An exact modal analysis approach to vibration analysis of structures with mass-spring subsystems and rotational joints

Failla, Giuseppe

doi:10.1016/j.jsv.2018.09.025

Cited by 21 publications

(10 citation statements)

References 48 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%

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%

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

et al. 2019

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“…In engineering design, however, analytical or semianalytical methods are more direct and effective for assessing the influences of parameters on the bending and vibration of discontinuous beams. Failla et al [21][22][23][24][25] presented a systematic study on the deformation and vibration of a Euler-Bernoulli discontinuous beam based on Green's functions, in which closed-form solutions were obtained. However, the effects of axial loads, shearing, and gyroscopic moments were not included in their work.…”

Section: Introductionmentioning

confidence: 99%

Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces

2020

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The transverse stiffness and vibration characteristics of discontinuous beams can significantly differ from those of continuous beams given that an abrupt change in stiffness may occur at the interface of the former. In this study, the equations for the deflection curve and vibration frequencies of a simply supported discontinuous beam under axial loads are derived analytically on the basis of boundary, continuity, and deformation compatibility conditions by using equivalent spring models. The equation for the deflection curve is solved using undetermined coefficient methods. The normal function of the transverse vibration equation is obtained by separating variables. The differential equations for the beam that consider moments of inertia, shearing effects, and gyroscopic moments are investigated using the transfer matrix method. The deflection and vibration frequencies of the discontinuous beam are studied under different axial loads and connection spring stiffness. Results show that deflection decreases and vibration frequencies increase exponentially with increasing connection spring stiffness. Moreover, both variables remain steady when connection spring stiffness reaches a considerable value. Lastly, an experimental study is conducted to investigate the vibration characteristics of a discontinuous beam with a curvic coupling, and the results exhibit a good match with the proposed model.

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“…The discontinuities are considered (as shown in Equation ( 14)) through the vector J x, x j which can be expanded as [37]:…”

Section: Eigensolutionmentioning

confidence: 99%

“…Considering the theory of separable variable, this can also take the following form in the time domain for an undamped system, which can be readily generalized for damped one [37,44]:…”

Section: Poissonian White Noise Processesmentioning

confidence: 99%

A Novel Solution to Find the Dynamic Response of an Euler–Bernoulli Beam Fitted with Intraspan TMDs under Poisson Type Loading

et al. 2020

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This contribution considers a virtual experiment on the vibrational response of rail and road bridges equipped with smart devices in the form of damping elements to mitigate vibrations. The internal damping of the bridge is considered a discontinuity that contain a dashpot. Exact complex eigenvalues and eigenfunctions are derived from a characteristic equation built as the determinant of a 4 × 4 matrix; this is accomplished through the use of the theory of generalized functions to find the response variables at the positions of the damping elements. To relate this to real world applications, the response of a bridge under Poisson type white noise is evaluated; this is similar to traffic loading that would be seen in a bridge’s service life. The contribution also discusses the importance of smart damping and dampers to sustainability efforts through the reduction of required materials, and it discusses the role played by robust mathematical modelling in the design phase.

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An exact modal analysis approach to vibration analysis of structures with mass-spring subsystems and rotational joints

Cited by 21 publications

References 48 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

Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces

A Novel Solution to Find the Dynamic Response of an Euler–Bernoulli Beam Fitted with Intraspan TMDs under Poisson Type Loading

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