Application of Orthogonal Functions to Equivalent Linearization Method for MDOF Duffing–Van der Pol Systems under Nonstationary Random Excitations
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 lineariza...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/11/1/8 |
| _version_ | 1797444173490552832 |
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| author | Amir Younespour Hosein Ghaffarzadeh Shaohong Cheng |
| author_facet | Amir Younespour Hosein Ghaffarzadeh Shaohong Cheng |
| author_sort | Amir Younespour |
| collection | DOAJ |
| description | 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–Van 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–Van 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. |
| first_indexed | 2024-03-09T13:07:45Z |
| format | Article |
| id | doaj.art-812070503f2d4291869efc406f42769f |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-09T13:07:45Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-812070503f2d4291869efc406f42769f2023-11-30T21:46:12ZengMDPI AGComputation2079-31972023-01-01111810.3390/computation11010008Application of Orthogonal Functions to Equivalent Linearization Method for MDOF Duffing–Van der Pol Systems under Nonstationary Random ExcitationsAmir Younespour0Hosein Ghaffarzadeh1Shaohong Cheng2Department of Civil and Environmental Engineering, University of Windsor, Windsor, ON N9B 3P4, CanadaDepartment of Civil and Environmental Engineering, University of Tabriz, Tabriz 51666-16471, IranDepartment of Civil and Environmental Engineering, University of Windsor, Windsor, ON N9B 3P4, CanadaMany 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–Van 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–Van 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.https://www.mdpi.com/2079-3197/11/1/8equivalent linearizationnonstationary excitationorthogonal functionsnonlinearityrandom vibration |
| spellingShingle | Amir Younespour Hosein Ghaffarzadeh Shaohong Cheng Application of Orthogonal Functions to Equivalent Linearization Method for MDOF Duffing–Van der Pol Systems under Nonstationary Random Excitations Computation equivalent linearization nonstationary excitation orthogonal functions nonlinearity random vibration |
| title | Application of Orthogonal Functions to Equivalent Linearization Method for MDOF Duffing–Van der Pol Systems under Nonstationary Random Excitations |
| title_full | Application of Orthogonal Functions to Equivalent Linearization Method for MDOF Duffing–Van der Pol Systems under Nonstationary Random Excitations |
| title_fullStr | Application of Orthogonal Functions to Equivalent Linearization Method for MDOF Duffing–Van der Pol Systems under Nonstationary Random Excitations |
| title_full_unstemmed | Application of Orthogonal Functions to Equivalent Linearization Method for MDOF Duffing–Van der Pol Systems under Nonstationary Random Excitations |
| title_short | Application of Orthogonal Functions to Equivalent Linearization Method for MDOF Duffing–Van der Pol Systems under Nonstationary Random Excitations |
| title_sort | application of orthogonal functions to equivalent linearization method for mdof duffing van der pol systems under nonstationary random excitations |
| topic | equivalent linearization nonstationary excitation orthogonal functions nonlinearity random vibration |
| url | https://www.mdpi.com/2079-3197/11/1/8 |
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