The complete synchronization condition in a network of piezoelectric micro-beams

Yolong, V Y Taffoti; Woafo, P.

doi:10.1007/s11071-008-9437-0

Cited by 6 publications

(4 citation statements)

References 32 publications

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“…1(a). Following Taffoti Yolong & Woafo [2009], we model one piezoelectric MEMS element as a stack of n disks of thickness h and cross section A, assuming that all the electrical and mechanical quantities are uniformly distributed in the linear transducer. This model can be found in technological devices where the inverse piezoelectric effect is brought into place.…”

Section: Model and Hamiltonian Functionmentioning

confidence: 99%

“…The values of the physical parameters of the piezoelectric transducer are presented in Table 1. The Lagrangian Γ of the piezoelectric MEMS is [Taffoti Yolong & Woafo, 2009]:…”

Section: Model and Hamiltonian Functionmentioning

confidence: 99%

“…Based on the analysis presented in [Taffoti Yolong & Woafo, 2009], we set the values of the parameters of Hamiltonian (4) to β 1 = 14.25, β 2 = 13.91, γ 1 = 0.21, γ 2 = 3.64 and ω 2 2 = 3.75 for our investigation. In all our simulations the absolute value of the relative energy error…”

Section: Dynamicsmentioning

confidence: 99%

“…In the present paper we use the PSS, the mLE and the SALI techniques to investigate the chaotic dynamics of a time dependent piezoelectric MEMS. In [Taffoti Yolong & Woafo, 2009] this system was studied in the framework of the Lagrangian formalism, but only its chaotic state was analyzed. Here, a Hamiltonian formulation of the problem is derived taking into account dissipation (friction) and time dependent forces.…”

Section: Introductionmentioning

confidence: 99%

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Chaotic dynamics of piezoelectric mems based on maximal Lyapunov exponent and Smaller Alignment Index computations

Tchakui¹,

Woafo²,

Skokos³

2019

Preprint

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We characterize the dynamical states of a piezoelectric microelectromechanical system (MEMS) using several numerical quantifiers including the maximal Lyapunov exponent, the Poincaré Surface of Section and a chaos detection method called the Smaller Alignment Index (SALI). The analysis makes use of the MEMS Hamiltonian. We start our study by considering the case of a conservative piezoelectric MEMS model and describe the behavior of some representative phase space orbits of the system. We show that the dynamics of the piezoelectric MEMS becomes considerably more complex as the natural frequency of the system's mechanical part decreases.This refers to the reduction of the stiffness of the piezoelectric transducer. Then, taking into account the effects of damping and time dependent forces on the piezoelectric MEMS, we derive the corresponding non-autonomous Hamiltonian and investigate its dynamical behavior. We find that the non-conservative system exhibits a rich dynamics, which is strongly influenced by the values of the parameters that govern the piezoelectric MEMS energy gain and loss. Our results provide further evidences of the ability of the SALI to efficiently characterize the chaoticity of dynamical systems.

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Section: Model and Hamiltonian Functionmentioning

confidence: 99%

“…The values of the physical parameters of the piezoelectric transducer are presented in Table 1. The Lagrangian Γ of the piezoelectric MEMS is [Taffoti Yolong & Woafo, 2009]:…”

Section: Model and Hamiltonian Functionmentioning

confidence: 99%

Section: Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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