Exact frequency response of two-node coupled bending-torsional beam element with attachments

Burlon, Andrea; Failla, Giuseppe; Arena, Felice

doi:10.1016/j.apm.2018.06.047

Cited by 12 publications

(11 citation statements)

References 46 publications

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“…The key is to demonstrate that the TMD acts an external support with a pertinent equivalent stiffness. This paves the way to obtain closed analytical expressions for frequency and impulse response functions of the system, using the theory of generalized functions [24][25][26][27][28][29][30][31][32][33][34][35]. The expressions can be used to construct analytical/numerical solutions under stationary and non-stationary loads in a straightforward manner, for any number of TMDs.…”

Section: Several Studies Have Sought Analytical or Numerical Solutionmentioning

confidence: 99%

“…The calculation will be pursued generalizing the approach recently proposed by some of the authors in ref. [9,30,32], in both frequency and time domains. Remarkably, the approach will provide the responses along the beam and in every TMD, as explained in the following.…”

Section: Analytical Solutions In Frequency and Timementioning

confidence: 99%

“…Finally, based on ref. [9,32] (27) where n is the number of modes retained in the modal representation of the response.…”

Section: Modal Response Functionsmentioning

confidence: 99%

“…The starting point are the following orthogonality conditions for the deflection modes , kn VV, derived following the approach in ref. [9,32]  …”

Section: Appendix Bmentioning

confidence: 99%

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Random vibration mitigation of beams via tuned mass dampers with spring inertia effects

et al. 2019

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The dynamics of beams equipped with tuned mass dampers is of considerable interest in engineering applications. Here, the purpose is to introduce a comprehensive framework to address the stochastic response of the system under stationary and nonstationary loads, considering inertia effects along the spring of every tuned mass damper applied to the beam. For this, the key step is to show that a tuned mass damper with spring inertia effects can be reverted to an equivalent external support, whose reaction force on the beam depends only on the deflection of the attachment point. On this basis, a generalized function approach provides closed analytical expressions for frequency and impulse response functions of the system. The expressions can be used for a straightforward calculation of the stochastic response, for any number of tuned mass dampers. Numerical results show that spring inertia effects may play an important role in applications, affecting considerably the system response.

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Section: Several Studies Have Sought Analytical or Numerical Solutionmentioning

confidence: 99%

Section: Analytical Solutions In Frequency and Timementioning

confidence: 99%

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Random vibration mitigation of beams via tuned mass dampers with spring inertia effects

et al. 2019

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“…The method relies on the theory of generalized functions to handle the discontinuities of the response variables, within a standard 1D formulation of the equation of motion. In another work, Burlon et al [9] presented an exact frequency response of two-node coupled bending-torsional beam element with attachments. Karakas and Gürgöze [10] extended the work in [3] in which the receptance matrix was obtained directly without using the iterations as presented in [3] to form the receptance matrix of non-proportionally damped dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and experimental analysis of the exact receptance function of a clamped-clamped beam with concentrated masses

Khoa

Thao

2020

Vietnam J. Mech.

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This paper establishes the exact receptance function of a clamped-clamped beam carrying concentrated masses. In this paper, the derivation of exact receptance and numerical simulations are provided. The proposed receptance function is convenient to apply for predicting the dynamic response at arbitrary point of the beam acted by a harmonic force applied at arbitrary point. The influence of the concentrated masses on the receptance is investigated. The numerical simulations show that a peak in the receptance decreases when there is a mass located close to that peak position. The numerical results have been compared to the experimental results has to justify the theory.

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A novel statistical linearization solution for randomly excited coupled bending-torsional beams resting on non-linear supports

2019

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Exact frequency response of two-node coupled bending-torsional beam element with attachments

Cited by 12 publications

References 46 publications

Random vibration mitigation of beams via tuned mass dampers with spring inertia effects

Random vibration mitigation of beams via tuned mass dampers with spring inertia effects

Theoretical and experimental analysis of the exact receptance function of a clamped-clamped beam with concentrated masses

A novel statistical linearization solution for randomly excited coupled bending-torsional beams resting on non-linear supports

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