摘要
对于受到由分数阶导数模拟的粘弹性阻尼的非线性随机振动结构,本文给出了一种计算响应的功率谱密度方法。借助标准的随机平均法,首先得到了振动结构随机响应振幅的稳态概率密度。对于原振动结构的非线性项,运用改进的统计线性化方法得到了均方意义下的等价线性振动结构,并求得了其响应的依赖于振幅的条件功率谱密度。综合以上的结果,针对随机振动响应的功率谱密度的估计,通过与数值模拟结果进行验证,从而证明了所提方法的有效性和准确性。
A procedure for the response power spectral density estimate of a fractionally damped stochastic nonlinear vibration structure is proposed.The stationary probability density function of the response is firstly obtained with the application of stochastic averaging technique;and then improved statistical linearization is adopted to transform the original system into its linear equivalent,for which the conditional power spectral density can be derived immediately.Finally,an analytical formula of the response power spectral density of the fractionally damped vibration structure is calculated by integrating the obtained results.Numerical simulation verifies the validity of the proposed procedure.
出处
《应用力学学报》
CAS
CSCD
北大核心
2013年第3期401-405,477,共5页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(11172233
11202160)
关键词
分数阶导数
粘弹性结构阻尼
随机平均法
统计线性化
功率谱密度
fractional derivative
viscoelastic structural damping
stochastic averaging
statistical linearization
power spectral density.
