Related Experiment Video
Updated: Mar 15, 2026

Measurement of Chladni Mode Shapes with an Optical Lever Method
Published on: June 5, 2020
Free and forced vibrations of SC-cut quartz crystal rectangular plates with the first-order Mindlin plate equations
Rongxing Wu1, Wenjun Wang2, Guijia Chen2
1Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, Zhejiang 315211, China; Department of Architectural Engineering, Ningbo Polytechnic, 1069 Xinda Road, Beilun District, Ningbo, Zhejiang 315800, China.
Abstract:
Mindlin plate theory was used to provide accurate solutions to thickness-shear vibrations of plates, which have a much higher frequency than usual flexural vibrations and are the functioning modes of quartz crystal resonators. The vibration frequency solutions obtained with the Mindlin plate theory are proven being accurate along with mode shapes. In this paper, straight-crested wave solutions of free and forced vibrations of doubly rotated SC-cut of quartz crystal plates of rectangular shapes with four free edges are obtained with validated Mindlin plate equations. A procedure has been established for the calculation of dispersion relations, frequency spectra, mode shapes, and capacitance ratios of forced vibrations needed in resonator design.
Related Concept Videos
Forced Oscillations
Standing Waves in a Cavity
Modes of Standing Waves: II
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end....
Modes of Standing Waves - I
Torsional Pendulum
As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played...
Fluid Pressure over Flat Plate of Constant Width
The resultant force...

