Solubility of the von Karman equations with nonhomogeneous boundary conditions in nonsmooth domains

1990 ◽  
Vol 50 (2) ◽  
pp. 1491-1497
Author(s):  
O. John ◽  
V. A. Kondratiev ◽  
D. M. Lekveishvili ◽  
J. Necas ◽  
O. A. Oleinik
Keyword(s):  
Boundary Conditions ◽  
Nonhomogeneous Boundary ◽  
Von Karman ◽  
Nonsmooth Domains ◽  
Von Kármán Equations ◽  
Nonhomogeneous Boundary Conditions ◽  
Von Kármán

On the swirling flow between rotating coaxial disks, asymptotic behaviour, II

1981 ◽  
Vol 90 (3-4) ◽  
pp. 317-346 ◽  
Author(s):  
Heinz Otto Kreiss ◽  
Seymour V. Parter
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Behaviour ◽  
Swirling Flow ◽  
Simple Zeros ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Image Position ◽  
Von Kármán

SynopsisConsider solutions 〈H(x, ε), G(x, ε)〉 of the von Kármán equations for the swirling flow between two rotating coaxial disksandWe assume that |H(x, ε)| + |Hʹ(x, ε)| + |G(x, ε)|≦B. This work considers shapes and asymptotic behaviour as ε→0+. We consider the type of limit functions 〈H(x), G(x)〉 that are permissible. In particular, if 〈H(x, ε), G(x, ε)〉 also satisfy the boundary conditions H(0, ε)=H(1, ε)=0, Hʹ(0, ε)=Hʹ(1, ε)=0 then H(x) has no simple zeros. That is, there does not exist a point Z ε [0, 1] such that H(x)=0, Hʹ(z)≠0. Moreover, the case of “cells” which oscillate is studied in detail.

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.

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