The dynamic stiffness matrix (DSM) of axially loaded multi-cracked frames

Caddemi, S.; Caliò, Ivo; Cannizzaro, Francesco

doi:10.1016/j.mechrescom.2017.06.012

Cited by 20 publications

(9 citation statements)

References 47 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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“…The dynamic stiffness matrix (DSM) method (Clough and Penzien, 1975; Oliveto, 1992) with the well-established W-W algorithm (Williams and Wittrick, 1970, 1983; Banerjee and Williams, 1985; Banerjee and Williams, 1996; Banerjee, 2003; Banerjee et al., 2008; Williams and Kennedy, 2010) is another classic method to solve the exact modes of multi-crack Euler–Bernoulli beams. The method has been successfully applied to complex structures besides multi-crack beams, like frames with multiple cracks (Caddemi and Caliò, 2013; Labib et al., 2014; Caddemi et al., 2017). Compared to the enhanced SEM that directly solves natural frequencies by finding zero-crossings, the W-W algorithm is an indirect method that calculates the number of natural frequencies that are below a given trial frequency value.…”

Section: High-order Modes Evaluationmentioning

confidence: 99%

Evaluation of high-order modes and damage effects of multi-crack beams using enhanced spectral element method

Cao

Bai

et al. 2018

Journal of Vibration and Control

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Exact evaluation of high-order modes of a multi-crack Euler–Bernoulli beam using the conventional spectral element method (SEM) suffers from the deficiency of numerical ill-conditioning, mainly due to round-off errors in floating-point computations involved in evaluating the spectral element stiffness matrix, therefore, the modeling of the multiple cracks intensively increases the complexity of the matrix. To address this limitation, an enhanced SEM with the spectral element stiffness matrix constructed in a set of local coordinate systems is developed. With the method, two sets of local coordinate systems are created to derive two types of spectral element stiffness matrices for a multi-crack beam. The proposed spectral element stiffness matrices are of improved capacities to characterize the high-order modes of a multi-crack beam by largely eliminating the round-off errors involved in the conventional SEM. Moreover, the function of evaluating high-order modes endows the enhanced SEM with distinctive capability to reveal the effect of multiple cracks on the modal property of a multi-crack beam. The effectiveness of the proposed method in evaluating high-order modes and revealing the effects of multiple cracks on the modal property of a beam is investigated on various damage cases.

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“…In a linear setting, this is represented by a matrix, originally introduced by Dimarag-onas and co-workers [8,9,10,11,3,12,13,14,14,15,16]. As for later studies, without pretending to be exhaustive, we may quote [17,18,19,20,21,22]. We may refer the interested readers to the early review article by Doebling et al [1] and to the recent review by Hou and Xia [23].…”

Section: Introductionmentioning

confidence: 99%