Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs
Random vibration analysis is a mathematical tool that offers great advantages in predicting the mechanical response of structural systems subjected to external dynamic loads whose nature is intrinsically stochastic, as in cases of sea waves, wind pressure, and vibrations due to road asperity. Using...
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MDPI AG
2024-03-01
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| author | M. Domaneschi R. Cucuzza L. Sardone S. Londoño Lopez M. Movahedi G. C. Marano |
| author_facet | M. Domaneschi R. Cucuzza L. Sardone S. Londoño Lopez M. Movahedi G. C. Marano |
| author_sort | M. Domaneschi |
| collection | DOAJ |
| description | Random vibration analysis is a mathematical tool that offers great advantages in predicting the mechanical response of structural systems subjected to external dynamic loads whose nature is intrinsically stochastic, as in cases of sea waves, wind pressure, and vibrations due to road asperity. Using random vibration analysis is possible, when the input is properly modeled as a stochastic process, to derive pieces of information about the structural response with a high quality (if compared with other tools), especially in terms of reliability prevision. Moreover, the random vibration approach is quite complex in cases of non-linearity cases, as well as for non-stationary inputs, as in cases of seismic events. For non-stationary inputs, the assessment of second-order spectral moments requires resolving the Lyapunov matrix differential equation. In this research, a numerical procedure is proposed, providing an expression of response in the state-space that, to our best knowledge, has not yet been presented in the literature, by using a formal justification in accordance with earthquake input modeled as a modulated white noise with evolutive parameters. The computational efforts are reduced by considering the symmetry feature of the covariance matrix. The adopted approach is applied to analyze a multi-story building, aiming to determine the reliability related to the maximum inter-story displacement surpassing a specified acceptable threshold. The building is presumed to experience seismic input characterized by a non-stationary process in both amplitude and frequency, utilizing a general Kanai–Tajimi earthquake input stationary model. The adopted case study is modeled in the form of a multi-degree-of-freedom plane shear frame system. |
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| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-04-24T18:26:02Z |
| publishDate | 2024-03-01 |
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| spelling | doaj.art-c1535e6cb6ac44bbaf8610de80579c182024-03-27T13:31:55ZengMDPI AGComputation2079-31972024-03-011235010.3390/computation12030050Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random InputsM. Domaneschi0R. Cucuzza1L. Sardone2S. Londoño Lopez3M. Movahedi4G. C. Marano5Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Turin, ItalyDepartment of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Turin, ItalyDepartment of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Turin, ItalyDepartment of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Turin, ItalyDepartment of Structural and Geotechnical Engineering, Széchenyi István University, Győr, HungaryDepartment of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Turin, ItalyRandom vibration analysis is a mathematical tool that offers great advantages in predicting the mechanical response of structural systems subjected to external dynamic loads whose nature is intrinsically stochastic, as in cases of sea waves, wind pressure, and vibrations due to road asperity. Using random vibration analysis is possible, when the input is properly modeled as a stochastic process, to derive pieces of information about the structural response with a high quality (if compared with other tools), especially in terms of reliability prevision. Moreover, the random vibration approach is quite complex in cases of non-linearity cases, as well as for non-stationary inputs, as in cases of seismic events. For non-stationary inputs, the assessment of second-order spectral moments requires resolving the Lyapunov matrix differential equation. In this research, a numerical procedure is proposed, providing an expression of response in the state-space that, to our best knowledge, has not yet been presented in the literature, by using a formal justification in accordance with earthquake input modeled as a modulated white noise with evolutive parameters. The computational efforts are reduced by considering the symmetry feature of the covariance matrix. The adopted approach is applied to analyze a multi-story building, aiming to determine the reliability related to the maximum inter-story displacement surpassing a specified acceptable threshold. The building is presumed to experience seismic input characterized by a non-stationary process in both amplitude and frequency, utilizing a general Kanai–Tajimi earthquake input stationary model. The adopted case study is modeled in the form of a multi-degree-of-freedom plane shear frame system.https://www.mdpi.com/2079-3197/12/3/50non-stationary random processcovariance analysisLyapunov equationdynamic response and reliability |
| spellingShingle | M. Domaneschi R. Cucuzza L. Sardone S. Londoño Lopez M. Movahedi G. C. Marano Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs Computation non-stationary random process covariance analysis Lyapunov equation dynamic response and reliability |
| title | Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs |
| title_full | Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs |
| title_fullStr | Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs |
| title_full_unstemmed | Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs |
| title_short | Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs |
| title_sort | numerical covariance evaluation for linear structures subject to non stationary random inputs |
| topic | non-stationary random process covariance analysis Lyapunov equation dynamic response and reliability |
| url | https://www.mdpi.com/2079-3197/12/3/50 |
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