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In This Article

  • Summary
  • Abstract
  • Introduction
  • Protocol
  • Representative Results
  • Discussion
  • Acknowledgements
  • Materials
  • References
  • Reprints and Permissions

Summary

A simple method of measuring the Chladni mode shape on an elastic plate by the principle of an optical lever is proposed.

Abstract

Quantitatively determining the Chladni pattern of an elastic plate is of great interest in both physical science and engineering applications. In this paper, a method of measuring mode shapes of a vibrating plate based on an optical lever method is proposed. Three circular acrylic plates were employed in the measurement under different center harmonic excitations. Different from a traditional method, only an ordinary laser pen and a light screen made of ground glass are employed in this novel approach. The approach is as follows: the laser pen projects a beam to the vibrating plate perpendicularly, and then the beam is reflected to the light screen in the distance, on which a line segment made of the reflected spot is formed. Due to the principle of vision persistence, the light spot could be read as a bright straight line. The relationship between the slope of the mode shape, length of the light spot and the distance of the vibrating plate and the light screen can be obtained with algebraic operations. Then the mode shape can be determined by integrating the slope distribution with suitable boundary conditions. The full-field mode shapes of Chladni plate could also be determined further in such a simple way.

Introduction

Chladni mode shapes are of great interest in both science and engineering applications. Chladni patterns are reactions of physical waves, and one can illustrate the wave pattern with various methods. It is a well-known method to show the various modes of vibration on an elastic plate by outlining the nodal lines. Small particles are always employed to show the Chladni patterns, since they can stop at the nodes where the relative vibrating amplitude of the plate is zero, and the positions of the nodes vary with resonant mode to form various Chladni patterns.

Many researchers have paid attention to various Chladni patterns, but they only show....

Protocol

1. Experimental setup and procedures

NOTE: Set up the experimental system as shown in Figure 2.

  1. Preparation of the vibration system
    1. Prepare three 1.0-mm-thickness mirrored circular acrylic plates with diameter of 150 mm, 200 mm and 250 mm respectively. Drill a hole of 3 mm in diameter at the center of each plate. Mark several black points every 5 mm along an arbitrary radius.
    2. Attach each plate to the actuate bar of the vibrator w.......

Representative Results

The excitation frequency that can excite axisymmetric Chladni pattern is determined through the frequency sweeping test. Three circular acrylic plates with diameters of 150 mm, 200 mm and 250 mm are tested, and results show that the first order axisymmetric resonance frequencies are 346 Hz, 214 Hz and 150 Hz for the three plates respectively. It is concluded that with larger diameter, the plate is more flexible, and the corresponding resonance frequency will be smaller. The Chladni patterns of the acrylic plate with diff.......

Discussion

The optical lever method is adopted in this paper to determine the mode shape of a plate, since the Chladni pattern can only show the nodal lines of a vibrating plate. To determine the mode shape of the plate, the relationship between the slope and distance of the light screen and spot length should be obtained in advance. Then through definite integration calculation, the mode shape of the Chladni pattern could be quantitatively determined.

Generally, the whole process of the present approach.......

Acknowledgements

This work was supported by National Natural Science Foundation of China (grant no. 11772045) and Education and Teaching Reform Project of University of Science and Technology Beijing (grant no. JG2017M58).

....

Materials

NameCompanyCatalog NumberComments
Acrylic platesDongguan Jinzhu Lens Products FactoryThree 1.0-mm-thickness mirrored circular acrylic plates with diameter of 150 mm, 200 mm and 250 mm respectively. They are easily deformed.
Laser penDeli Group2802Red laser is more friendly to the viewer. The finer the laser beam, the better.
Light screenNorthern Tempered Glass Custom Taobao StoreSeveral layers of frosted stickers can be placed on the glass to achieve the effect of frosted glass.
RulerDeli GroupDL8015The length is 1m and the division value is 1mm.
Signal generatorDayang Science Education Taobao StoreTFG6920ACommon ones in university laboratories are available.
VibratorDayang Science Education Taobao StoreThe maximum amplitude is 1.5cm.The power is large enough to cause a noticeable phenomenon when the board vibrates. Otherwise, add a power amplifier.

References

  1. Waller, M. D. Vibrations of free circular plates. Part 1: Normal modes. Proceedings of the Physical Society. 50 (1), 70-76 (1938).
  2. Waller, M. D. Vibrations of free square plates: part I. Normal vibrating modes.

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Chladni Mode ShapesOptical Lever MethodVibration SystemResonance FrequencyLight PathMeasurement System

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