Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation
In this work, the effect of vibro-impact nonlinear, forced, and damped oscillator on the dynamics of the electromagnetic actuation (EA) near primary resonance is studied. The vibro-impact regime is given by the presence of the Hertzian contact. The EA is supplied by a constant current generating a s...
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/9/2194 |
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| author | Nicolae Herisanu Bogdan Marinca Livija Cveticanin Vasile Marinca |
| author_facet | Nicolae Herisanu Bogdan Marinca Livija Cveticanin Vasile Marinca |
| author_sort | Nicolae Herisanu |
| collection | DOAJ |
| description | In this work, the effect of vibro-impact nonlinear, forced, and damped oscillator on the dynamics of the electromagnetic actuation (EA) near primary resonance is studied. The vibro-impact regime is given by the presence of the Hertzian contact. The EA is supplied by a constant current generating a static force and by an actuation generating a fast alternative force. The deformations between the solids in contact are supposed to be elastic and the contact is maintained. In this study, a single degree of freedom nonlinear damped oscillator under a static normal load is considered. An analytical approximate solution of this problem is obtained using the Optimal Auxiliary Functions Method (OAFM). By means of some auxiliary functions and introducing so-called convergence-control parameters, a very accurate approximate solution of the governing equation can be obtained. We need only the first iteration for this technique, applying a rigorous mathematical procedure in finding the optimal values of the convergence-control parameters. Local stability by means of the Routh-Hurwitz criteria and global stability using the Lyapunov function are also studied. It should be emphasized that the amplitude of AC excitation voltage is not considered much lower than bias voltage (in contrast to other studies). Also, the Hertzian contact coupled with EA is analytically studied for the first time in the present work. The approximate analytical solution is determined with a high accuracy on two domains. Local stability is established in five cases with some cases depending on the trace of the Jacobian matrix and of the discriminant of the characteristic equation. In the study of global stability, the estimate parameters which are components of the Lyapunov function are given in a closed form and a graphical form and therefore the Lyapunov function is well-determined. |
| first_indexed | 2024-03-11T04:12:10Z |
| format | Article |
| id | doaj.art-64aaed284d514a6d9f99fce9388e7eba |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:12:10Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-64aaed284d514a6d9f99fce9388e7eba2023-11-17T23:21:14ZengMDPI AGMathematics2227-73902023-05-01119219410.3390/math11092194Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic ActuationNicolae Herisanu0Bogdan Marinca1Livija Cveticanin2Vasile Marinca3Department of Mechanics and Strength of Materials, University Politehnica Timisoara, 300006 Timisoara, RomaniaDepartment of Applied Electronics, University Politehnica Timisoara, 300006 Timisoara, RomaniaFaculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, SerbiaDepartment of Mechanics and Strength of Materials, University Politehnica Timisoara, 300006 Timisoara, RomaniaIn this work, the effect of vibro-impact nonlinear, forced, and damped oscillator on the dynamics of the electromagnetic actuation (EA) near primary resonance is studied. The vibro-impact regime is given by the presence of the Hertzian contact. The EA is supplied by a constant current generating a static force and by an actuation generating a fast alternative force. The deformations between the solids in contact are supposed to be elastic and the contact is maintained. In this study, a single degree of freedom nonlinear damped oscillator under a static normal load is considered. An analytical approximate solution of this problem is obtained using the Optimal Auxiliary Functions Method (OAFM). By means of some auxiliary functions and introducing so-called convergence-control parameters, a very accurate approximate solution of the governing equation can be obtained. We need only the first iteration for this technique, applying a rigorous mathematical procedure in finding the optimal values of the convergence-control parameters. Local stability by means of the Routh-Hurwitz criteria and global stability using the Lyapunov function are also studied. It should be emphasized that the amplitude of AC excitation voltage is not considered much lower than bias voltage (in contrast to other studies). Also, the Hertzian contact coupled with EA is analytically studied for the first time in the present work. The approximate analytical solution is determined with a high accuracy on two domains. Local stability is established in five cases with some cases depending on the trace of the Jacobian matrix and of the discriminant of the characteristic equation. In the study of global stability, the estimate parameters which are components of the Lyapunov function are given in a closed form and a graphical form and therefore the Lyapunov function is well-determined.https://www.mdpi.com/2227-7390/11/9/2194vibro-impactelectromagnetic actuationresonanceoptimal auxiliary functions methodstability |
| spellingShingle | Nicolae Herisanu Bogdan Marinca Livija Cveticanin Vasile Marinca Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation Mathematics vibro-impact electromagnetic actuation resonance optimal auxiliary functions method stability |
| title | Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation |
| title_full | Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation |
| title_fullStr | Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation |
| title_full_unstemmed | Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation |
| title_short | Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation |
| title_sort | analysis of the vibro impact nonlinear damped and forced oscillator in the dynamics of the electromagnetic actuation |
| topic | vibro-impact electromagnetic actuation resonance optimal auxiliary functions method stability |
| url | https://www.mdpi.com/2227-7390/11/9/2194 |
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