{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T22:31:45Z","timestamp":1770330705114,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,5]],"date-time":"2023-01-05T00:00:00Z","timestamp":1672876800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Many mechanical systems manifest nonlinear behavior under nonstationary random excitations. Neglecting this nonlinearity in the modeling of a dynamic system would result in unacceptable results. However, it is challenging to find exact solutions to nonlinear problems. Therefore, equivalent linearization methods are often used to seek approximate solutions for this kind of problem. To overcome the limitations of the existing equivalent linearization methods, an orthogonal-function-based equivalent linearization method in the time domain is proposed for nonlinear systems subjected to nonstationary random excitations. The proposed method is first applied to a single-degree-of-freedom (SDOF) Duffing\u2013Van der Pol oscillator subjected to stationary and nonstationary excitations to validate its accuracy. Then, its applicability to nonlinear MDOF systems is depicted by a 5DOF Duffing\u2013Van der Pol system subjected to nonstationary excitation, with different levels of system nonlinearity strength considered in the analysis. Results show that the proposed method has the merit of predicting the nonlinear system response with high accuracy and computation efficiency. In addition, it is applicable to any general type of nonstationary random excitation.<\/jats:p>","DOI":"10.3390\/computation11010008","type":"journal-article","created":{"date-parts":[[2023,1,6]],"date-time":"2023-01-06T03:19:54Z","timestamp":1672975194000},"page":"8","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Application of Orthogonal Functions to Equivalent Linearization Method for MDOF Duffing\u2013Van der Pol Systems under Nonstationary Random Excitations"],"prefix":"10.3390","volume":"11","author":[{"given":"Amir","family":"Younespour","sequence":"first","affiliation":[{"name":"Department of Civil and Environmental Engineering, University of Windsor, Windsor, ON N9B 3P4, Canada"}]},{"given":"Hosein","family":"Ghaffarzadeh","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, University of Tabriz, Tabriz 51666-16471, Iran"}]},{"given":"Shaohong","family":"Cheng","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, University of Windsor, Windsor, ON N9B 3P4, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1700","DOI":"10.1121\/1.1918792","article-title":"Perturbation Techniques for Random Vibration of Nonlinear Systems","volume":"35","author":"Crandall","year":"1963","journal-title":"J. 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