Random vibration of linear and nonlinear structural systems with singular matrices: A frequency domain approach

Kougioumtzoglou, Ioannis A.; Fragkoulis, Vasileios C.; Pantelous, Athanasios A.; Pirrotta, Antonina

doi:10.1016/j.jsv.2017.05.038

Cited by 37 publications

(27 citation statements)

References 23 publications

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“…In this setting, a simple iterative while-loop is sufficient to simultaneously satisfy the system equations until convergence of the equivalent linear parameters is achieved within a pre-specified tolerance (e.g. [2,26]).…”

Section: Statistical Linearization For Nonlinear Systems Under Stochamentioning

confidence: 99%

“…Relying on the Markovian assumption for the process the joint oscillatory response amplitude PDF is provided as Next, considering and manipulating Eqs. (26)(27)(28) yields the following expression for the joint response system amplitude PDF which is identified as an essential prerequisite in the process of defining the limit-state firstexcursion probability provided in the following subsection.…”

Section: Marginal Transition and Joint Nonlinear System Response Ampmentioning

confidence: 99%

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First-excursion stochastic incremental dynamics methodology for hysteretic structural systems subject to seismic excitation

Mitseas

Beer

2021

Computers & Structures

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A novel efficient stochastic incremental dynamics methodology considering first-excursion probability for nonlinear structural systems subject to stochastic seismic excitations in alignment with contemporary aseismic codes provisions is developed. To this aim, an approximate nonlinear stochastic dynamics technique for conducting first-passage probability density function (PDF) based stochastic incremental dynamic analysis is developed. Firstly, an efficient stochastic iterative linearization methodology is devised achieving convergence of the equivalent system damping ratios with the damping premises of the excitation response spectrum leading to a coherent determination of a robust scalable intensity measure (IM) which bears direct relation to its damaging potential. Subsequently, utilizing the stochastically derived time-varying forced vibrational system properties in conjunction with a combination of deterministic and stochastic averaging treatment the first-excursion PDF is efficiently determined for each and every of the considered limit-state rules (LSs). Lastly, an incremental mechanization analogous to the one used in normal incremental dynamic analysis (IDA) is proposed to ensure the necessary compatibility for applications in the fields of structural and earthquake engineering. The back-and-forth twisting pattern of IDA curves which is related with the multiple points satisfaction of the very same limit-state rule encourages the study of the problem from a first-passage perspective considering timing in addition to the intensity of the excitation variable. The selected engineering demand parameter (EDP) of the firstexcursion time constitutes an excellent response related variable with twofold meaning; it performs structural behavior monitoring considering intensity and timing information whereas it is inherently coupled with limit-state requirements. The developed stochastic dynamics technique provides with reliable higher order statistics (i.e., PDF) of the chosen EDP. A structural system comprising the bilinear hysteretic model serves as a numerical example for demonstrating the reliability of the proposed first-excursion PDF-based stochastic incremental dynamics methodology. Nonlinear response time-history analysis involving a large ensemble of Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed methodology in a Monte Carlo-based context.

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Section: Statistical Linearization For Nonlinear Systems Under Stochamentioning

confidence: 99%

Section: Marginal Transition and Joint Nonlinear System Response Ampmentioning

confidence: 99%

First-excursion stochastic incremental dynamics methodology for hysteretic structural systems subject to seismic excitation

Mitseas

Beer

2021

Computers & Structures

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“…(13)(14)(15)(16)(17)(18) until convergence of the elements of and matrices is achieved within a pre-specified tolerance (e.g. [19,25]). The iterations are initialized by neglecting the and matrices in Eq.…”

Section: Statistical Linearization For Non-classically Damped Nonlinementioning

confidence: 99%

Modal decomposition method for response spectrum based analysis of nonlinear and non-classically damped systems

Mitseas

Beer

2019

Mechanical Systems and Signal Processing

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“…[14][15][16] or in combination of various advanced method of stochastic dynamics e.g. [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Non-linear dynamic response of a cable system with a tuned mass damper to stochastic base excitation via equivalent linearization technique

2020

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Non-linear dynamic model of a cable–mass system with a transverse tuned mass damper is considered. The system is moving in a vertical host structure therefore the cable length varies slowly over time. Under the time-dependent external loads the sway of host structure with low frequencies and high amplitudes can be observed. That yields the base excitation which in turn results in the excitation of a cable system. The original model is governed by a system of non-linear partial differential equations with corresponding boundary conditions defined in a slowly time-variant space domain. To discretise the continuous model the Galerkin method is used. The assumption of the analysis is that the lateral displacements of the cable are coupled with its longitudinal elastic stretching. This brings the quadratic couplings between the longitudinal and transverse modes and cubic nonlinear terms due to the couplings between the transverse modes. To mitigate the dynamic response of the cable in the resonance region the tuned mass damper is applied. The stochastic base excitation, assumed as a narrow-band process mean-square equivalent to the harmonic process, is idealized with the aid of two linear filters: one second-order and one first-order. To determine the stochastic response the equivalent linearization technique is used. Mean values and variances of particular random state variable have been calculated numerically under various operational conditions. The stochastic results have been compared with the deterministic response to a harmonic process base excitation.

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Random vibration of linear and nonlinear structural systems with singular matrices: A frequency domain approach

Cited by 37 publications

References 23 publications

First-excursion stochastic incremental dynamics methodology for hysteretic structural systems subject to seismic excitation

First-excursion stochastic incremental dynamics methodology for hysteretic structural systems subject to seismic excitation

Modal decomposition method for response spectrum based analysis of nonlinear and non-classically damped systems

Non-linear dynamic response of a cable system with a tuned mass damper to stochastic base excitation via equivalent linearization technique

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