Closure to “Discussion of ‘An Approximate Solution of the Axisymmetric von Karman Equations for a Point-Loaded Circular Plate’” (1988, ASME J. Appl. Mech., 55, pp. 746–747)

1988 ◽  
Vol 55 (3) ◽  
pp. 747-747
Author(s):  
A. T. Dolovich ◽  
G. W. Brodland ◽  
A. B. Thornton-Trump
Keyword(s):  
Approximate Solution ◽  
Circular Plate ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Von Kármán

An Approximate Solution of the Axisymmetric von Karman Equations for a Point-Loaded Circular Plate

1988 ◽  
Vol 55 (1) ◽  
pp. 241-243 ◽  
Author(s):  
A. T. Dolovich ◽  
G. W. Brodland ◽  
A. B. Thornton-Trump
Keyword(s):  
Approximate Solution ◽  
Circular Plate ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Von Kármán

scholarly journals A Review on Analytical Modeling for Collapse Mode Capacitive Micromachined Ultrasonic Transducer of the Collapse Voltage and the Static Membrane Deflections

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 714
Author(s):  
Jiujiang Wang ◽  
Xin Liu ◽  
Yuanyu Yu ◽  
Yao Li ◽  
Ching-Hsiang Cheng ◽  
...  
Keyword(s):  
Analytical Modeling ◽  
Ultrasonic Transducer ◽  
Governing Equations ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Collapse Mode ◽  
Capacitive Micromachined Ultrasonic Transducer ◽  
Gap Height ◽  
Von Kármán ◽  
Analytical Expressions

Analytical modeling of capacitive micromachined ultrasonic transducer (CMUT) is one of the commonly used modeling methods and has the advantages of intuitive understanding of the physics of CMUTs and convergent when modeling of collapse mode CMUT. This review article summarizes analytical modeling of the collapse voltage and shows that the collapse voltage of a CMUT correlates with the effective gap height and the electrode area. There are analytical expressions for the collapse voltage. Modeling of the membrane deflections are characterized by governing equations from Timoshenko, von Kármán equations and the 2D plate equation, and solved by various methods such as Galerkin’s method and perturbation method. Analytical expressions from Timoshenko’s equation can be used for small deflections, while analytical expression from von Kármán equations can be used for both small and large deflections.

ON A NONLOCAL FUNCTIONAL ARISING IN THE STUDY OF THIN-FILM BLISTERING

2010 ◽  
Vol 08 (02) ◽  
pp. 109-123
Author(s):  
N. ANSINI ◽  
V. VALENTE
Keyword(s):  
Thin Film ◽  
Asymptotic Analysis ◽  
Circular Plate ◽  
One Dimensional ◽  
Von Karman ◽  
Nonlocal Functional ◽  
Γ Convergence ◽  
Von Kármán

The energy of a Von Kármán circular plate is described by a nonlocal nonconvex one-dimensional functional depending on the thickness ε. Here we perform the asymptotic analysis via Γ-convergence as the parameter ε goes to zero.

scholarly journals Elastohydrodynamics of a pre-stretched finite elastic sheet lubricated by a thin viscous film with application to microfluidic soft actuators

2019 ◽  
Vol 862 ◽  
pp. 732-752 ◽  
Author(s):  
Evgeniy Boyko ◽  
Ran Eshel ◽  
Khaled Gommed ◽  
Amir D. Gat ◽  
Moran Bercovici
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Finite Domain ◽  
Viscous Film ◽  
Elastic Sheet ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Wide Range ◽  
Soft Actuators ◽  
Von Kármán

The interaction of a thin viscous film with an elastic sheet results in coupling of pressure and deformation, which can be utilized as an actuation mechanism for surface deformations in a wide range of applications, including microfluidics, optics and soft robotics. Implementation of such configurations inherently takes place over finite domains and often requires some pre-stretching of the sheet. Under the assumptions of strong pre-stretching and small deformations of the lubricated elastic sheet, we use the linearized Reynolds and Föppl–von Kármán equations to derive closed-form analytical solutions describing the deformation in a finite domain due to external forces, accounting for both bending and tension effects. We provide a closed-form solution for the case of a square-shaped actuation region and present the effect of pre-stretching on the dynamics of the deformation. We further present the dependence of the deformation magnitude and time scale on the spatial wavenumber, as well as the transition between stretching- and bending-dominant regimes. We also demonstrate the effect of spatial discretization of the forcing (representing practical actuation elements) on the achievable resolution of the deformation. Extending the problem to an axisymmetric domain, we investigate the effects arising from nonlinearity of the Reynolds and Föppl–von Kármán equations and present the deformation behaviour as it becomes comparable to the initial film thickness and dependent on the induced tension. These results set the theoretical foundation for implementation of microfluidic soft actuators based on elastohydrodynanmics.

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