higher frequencies of CF beams. The influence of the modulus elasticity change is relatively small on the lower natural frequencies of all types of beams except for CF beams, and its effect is relatively large on the higher natural frequencies of the most types of beams and comparatively less on the CF beams. The effect of varying the values of mass density is relatively small on the low natural frequencies of all types of beams except for CF beams, and its effect is comparatively large on the higher natural frequencies of all types of beams and relatively less on the CF beams.

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“…An elastic layer between them having the elastic stiffness (Ke) connects these beams. The Bernoulli-Euler beam theory for vibrations is utilized to relate the equations of motion [12,13]:…”

Section: Theoretical Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Behavior of the Synchronous and Asynchronous Natural Frequencies for Asymmetric Double Beams

Atiyah¹,

Abdulsahib²

2022

MMEP

View full text Add to dashboard Cite

show abstract

“…Using ABAQUS software, He [11] numerically studied the dynamic reaction of a single thin rectangular plate, and the results were compared experimentally. Abdulsahib and Atiyah [12] have examined the vibration of double beams using an elastic connecting layer. The beam has been considered to be a Bernoulli-Euler beam.…”

Section: Introductionmentioning

confidence: 99%

Effect of the Cross-Sectional Shape on the Dynamic Response of a Cantilever Steel Beam Using Three Modal Analysis Methods

Abdulrazzaq,

Ali,

Sultan

et al. 2024

MMEP

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The main method for determining the vibration characteristics of engineering constructions is modal analysis. It's a way of analyzing a system's mode shapes, natural frequencies, and damping factor. The dynamic response of cantilever beams is determined in this work with different cross-sectional shapes to find the effect of eccentricity on the dynamic response of the cantilever beam. The main goal of this research is to find and detect the natural frequencies and mode shapes of a Structural Steel cantilever beam with different eccentricities and to identify flexural or torsional natural frequencies, as well as their mode shapes that could be confused with transverse natural frequencies, and to compare the results with analytical and experimental methodologies. Results showed that torsional natural frequencies remained within the transverse natural frequency. It can be shown that, the increase of eccentricity in the cross section decreases the natural frequencies and especially the torsional natural frequencies. The results were compared experimentally and numerically using ANSYS 16.1 software. There is a strong link between the mathematical, FEA, and experimental results. The latest results can be used to calculate failure loads in a variety of situations. The mathematical application of Euler's Bernoulli's beam concept was applied. The results of the three ways have been declared satisfactory.

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Compressive forces influence on the vibrations of double beams

Atiyah

Abdulsahib

2023

Open Engineering

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The influence of compressive forces on the lower and upper natural frequencies of the double beams has been studied in this article. Euler–Bernoulli’s hypotheses have been used to derive the natural frequency equations. Two asymmetric beams were assumed in this work, and four different boundary conditions were applied in these equations: Pinned–Pinned, Clamped–Clamped, Clamped–Free, and Clamped–Pinned. When the axial compressive force is increased about 18 times, it is observed that the lower natural frequencies decreased by 19% for PP beam, 8% for CC beam, 81% for CF beam, and 12% for CP beam. However, the greatest effect of the axial force on the higher frequencies is by reducing it in the CC beam by a ratio that does not exceed 2%. A rise in the values of axial compressive force causes a reduction in the lower natural frequencies, mostly for the CF beam, while it has a little effect on the higher natural frequencies. Similarly, when the compressive forces on the upper and lower beams fluctuate simultaneously, their effect is doubled on the frequencies when the axial compressive force on one of the two beams changes only.

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Vibration Analysis of a Symmetric Double-Beam with an Elastic Middle Layer at Arbitrary Boundary Conditions

Cited by 3 publications

References 8 publications

The Behavior of the Synchronous and Asynchronous Natural Frequencies for Asymmetric Double Beams

The Behavior of the Synchronous and Asynchronous Natural Frequencies for Asymmetric Double Beams

Effect of the Cross-Sectional Shape on the Dynamic Response of a Cantilever Steel Beam Using Three Modal Analysis Methods

Compressive forces influence on the vibrations of double beams

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