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

Mitseas, Ioannis P.; Beer, Michael

doi:10.1016/j.ymssp.2019.05.056

Cited by 20 publications

(9 citation statements)

References 35 publications

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“…The stochastic component x s (t) of the system response is treated by resorting to the generalized statistical linearization methodology for systems with singular parameter matrices [12,13]; see also [16,17,18,19,20,21,22,23] for a broader perspective, as well as several examples pertaining to application of the method. First, the difference between the systems in Eqs.…”

Section: Application Of the Statistical Linearization Methods For Treating The Stochastic Component Of The Responsementioning

confidence: 99%

Stochastic Nonlinear Response of Structural Systems Endowed With Singular Matrices Subject to Combined Periodic and Stochastic Excitations

Ni¹,

Fragkoulis²,

Kong³

et al. 2021

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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A new technique is proposed for determining the response of multi-degree-of-freedom nonlinear complex multi-body systems with singular parameter matrices subject to combined periodic and stochastic loads. The singular parameter matrices are due to adopting redundant coordinates for modeling the system governing equations of motion. Considering that the system response has a periodic as well as a stochastic component, a harmonic balance methodbased scheme is used for treating the deterministic component, followed by the application of the generalized statistical linearization method, in conjunction with an averaging treatment to account for the stochastic component. The validity of the proposed technique is demonstrated by pertinent numerical examples.

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Section: Application Of the Statistical Linearization Methods For Treating The Stochastic Component Of The Responsementioning

confidence: 99%

Stochastic Nonlinear Response of Structural Systems Endowed With Singular Matrices Subject to Combined Periodic and Stochastic Excitations

Ni¹,

Fragkoulis²,

Kong³

et al. 2021

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

Self Cite

View full text Add to dashboard Cite

show abstract

“…For a more detailed presentation as well as pertinent commentary on the topic the interested reader may resort to the works (e.g. [13,14]). The nonlinear stochastic dynamics technique unfolded in the following subsections is independent from the herein presented approach which only works as a necessary stepping stone allowing for the generation of power spectra characterizing the underlying codecompliant stochastic processes corresponding to the strong part of the imposed seismic excitation.…”

Section: Power Spectra Derivation For the Response Spectrum Compatiblmentioning

confidence: 99%

“…The Gaussian assumption which finds application in a number of studies in the earthquake engineering field (e.g. [2,14,15]) constitutes a stepping stone for the development of the herein proposed nonlinear stochastic dynamics methodology. Relying on the standard assumption that the response processes are Gaussian, and following statistical linearization (e.g.…”

Section: Statistical Linearization For Nonlinear Systems Under Stochamentioning

confidence: 99%

“…4(b), constitutes a commonly employed model to capture the hysteretic behavior of structural systems under seismic excitation (e.g. [14,20,21]). The governing equation of motion for a bilinear hysteretic oscillator can be expressed with the aid of an auxiliary state (e.g.…”

Section: Statistical Linearization For Nonlinear Systems Under Stochamentioning

confidence: 99%

“…It can be readily seen that Eqs. (12)(13)(14) and Eqs. (17-18) constitute a coupled nonlinear system of algebraic equations to be solved iteratively for the system ELPs determination.…”

Section: Statistical Linearization For Nonlinear Systems Under Stochamentioning

confidence: 99%

See 2 more Smart Citations

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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Probabilistic generation of hazard‐consistent suites of fully non‐stationary seismic records

Yanni,

Fragiadakis,

Mitseas

2024

Earthq Engng Struct Dyn

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A novel, practical, and computationally efficient probabilistic methodology for the stochastic generation of suites of fully non‐stationary artificial accelerograms is presented. The proposed methodology ensures that the produced ground motion suites match a given target spectral mean and target variability for the whole period range of interest. This is achieved by first producing an ensemble of random target spectra with the given mean and variability and then using them to generate artificial, target spectrum‐compatible, acceleration time‐histories with spectral representation techniques. Spectral correlation can also be assumed for the generated ground motion spectra. Based on the same backbone, two different formulations are proposed for generating spectrum‐compatible acceleration time‐histories of the non‐stationary kind. The distinction between these two variants lies in the techniques employed for modeling the temporal and spectral modulation, focusing on the site‐compatibility of the produced records. The first approach uses past‐recorded seismic accelerograms as seed records, and the second proposes and uses a new, probabilistic time‐frequency modulating function. The outcome of the proposed methodology is suites containing site‐compatible ground motion time‐histories whose spectral mean and variability match those obtained from any of the usually employed target spectra used in the earthquake engineering practice. An online tool implementing the proposed methodology is also freely provided.

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

Abstract: This is a repository copy of Modal decomposition method for response spectrum based analysis of nonlinear and non-classically damped systems.

Cited by 20 publications

References 35 publications

Stochastic Nonlinear Response of Structural Systems Endowed With Singular Matrices Subject to Combined Periodic and Stochastic Excitations

Stochastic Nonlinear Response of Structural Systems Endowed With Singular Matrices Subject to Combined Periodic and Stochastic Excitations

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

Probabilistic generation of hazard‐consistent suites of fully non‐stationary seismic records

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