Dynamics Of Cantilever Beams With Variable Cross-section And Its Application In Piezoelectric Energy Harvester

Piezoelectric vibration energy harvester is a kind of electromechanical coupling system that can convert vibrational energy to electric with the advantages of fast response,no pollution,long service life,simple structure and easy to assemble,for microelectronics,remote monitoring and other low-power components to provide power supply.Piezoelectric energy harvester structure dynamics analysis is the key of How to improve the energy conversion efficiency.Now,the piezoelectric energy harvester mostly adopts the uniform beam.In recent years,relevant studies have shown that the beam with variable section has uniform stress and strain distribution,which is conducive to improving the energy collection efficiency of piezoelectric energy harvester.This paper is considered using a variable cross-section cantilever beam as the piezoelectric energy harvester in the form of the vibrator structure form.Firstly,the natural frequency is solved by asymptotic perturbation analysis.Then,the dynamic response of variable cross-section cantilever beam is solved by the multi-scale(MTS)method.In the end,the finite element method is used for studying the influence of variable section parameters of piezoelectric vibration energy harvester on its output voltage.The main research contents of this paper are divided into the following parts:(1)Analysis of natural frequency of variable section beam.The natural frequency of the variable section beam is studied.Based on the vibration theory,the model is simplified as Euler-Bernoulli beam,and the differential equation of free vibration of variable section beam is established.Asymptotic perturbation analysis is used for solving the natural frequency of the variable cross-section beam.After that,the numerical results are compared with the finite element simulation,experimental examples and examples of other methods in literature to testify the effectiveness of present analysis.(2)Dynamic response analysis of variable cross-section cantilever beams.The differential equation of motion of the variable section beam suffering the basic excitation is obtained using the Newton's law of motion.By applying the MTS method to analyze the differential equation of motion with perturbation,the amplitude frequency response equation is obtained.Numerical simulation results are used to analyze the influence of variable cross-section,the basic excitation and damping on structural response.(3)Analysis of power generation characteristics of piezoelectric energy harvester with variable cross-section cantilever beam.Using variable cross-section cantilever beam structure as the oscillator structure of the piezoelectric energy harvester,the finite element method is used for simulating variable cross-section piezoelectric energy harvesters by changing the width ratio between the free end of the fixed end in modal analysis and harmonic response analysis.The influence of the width of the piezoelectric energy harvester in the same natural frequency on the output energy density is simulated.