An effective method for the evaluation of the pdf response of dynamic systems subjected to non-stationary loads
•I propose an extension of the new version of the Probabilistic Transformation Method (PTM) to dynamic problems.•The proposed approach can be applied indifferently both for stationary and non-stationary input processes.•Two explicit solutions are proposed for the response characteristic function (cf...
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| Published in | Engineering structures Vol. 84; pp. 419 - 429 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.02.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0141-0296 1873-7323 |
| DOI | 10.1016/j.engstruct.2014.11.040 |
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| Abstract | •I propose an extension of the new version of the Probabilistic Transformation Method (PTM) to dynamic problems.•The proposed approach can be applied indifferently both for stationary and non-stationary input processes.•Two explicit solutions are proposed for the response characteristic function (cf).
This paper deals with the evaluation of the response probability density function (pdf) and/or characteristic function (cf) of linear systems subject to stochastic loads. It proposes a new method based on the new version of Probabilistic Transformation Method (PTM). An important aspect of the proposed approach is the ability to join directly the pdf of the input load with that of the response. Working in term of pdfs and/or cfs, the stochastic properties of the response process are full described. This enables to take into account the non Gaussianity and non stationarity of the process. Based on the step-by-step integration method, explicit solutions will be proposed for the random response of systems driven by loads stochastically defined by their cf or loads defined by a quadratic relation of a Gaussian process. |
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| AbstractList | •I propose an extension of the new version of the Probabilistic Transformation Method (PTM) to dynamic problems.•The proposed approach can be applied indifferently both for stationary and non-stationary input processes.•Two explicit solutions are proposed for the response characteristic function (cf).
This paper deals with the evaluation of the response probability density function (pdf) and/or characteristic function (cf) of linear systems subject to stochastic loads. It proposes a new method based on the new version of Probabilistic Transformation Method (PTM). An important aspect of the proposed approach is the ability to join directly the pdf of the input load with that of the response. Working in term of pdfs and/or cfs, the stochastic properties of the response process are full described. This enables to take into account the non Gaussianity and non stationarity of the process. Based on the step-by-step integration method, explicit solutions will be proposed for the random response of systems driven by loads stochastically defined by their cf or loads defined by a quadratic relation of a Gaussian process. |
| Author | Settineri, D. |
| Author_xml | – sequence: 1 givenname: D. surname: Settineri fullname: Settineri, D. email: dsettineri@unime.it organization: Dipartimento di Ingegneria Civile, Informatica, Edile, Ambientale e Matematica Applicata, University of Messina, c.da Di Dio, 98166 Messina, Italy |
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| CitedBy_id | crossref_primary_10_1155_2015_102680 crossref_primary_10_1016_j_ijmecsci_2020_106048 crossref_primary_10_1016_j_jsv_2020_115648 crossref_primary_10_1016_j_compstruc_2021_106583 crossref_primary_10_1016_j_jweia_2022_105054 crossref_primary_10_1016_j_ymssp_2021_108735 crossref_primary_10_1016_j_engstruct_2020_111786 crossref_primary_10_1142_S1793962318500575 |
| Cites_doi | 10.1002/eqe.4290200804 10.1016/j.probengmech.2009.05.002 10.1016/j.probengmech.2013.03.003 10.1016/j.probengmech.2010.11.011 10.1006/jsvi.1995.0205 10.2514/6.2007-1957 10.1006/jsvi.1996.0573 10.1016/j.strusafe.2006.08.001 10.1016/j.probengmech.2004.06.001 10.1016/S0266-8920(02)00037-1 10.1016/j.jsv.2010.12.020 10.1016/S0167-4730(99)00022-3 10.1016/j.probengmech.2013.10.001 10.1016/j.engstruct.2008.04.015 10.1016/j.probengmech.2011.08.019 10.1016/0266-8920(95)00026-7 10.1115/1.3139636 10.1111/j.2517-6161.1965.tb01488.x 10.1016/j.strusafe.2010.03.009 10.1016/j.probengmech.2013.03.001 10.1016/j.probengmech.2007.10.009 |
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An extended statistical linearization technique publication-title: J Dynam Syst Measur Control ASME doi: 10.1115/1.3139636 – volume: 10 start-page: 225 year: 1985 ident: 10.1016/j.engstruct.2014.11.040_b0045 article-title: Transient spectral moments of linear systems publication-title: SM Arch – volume: 3 start-page: 49 year: 2012 ident: 10.1016/j.engstruct.2014.11.040_b0115 article-title: The application of the probability transformation method for the solution of some nonlinear structural relationships publication-title: Meccanica delle Strutture e dei materiali – volume: 27 start-page: 204 year: 1965 ident: 10.1016/j.engstruct.2014.11.040_b0160 article-title: Evolutionary spectra and non-stationary processes publication-title: J Roy Stat Soc doi: 10.1111/j.2517-6161.1965.tb01488.x – volume: 32 start-page: 275 year: 2010 ident: 10.1016/j.engstruct.2014.11.040_b0085 article-title: Local domain Monte Carlo simulation publication-title: Struct Safety doi: 10.1016/j.strusafe.2010.03.009 – volume: 33 start-page: 86 year: 2013 ident: 10.1016/j.engstruct.2014.11.040_b0125 article-title: Explicit solutions for the response probability density function of linear systems subjected to random static loads publication-title: Probabilist Eng Mech doi: 10.1016/j.probengmech.2013.03.001 – ident: 10.1016/j.engstruct.2014.11.040_b0140 – year: 1993 ident: 10.1016/j.engstruct.2014.11.040_b0165 – volume: 23 start-page: 416 year: 2008 ident: 10.1016/j.engstruct.2014.11.040_b0035 article-title: Spectral characteristics of non-stationary random processes: theory and applications to linear structural models publication-title: Probabilist Eng Mech doi: 10.1016/j.probengmech.2007.10.009 – volume: 26 start-page: 1201 year: 1965 ident: 10.1016/j.engstruct.2014.11.040_b0080 article-title: Generalization of the method of statistical linearization to multidimensional systems publication-title: Auto Remote Control |
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