TY - JOUR
T1 - Odd periodic oscillations in Comb-drive finger actuators
AU - Núñez, D.
AU - Larreal, O.
AU - Murcia, L.
N1 - Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2021/10
Y1 - 2021/10
N2 - In this work we consider the existence of solutions of a Dirichlet problem with a prescribed number of zeros for a large class of second order differential equations with singularities. Additionally, for the model of a well known kind of micro-electromechanical system, the transverse Comb-drive finger device, we provide sufficient conditions in terms of control parameters that lead to odd periodic oscillations with a certain number of zeros that ranges from zero to some positive integer. This work is motivated and follows the lines of R. Ortega (2016) where the existence of odd periodic oscillations was studied for second order differential equations without singularities, in particular, for the Sitnikov problem. The main results of this paper are obtained through a truncation process, the application of classical tools as the shooting method, and the Sturm comparison theory. A numerical approach based on a bisection method is employed to illustrate the main results with simulations by using literature reference parameters.
AB - In this work we consider the existence of solutions of a Dirichlet problem with a prescribed number of zeros for a large class of second order differential equations with singularities. Additionally, for the model of a well known kind of micro-electromechanical system, the transverse Comb-drive finger device, we provide sufficient conditions in terms of control parameters that lead to odd periodic oscillations with a certain number of zeros that ranges from zero to some positive integer. This work is motivated and follows the lines of R. Ortega (2016) where the existence of odd periodic oscillations was studied for second order differential equations without singularities, in particular, for the Sitnikov problem. The main results of this paper are obtained through a truncation process, the application of classical tools as the shooting method, and the Sturm comparison theory. A numerical approach based on a bisection method is employed to illustrate the main results with simulations by using literature reference parameters.
KW - Comb-drive finger model
KW - Odd periodic solutions
KW - Second-order differential equations
UR - http://www.scopus.com/inward/record.url?scp=85105355400&partnerID=8YFLogxK
U2 - 10.1016/j.nonrwa.2021.103347
DO - 10.1016/j.nonrwa.2021.103347
M3 - Article
AN - SCOPUS:85105355400
SN - 1468-1218
VL - 61
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
M1 - 103347
ER -