Parametrically Excited Vibrations in a Nonlinear Damped Triple-Well Oscillator with Resonant Frequency

Chen, Daomin; Wang, Ning; Chen, Zhenyu; Yu, Yue

doi:10.1007/s42417-021-00408-5

Cited by 7 publications

(2 citation statements)

References 35 publications

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“…Eringen's nonlocal elasticity theory of was applied to Euler-Bernoulli and Timoshenko beams, and an analytical solution of the governing equations was obtained using the Laplace transform function. Recently, other interesting studies in the field have been reported in [29][30][31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Longitudinal–Transverse Vibration of a Functionally Graded Nanobeam Subjected to Mechanical Impact and Electromagnetic Actuation

Herişanu

Marinca

2023

Symmetry

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This study addresses the nonlinear forced vibration of a functionally graded (FG) nanobeam subjected to mechanical impact and electromagnetic actuation. Two symmetrical actuators were present in the mechanical model, and their mechanical behaviors were analyzed considering the symmetry in actuation. The model considered the longitudinal–transverse vibration of a simple supported Euler–Bernoulli beam, which accounted for von Kármán geometric nonlinearity, including the first-order strain–displacement relationship. The FG nanobeam was made of a mixture of metals and ceramics, while the volume fraction varied in terms of thickness when a power law function was used. The nonlocal Eringen theory of elasticity was used to study the simple supported Euler–Bernoulli nanobeam. The nonlinear governing equations of the FG nanobeam and the associated boundary conditions were gained using Hamilton’s principle. To truncate the system with an infinite degree of freedom, the coupled longitudinal–transverse governing equations were discretized using the Galerkin–Bubnov approach. The resulting nonlinear, ordinary differential equations, which took into account the curvature of the nanobeam, were studied via the Optimal Auxiliary Functions Method (OAFM). For this complex nonlinear problem, an explicit, analytical, approximate solution was proposed near the primary resonance. The simultaneous effects of the following elements were considered in this paper: the presence of a curved nanobeam; the transversal inertia, which is not neglected in this paper; the mechanical impact; and electromagnetic actuation. The present study proposes a highly accurate analytical solution to the abovementioned conditions. Moreover, in these conditions, the study of local stability was developed using two variable expansion methods, the Jacobian matrix and Routh–Hurwitz criteria, and global stability was studied using the Lyapunov function.

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Section: Introductionmentioning

confidence: 99%

Longitudinal–Transverse Vibration of a Functionally Graded Nanobeam Subjected to Mechanical Impact and Electromagnetic Actuation

Herişanu

Marinca

2023

Symmetry

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“…Yu et al [ 25 ] performed analytical investigations on symmetric jump phenomena reflecting multi-timescale dynamics in a nonlinear shape memory alloy oscillator with parametric and external cosinoidal excitations. Chen et al [ 26 ] proposed the parametrically excited vibrations and mode transitions of a nonlinear damped triple-well oscillator, revealing the multiple timescale structure of an oscillator with resonant frequency. Zhang et al [ 27 ] explored novel multiple-frequency bursting of a shape memory oscillator under parametrical and external excitation.…”

Section: Introductionmentioning

confidence: 99%

Improving the Performance of a Post-Buckled Beam Harvester under Combined External and Parametrical Slow Excitations

2023

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In this paper, we consider novel bursting energy harvesting under combined external and parametrical slow excitations, and a harvester is realized by employing an externally and parametrically excited post-buckled beam. Based on the method of fast–slow dynamics analysis, multiple-frequency oscillation, with two slow commensurate excitation frequencies, is used to observe complex bursting patterns, the behaviors of the bursting response are presented, and some novel one-parameter bifurcation patterns are observed. Furthermore, the bursting harvesting performances of the single and the two slow commensurate excitation frequencies are compared, and it was found that the two slow commensurate excitation frequencies can be used to improve the harvesting voltage.

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Control and synchronization in the Duffing-van der Pol and $$\Phi ^6$$ Duffing oscillators

Uriostegui-Legorreta

Tututi

2023

Indian J Phys

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Parametrically Excited Vibrations in a Nonlinear Damped Triple-Well Oscillator with Resonant Frequency

Cited by 7 publications

References 35 publications

Longitudinal–Transverse Vibration of a Functionally Graded Nanobeam Subjected to Mechanical Impact and Electromagnetic Actuation

Longitudinal–Transverse Vibration of a Functionally Graded Nanobeam Subjected to Mechanical Impact and Electromagnetic Actuation

Improving the Performance of a Post-Buckled Beam Harvester under Combined External and Parametrical Slow Excitations

Control and synchronization in the Duffing-van der Pol and $$\Phi ^6$$ Duffing oscillators

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