On the Nonlinear Forced Vibration of the Magnetostrictive Laminated Beam in a Complex Environment
The present study dealt with a comprehensive mathematical model to explore the nonlinear forced vibration of a magnetostrictive laminated beam. This system was subjected to mechanical impact, a nonlinear Winkler–Pasternak foundation, and an electromagnetic actuator considering the thickness effect....
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/23/3836 |
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| author | Nicolae Herisanu Bogdan Marinca Vasile Marinca |
| author_facet | Nicolae Herisanu Bogdan Marinca Vasile Marinca |
| author_sort | Nicolae Herisanu |
| collection | DOAJ |
| description | The present study dealt with a comprehensive mathematical model to explore the nonlinear forced vibration of a magnetostrictive laminated beam. This system was subjected to mechanical impact, a nonlinear Winkler–Pasternak foundation, and an electromagnetic actuator considering the thickness effect. The expressions of the nonlinear differential equations were obtained for the pinned–pinned boundary conditions with the help of the Galerkin–Bubnov procedure and Hamiltonian approach. The nonlinear differential equations were studied using an original, explicit, and very efficient technique, namely the optimal auxiliary functions method (OAFM). It should be emphasized that our procedure assures a rapid convergence of the approximate analytical solutions after only one iteration, without the presence of a small parameter in the governing equations or boundary conditions. Detailed results are presented on the effects of some parameters, among them being analyzed were the damping, frequency, electromagnetic, and nonlinear elastic foundation coefficients. The local stability of the equilibrium points was performed by introducing two variable expansion method, the homotopy perturbation method, and then applying the Routh–Hurwitz criteria and eigenvalues of the Jacobian matrix. |
| format | Article |
| id | doaj-art-4ec7ecdbe1df4e5f9993ee0b0a5d7e65 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-4ec7ecdbe1df4e5f9993ee0b0a5d7e652025-08-20T02:50:33ZengMDPI AGMathematics2227-73902024-12-011223383610.3390/math12233836On the Nonlinear Forced Vibration of the Magnetostrictive Laminated Beam in a Complex EnvironmentNicolae Herisanu0Bogdan Marinca1Vasile Marinca2Department of Mechanics and Strength of Materials, University Politehnica Timisoara, 300222 Timisoara, RomaniaDepartment of Applied Electronics, University Politehnica Timisoara, 300006 Timisoara, RomaniaDepartment of Mechanics and Strength of Materials, University Politehnica Timisoara, 300222 Timisoara, RomaniaThe present study dealt with a comprehensive mathematical model to explore the nonlinear forced vibration of a magnetostrictive laminated beam. This system was subjected to mechanical impact, a nonlinear Winkler–Pasternak foundation, and an electromagnetic actuator considering the thickness effect. The expressions of the nonlinear differential equations were obtained for the pinned–pinned boundary conditions with the help of the Galerkin–Bubnov procedure and Hamiltonian approach. The nonlinear differential equations were studied using an original, explicit, and very efficient technique, namely the optimal auxiliary functions method (OAFM). It should be emphasized that our procedure assures a rapid convergence of the approximate analytical solutions after only one iteration, without the presence of a small parameter in the governing equations or boundary conditions. Detailed results are presented on the effects of some parameters, among them being analyzed were the damping, frequency, electromagnetic, and nonlinear elastic foundation coefficients. The local stability of the equilibrium points was performed by introducing two variable expansion method, the homotopy perturbation method, and then applying the Routh–Hurwitz criteria and eigenvalues of the Jacobian matrix.https://www.mdpi.com/2227-7390/12/23/3836magnetostrictive materialcomposite beamcurvaturethickness effectWinkler–Pasternak foundationelectromagnetic actuator |
| spellingShingle | Nicolae Herisanu Bogdan Marinca Vasile Marinca On the Nonlinear Forced Vibration of the Magnetostrictive Laminated Beam in a Complex Environment Mathematics magnetostrictive material composite beam curvature thickness effect Winkler–Pasternak foundation electromagnetic actuator |
| title | On the Nonlinear Forced Vibration of the Magnetostrictive Laminated Beam in a Complex Environment |
| title_full | On the Nonlinear Forced Vibration of the Magnetostrictive Laminated Beam in a Complex Environment |
| title_fullStr | On the Nonlinear Forced Vibration of the Magnetostrictive Laminated Beam in a Complex Environment |
| title_full_unstemmed | On the Nonlinear Forced Vibration of the Magnetostrictive Laminated Beam in a Complex Environment |
| title_short | On the Nonlinear Forced Vibration of the Magnetostrictive Laminated Beam in a Complex Environment |
| title_sort | on the nonlinear forced vibration of the magnetostrictive laminated beam in a complex environment |
| topic | magnetostrictive material composite beam curvature thickness effect Winkler–Pasternak foundation electromagnetic actuator |
| url | https://www.mdpi.com/2227-7390/12/23/3836 |
| work_keys_str_mv | AT nicolaeherisanu onthenonlinearforcedvibrationofthemagnetostrictivelaminatedbeaminacomplexenvironment AT bogdanmarinca onthenonlinearforcedvibrationofthemagnetostrictivelaminatedbeaminacomplexenvironment AT vasilemarinca onthenonlinearforcedvibrationofthemagnetostrictivelaminatedbeaminacomplexenvironment |