Modelling of nonlinear circular plates using modal analysis: simulation and model validation

Abstract

To cite this version:Eric Colinet, Jérôme Juillard. Modelling of nonlinear circular plates using modal analysis: simulation and model validation.

Modeling and Control of Deformable Membrane Mirrors

“…Deformable membrane mirrors with non-contacting actuators are often represented by static models approximating the nonreactive deformation of the mirror surface. Thereby, both Kirchoff and van Kármán theory is used to describe plate deformations smaller than the plate thickness [23][24][25][26] and deformations close to the thickness of the mirror plate [27][28][29], respectively. Additionally, finite element methods are used to model deformable mirrors, in particular for the development large deformable secondary mirrors in astronomy [30][31][32][33][34][35][36].…”

“…For dynamic analysis, large deflections of the plate are not considered and nonlinear effects such as tensile stresses of the plate are neglected [28,41,42]. Secondly, it is assumed that a native curvature of the shell can be neglected due to only small deflections perpendicular to the surface.…”

Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates

“…Since h /ℓ ≪ 1, an approximate distributed model can be employed, where the system kinematics is described only through the displacement of points on the movable electrode mid-surface, see for example [15]. Linear and nonlinear problems for microplates have been studied in [16–23]. When the bending stiffness of the deformable electrode is negligible as compared to its in-plane stretching and g 0 /ℓ ≪ 1, where g 0 is the initial gap, the electrode can be regarded as a linear elastic membrane.…”

Microbeam dynamic shaping by closed-loop electrostatic actuation using modal control

“…In many applications, the system is considered as a second order mass-spring system, representing only the first mode by considering the beam as a plane one-block non-deformable mass moving or vibrating in one dimension, neglecting also the elongation of the beam as in [3][4][5][6]. This can be done when considering small displacements of the microstructure [9], which allows linearizing the model close to a working point [10]. Other applications which use deformable membranes describe the behaviour by two purely linear modes corresponding to whether bending stresses or tensile stresses are dominant [11].…”