摘要
利用小波的时间-频率联合分辨率,提出了一种在完全非平稳随机激励下,计算分数阶阻尼线性系统响应功率谱密度的方法。方法的思路在于选用广义谐和小波,并利用小波-Galerkin近似,将具有分数阶导数的运动微分方程转化为一组以响应小波变换为未知量的代数方程,解之并求得响应小波变换后,结合随机过程功率谱密度的小波变换表达得到激励与响应功率谱密度之间的关系。为此,在频域中推导了小波-Galerkin方法必需的小波整数阶与分数阶联系系数。数值算例表明:对具有不同分数阶导数的系统,所建议的方法具有较好的适用性。
A wavelet-based approach for calculating response evolutionary power spectral density(EPSD)of the linear dynamic system endowed with fractional derivative damping subject to joint time-frequency non-stationary excitation is presented.The core of this approach is the utilizing of the generalized harmonic wavelets(GHW)and Galerkin technique to transform the fractional differential equation of motion into a set of linear algebra equations in terms of unknown wavelet coefficients of the response.Combing with the wavelet representation of the power spectral density of the non-stationary stochastic process,a relationship between the PSD of excitation and of the response is obtained.For this purpose,the GHW connection coefficients of the integer and fractional order involved in the wavelet-Galerkin technique are derived in the frequency domain for the first time.Pertinent numerical examples are presented for systems with different order fractional derivatives demonstrating the reliability of the proposed approach.
作者
孔凡
王恒
徐军
李书进
KONG Fan;WANG Heng;XU Jun;LI Shu-jin(Building Engineering Department,Wuhan University of Technology,Wuhan 430070,China;College of Civil Engineering,Hunan University,Changsha 410082,China)
出处
《振动工程学报》
EI
CSCD
北大核心
2018年第4期671-680,共10页
Journal of Vibration Engineering
基金
国家自然科学青年基金资助项目(51408451)
国家自然科学基金面上项目(51678464)
武汉理工大学研究生优秀学位论文培养项目(2017-YS-040)
关键词
随机振动
功率谱密度
广义谐和小波
联系系数
分数阶导数
random vibration
power spectral density
generalized harmonic wavelet
connection coefficient
fractional derivative
