scholarly journals An asymptotic strain gradient Reissner-Mindlin plate model

Meccanica ◽  
2013 ◽  
Vol 48 (8) ◽  
pp. 2007-2018 ◽  
Author(s):  
Michele Serpilli ◽  
Françoise Krasucki ◽  
Giuseppe Geymonat
Keyword(s):  
Strain Gradient ◽  
Mindlin Plate ◽  
Plate Model

Modelling the radially polarised annular stator of a piezoelectric travelling wave ultrasonic motor based on the shear effect

2019 ◽  
Vol 30 (8) ◽  
pp. 1225-1238 ◽  
Author(s):  
Ana Costa Conrado
Keyword(s):  
Travelling Waves ◽  
Travelling Wave ◽  
Ultrasonic Motor ◽  
Free Vibrations ◽  
Mindlin Plate ◽  
Vibration Modes ◽  
Shear Effect ◽  
Plate Model ◽  
Voltage Inverter ◽  
Contact Points

This article deals with the mathematical–analytical model of a radially polarised stator, part of a piezoelectric travelling wave ultrasonic motor based on the shear effect. The stator is treated with a Reissner–Mindlin plate model containing piezoelectric terms. The so-obtained mathematical description of the disc stator takes into account its geometry, kinematics and characteristics that influence efficiency and torque. Rayleigh–Ritz discretisation is used to obtain eigenfrequencies and eigenmodes of the stator plate. In addition, there are often teeth over the contact surface of ring-shaped stators to minimise the friction losses during operation of the motor, and possible vibration modes are compared with respect to the deflexion of the contact points. In the laboratory, measured eigenfrequencies of the free vibrations of the plate corroborate the numerical method. Particularly, the generation of travelling waves requests the excitation of two degenerated vibration modes in a certain electrode configuration. A voltage inverter was designed for this purpose.

scholarly journals Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model

CALCOLO ◽  
2014 ◽  
Vol 52 (3) ◽  
pp. 343-369
Author(s):  
Gabriel R. Barrenechea ◽  
Tomás P. Barrios ◽  
Andreas Wachtel
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Bending Moment ◽  
Mindlin Plate ◽  
Plate Model
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