Description of the solution set of the von Kármán equations for a circular plate in a small neighbourhood of a simple bifurcation point

2006 ◽  
Vol 13 (3) ◽  
pp. 337-348
Author(s):  
Joanna Janczewska
Keyword(s):  
Circular Plate ◽  
Bifurcation Point ◽  
Solution Set ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Von Kármán ◽  
Simple Bifurcation Point

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 Stable and unstable bifurcation in the von Kármán problem for a circular plate

2005 ◽  
Vol 2005 (8) ◽  
pp. 889-899 ◽  
Author(s):  
Andrei Borisovich ◽  
Joanna Janczewska
Keyword(s):  
Circular Plate ◽  
Elastic Plate ◽  
Analytical Methods ◽  
Compressive Force ◽  
Elastic Base ◽  
Solution Set ◽  
Simply Supported ◽  
Bifurcation Points ◽  
Von Karman ◽  
Von Kármán

In this work, we study bifurcation in the von Kármán equations for a thin circular elastic plate which lies on the elastic base and is simply supported and subjected to a compressive force along the boundary. Applying analytical methods, we prove the existence of stable and unstable simple bifurcation points in the solution set of these equations.

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.

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