Periodic solutions of the Nathanson's and the Comb-drive models

Jaume Llibre; Daniel Elías Nuñez Lopez; Andrés  Rivera

doi:10.1016/j.ijnonlinmec.2018.05.009

Periodic solutions of the Nathanson's and the Comb-drive models

Autonomous University of Barcelona

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We provide sufficient conditions for the existence and stability properties of periodic solutions of the second-order non-autonomous differential equation of the Nathanson's model ẍ+x+aẋ−[Formula presented]=0,and of the Comb-drive model ẍ+x+aẋ−[Formula presented]=0,where x∈R, a, b, v₀, δ are positive parameters and v(ωt) is a 2π∕ω-periodic function. The results are obtained using the averaging theory and the lower and upper solution method.

Translated title of the contribution	Soluciones Periódicas en los modelos de Nathanson y actuador tipo peine
Original language	English
Pages (from-to)	109-115
Number of pages	7
Journal	International Journal of Non-Linear Mechanics
Volume	104
Issue number	1
DOIs	https://doi.org/10.1016/j.ijnonlinmec.2018.05.009
State	Published - Sep 2018

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10.1016/j.ijnonlinmec.2018.05.009

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title = "Periodic solutions of the Nathanson's and the Comb-drive models",

abstract = "We provide sufficient conditions for the existence and stability properties of periodic solutions of the second-order non-autonomous differential equation of the Nathanson's model ẍ+x+aẋ−[Formula presented]=0,and of the Comb-drive model ẍ+x+aẋ−[Formula presented]=0,where x∈R, a, b, v0, δ are positive parameters and v(ωt) is a 2π∕ω-periodic function. The results are obtained using the averaging theory and the lower and upper solution method.",

keywords = "Nathanson's model, Comb-drive model, Periodic solutions, Averaging theory",

author = "Jaume Llibre and \{Nu{\~n}ez Lopez\}, \{Daniel El{\'i}as\} and Andr{\'e}s Rivera",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Ltd",

year = "2018",

month = sep,

doi = "10.1016/j.ijnonlinmec.2018.05.009",

language = "English",

volume = "104",

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journal = "International Journal of Non-Linear Mechanics",

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TY - JOUR

T1 - Periodic solutions of the Nathanson's and the Comb-drive models

AU - Llibre, Jaume

AU - Nuñez Lopez, Daniel Elías

AU - Rivera, Andrés

PY - 2018/9

Y1 - 2018/9

N2 - We provide sufficient conditions for the existence and stability properties of periodic solutions of the second-order non-autonomous differential equation of the Nathanson's model ẍ+x+aẋ−[Formula presented]=0,and of the Comb-drive model ẍ+x+aẋ−[Formula presented]=0,where x∈R, a, b, v0, δ are positive parameters and v(ωt) is a 2π∕ω-periodic function. The results are obtained using the averaging theory and the lower and upper solution method.

AB - We provide sufficient conditions for the existence and stability properties of periodic solutions of the second-order non-autonomous differential equation of the Nathanson's model ẍ+x+aẋ−[Formula presented]=0,and of the Comb-drive model ẍ+x+aẋ−[Formula presented]=0,where x∈R, a, b, v0, δ are positive parameters and v(ωt) is a 2π∕ω-periodic function. The results are obtained using the averaging theory and the lower and upper solution method.

KW - Nathanson's model

KW - Comb-drive model

KW - Periodic solutions

KW - Averaging theory

UR - https://www.scopus.com/pages/publications/85047188206

U2 - 10.1016/j.ijnonlinmec.2018.05.009

DO - 10.1016/j.ijnonlinmec.2018.05.009

M3 - Article

AN - SCOPUS:85047188206

SN - 0020-7462

VL - 104

SP - 109

EP - 115

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

IS - 1

ER -

Periodic solutions of the Nathanson's and the Comb-drive models

Abstract

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