Nonlinear Dynamics of an Electromagnetically Actuated Cantilever Beam Under Harmonic External Excitation
The present work is devoted to the study of nonlinear vibrations of an electromagnetically actuated cantilever beam subject to harmonic external excitation. The soft actuator that controls the vibratory motion of such components of a robotic structure led to a strongly nonlinear governing differenti...
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MDPI AG
2024-11-01
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| author | Nicolae Herisanu Bogdan Marinca Vasile Marinca |
| author_facet | Nicolae Herisanu Bogdan Marinca Vasile Marinca |
| author_sort | Nicolae Herisanu |
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| description | The present work is devoted to the study of nonlinear vibrations of an electromagnetically actuated cantilever beam subject to harmonic external excitation. The soft actuator that controls the vibratory motion of such components of a robotic structure led to a strongly nonlinear governing differential equation, which was solved in this work by using a highly accurate technique, namely the Optimal Auxiliary Functions Method. Comparisons between the results obtained using our original approach with those of numerical integration show the efficiency and reliability of our procedure, which can be applied to give an explicit analytical approximate solution in two cases: the nonresonant case and the nearly primary resonance. Our technique is effective, simple, easy to use, and very accurate by means of only the first iteration. On the other hand, we present an analysis of the local stability of the model using Routh–Hurwitz criteria and the eigenvalues of the Jacobian matrix. Global stability is analyzed by means of Lyapunov’s direct method and LaSalle’s invariance principle. For the first time, the Lyapunov function depends on the approximate solution obtained using OAFM. Also, Pontryagin’s principle with respect to the control variable is applied in the construction of the Lyapunov function. |
| format | Article |
| id | doaj-art-bf533e96e8f54b7391cf9e5ac87809c5 |
| institution | Kabale University |
| issn | 2076-3417 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-bf533e96e8f54b7391cf9e5ac87809c52024-11-26T17:48:21ZengMDPI AGApplied Sciences2076-34172024-11-0114221033510.3390/app142210335Nonlinear Dynamics of an Electromagnetically Actuated Cantilever Beam Under Harmonic External ExcitationNicolae 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 work is devoted to the study of nonlinear vibrations of an electromagnetically actuated cantilever beam subject to harmonic external excitation. The soft actuator that controls the vibratory motion of such components of a robotic structure led to a strongly nonlinear governing differential equation, which was solved in this work by using a highly accurate technique, namely the Optimal Auxiliary Functions Method. Comparisons between the results obtained using our original approach with those of numerical integration show the efficiency and reliability of our procedure, which can be applied to give an explicit analytical approximate solution in two cases: the nonresonant case and the nearly primary resonance. Our technique is effective, simple, easy to use, and very accurate by means of only the first iteration. On the other hand, we present an analysis of the local stability of the model using Routh–Hurwitz criteria and the eigenvalues of the Jacobian matrix. Global stability is analyzed by means of Lyapunov’s direct method and LaSalle’s invariance principle. For the first time, the Lyapunov function depends on the approximate solution obtained using OAFM. Also, Pontryagin’s principle with respect to the control variable is applied in the construction of the Lyapunov function.https://www.mdpi.com/2076-3417/14/22/10335electromagnetic actuatoroptimal auxiliary functions methodresonanceRouth–HurwitzLyapunov |
| spellingShingle | Nicolae Herisanu Bogdan Marinca Vasile Marinca Nonlinear Dynamics of an Electromagnetically Actuated Cantilever Beam Under Harmonic External Excitation Applied Sciences electromagnetic actuator optimal auxiliary functions method resonance Routh–Hurwitz Lyapunov |
| title | Nonlinear Dynamics of an Electromagnetically Actuated Cantilever Beam Under Harmonic External Excitation |
| title_full | Nonlinear Dynamics of an Electromagnetically Actuated Cantilever Beam Under Harmonic External Excitation |
| title_fullStr | Nonlinear Dynamics of an Electromagnetically Actuated Cantilever Beam Under Harmonic External Excitation |
| title_full_unstemmed | Nonlinear Dynamics of an Electromagnetically Actuated Cantilever Beam Under Harmonic External Excitation |
| title_short | Nonlinear Dynamics of an Electromagnetically Actuated Cantilever Beam Under Harmonic External Excitation |
| title_sort | nonlinear dynamics of an electromagnetically actuated cantilever beam under harmonic external excitation |
| topic | electromagnetic actuator optimal auxiliary functions method resonance Routh–Hurwitz Lyapunov |
| url | https://www.mdpi.com/2076-3417/14/22/10335 |
| work_keys_str_mv | AT nicolaeherisanu nonlineardynamicsofanelectromagneticallyactuatedcantileverbeamunderharmonicexternalexcitation AT bogdanmarinca nonlineardynamicsofanelectromagneticallyactuatedcantileverbeamunderharmonicexternalexcitation AT vasilemarinca nonlineardynamicsofanelectromagneticallyactuatedcantileverbeamunderharmonicexternalexcitation |