变截面压电悬臂梁能量采集器在高斯白噪声激励下的稳态统计特性研究  

Study on the steady state statistical characteristics of variable-section piezoelectric cantilever energy harvester under Gaussian white noise excitation

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作  者:周坤涛 杨涛[1] 葛根[1] 郝淑英[3] 冯晶晶[3] 张琪昌[4] ZHOU Kun-tao;YANG Tao;GE Gen;HAO Shu-ying;FENG Jing-jing;ZHANG Qi-chang(School of Mechanical Engineering,Tiangong University,Tianjin 300387,China;Engineering Training Center,Tianjin University of Technology,Tianjin 300384,China;School of Mechanical Engineering,Tianjin University of Technology,Tianjin 300384,China;School of Mechanical Engineering,Tianjin University,Tianjin 300072,China)

机构地区:[1]天津工业大学机械工程学院,天津300387 [2]天津理工大学工程训练中心,天津300384 [3]天津理工大学机械工程学院,天津300384 [4]天津大学机械工程学院,天津300072

出  处:《振动工程学报》2024年第5期864-874,共11页Journal of Vibration Engineering

基  金:国家自然科学基金资助项目(12072234,12072233,11872044)。

摘  要:环境振动是一种非周期、随机的宽频激励,研究振动能量采集器在环境振动下的能量采集特性具有重要意义。本文采用改进随机平均法,求解了变截面压电梁在高斯白噪声激励下的等效振幅、位移、速度的稳态概率密度函数,位移与速度的联合概率密度函数以及稳态均方输出电压,随后研究了变截面压电梁的能量采集效能。结果表明:负载电阻一定时,截面系数β>0时的变截面压电梁相比β=0时的等截面压电梁有更好的稳态均方输出电压;截面系数β>0时,随着电阻电容乘积的倒数的增加,变截面压电梁的均方电压均呈现逐渐减小的趋势,当电阻电容乘积的倒数值一定时,β值越大,均方电压也越高;随着噪声强度的增加,变截面压电梁的均方电压均呈现逐渐增大的趋势,当噪声强度一定时,β值越大,均方电压也越高。本文研究结果可为变截面压电悬臂梁能量采集系统的设计及应用提供理论依据。Environmental vibration is one of the non-periodic and random broadband excitations.It is of great significance to study the characteristics of vibration energy harvesters under environmental vibrations.In this paper,the modified stochastic averaging method is used to solve the following parameters of piezoelectric beam with a variable cross-section:steady-state probability density function of equivalent amplitude,displacement and velocity,joint probability density function of displacement,and velocity and steady-state mean square output voltage.Then the study investigates the energy acquisition efficiency of a piezoelectric beam with a variable cross-section under Gaussian white noise excitation.The results show that when the load resistance reaches a certain value,the variable section piezoelectric beam with a section coefficient β>0 can produce better steady-state mean square output voltage than the constant section piezoelectric beam with β=0;when the section coefficient β>0,with the increase of the reciprocal of the product of resistance and capacitance,the mean square voltage of the variable-section piezoelectric beam shows a gradually decreasing trend.The trend shows the following rules:when the reciprocal value of the resistance and capacitance reaches a certain value,the larger the β value is,the higher the mean square voltage will become;with the increase of the noise intensity,the mean square voltage of the variable-section piezoelectric beams shows a trend of increasing gradually;when the noise intensity reaches a certain value,the larger the β value is,the higher the mean square voltage will become.The research results in this paper can provide a theoretical basis for the design and application of the variable-section piezoelectric cantilever energy harvesting system.

关 键 词:能量采集器 变截面压电悬臂梁 高斯白噪声激励 稳态概率密度 均方电压 

分 类 号:O324[理学—一般力学与力学基础] TB34[理学—力学] TM91[一般工业技术—材料科学与工程]

 

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