Coiflets solutions for Föppl-von Kármán equations governing large deflection of a thin flat plate by a novel wavelet-homotopy approach

2018 ◽  
Vol 79 (4) ◽  
pp. 993-1020 ◽  
Author(s):  
Qiang Yu ◽  
Hang Xu ◽  
Shijun Liao
Keyword(s):  
Flat Plate ◽  
Large Deflection ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Von Kármán

Improved Analytical Modeling of Membrane Large Deflection With Lateral Force for the Underwater CMUT Based on Von Kármán Equations

2016 ◽  
Vol 16 (17) ◽  
pp. 6633-6640 ◽  
Author(s):  
Jiujiang Wang ◽  
Sio Hang Pun ◽  
Peng Un Mak ◽  
Ching-Hsiang Cheng ◽  
Yuanyu Yu ◽  
...  
Keyword(s):  
Analytical Modeling ◽  
Large Deflection ◽  
Lateral Force ◽  
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.

Dynamic-relaxation solution for the large deflection of plates with specified boundary stresses

1969 ◽  
Vol 4 (2) ◽  
pp. 75-80 ◽  
Author(s):  
K R Rushton
Keyword(s):  
Large Deflection ◽  
Relaxation Method ◽  
Plane Boundary ◽  
Dynamic Relaxation ◽  
Simply Supported ◽  
Von Karman ◽  
Relaxation Solution ◽  
Von Kármán Equations ◽  
Mesh Spacing ◽  
Dynamic Relaxation Method

The von Kármán equations for the large deflection of plates are solved by the dynamic-relaxation method. Detailed results are presented for square plates having simply supported edges with zero in-plane boundary stresses. The results show that high stresses occur towards the corners of the plates. The mesh effect is investigated and recommendations are made for the optimum mesh spacing.

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