Modeling and Analysis of Multiple Attached Masses Tuning a Piezoelectric Cantilever Beam Resonant Frequency

Yuejuan Li,Wei Qi,Xiaolu Zhang,Qiubo Wang,Xulei Hou,Sara Amoroso

doi:10.1155/2020/6971983

Abstract

Mechanical vibrations have been an important sustainable energy source, and piezoelectric cantilevers operating at the resonant frequency are regarded as one of the effective mechanisms for converting vibration energy to electricity. This paper focuses on model and experimental investigations of multiple attached masses on tuning a piezoelectric cantilever resonant frequency. A discrete model is developed to estimate the resonant frequencies’ change of a cantilever caused by multiple masses’ distribution on it. A mechanism consisted of a piezoelectric cantilever with a 0.3 g and a 0.6 g movable mass along it, respectively, is used to verify the accuracy of the proposed model experimentally. And another mechanism including a piezoelectric cantilever with two 0.3 g attached masses on it is also measured in the designed experiment to verify the discrete model. Meanwhile, the results from the second mechanism were compared with the results from the first one in which the single attached mass is 0.6 g. Two mechanisms have wildly different frequency bandwidths and sensitivities although the total weight of attached masses is the same, 0.6 g. The model and experimental results showed that frequency bandwidth and sensitivity of a piezoelectric cantilever beam can be adjusted effectively by changing the weight, location, and quantity of attached masses.

Highlights

Mechanical vibrations have been an important sustainable energy source, and piezoelectric cantilevers operating at the resonant frequency are regarded as one of the effective mechanisms for converting vibration energy to electricity. is paper focuses on model and experimental investigations of multiple attached masses on tuning a piezoelectric cantilever resonant frequency
Introduction e mechanical vibration is one of the most important sustainable energy sources for several decades and it can be converted to electricity by electrostatic, electromagnetic, and piezoelectric transductions
To validate the variation of resonant frequency due to attached masses, a piezoelectric cantilever beam that converts deflection caused by mechanical vibration into electricity is used to verify the developed model. e piezoelectric cantilever beam DT2-028K produced by Measurement Specialties Inc. is adopted in this experiment

Summary

Modelling of Cantilever Beam-Attached Multiple Masses

Where vn is the dimensionless nth-mode eigenvalue, l is the length of cantilever, E is the elasticity modulus, I is the area moment of inertia about the neutral axis, and m’ is the mass per unit length of the cantilever beam This equation can only identify the resonant frequency of a cantilever beam with fixed configuration. Once multimodes’ vibration needs to be taken into consideration, the advantage of Rayleigh’s method will no longer exist since it is difficult to get deflection at all positions In this case, Newton’s second law will be adopted to obtain resonant frequencies of multimodes’ vibration. Instead of the continuous approach of Rayleigh’s method, the cantilever beam can be separated into multiple segments with Newton’s second law to derive the equations of motion for individual segments With this discrete approach, the resonant frequencies can be obtained by lumping all the segments into a matrix representation.

A2 A3 A4

Experimental Validation of the Proposed Model by Piezoelectric Cantilever

Case I

Case II

Conclusion