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程长明 彭志科 孟光. 一类非线性系统的随机振动频率响应分析研究[J]. 力学学报, 2011, 43(5): 905-913. DOI: 10.6052/0459-1879-2011-5-lxxb2010-741
引用本文: 程长明 彭志科 孟光. 一类非线性系统的随机振动频率响应分析研究[J]. 力学学报, 2011, 43(5): 905-913. DOI: 10.6052/0459-1879-2011-5-lxxb2010-741
Changming Cheng Zhike Peng Guang Meng. Random vibration frequency response analysis of nonlinear systems based on volterra series[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 905-913. DOI: 10.6052/0459-1879-2011-5-lxxb2010-741
Citation: Changming Cheng Zhike Peng Guang Meng. Random vibration frequency response analysis of nonlinear systems based on volterra series[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 905-913. DOI: 10.6052/0459-1879-2011-5-lxxb2010-741

一类非线性系统的随机振动频率响应分析研究

Random vibration frequency response analysis of nonlinear systems based on volterra series

  • 摘要: Volterra级数是研究非线性系统的一种重要数学工具, 它可看作线性系统理论中的卷积运算在非线性系统分析中的推广. 基于Volterra级数, 给出了受高斯白噪声激励下的非线性系统输出功率谱的计算公式. 公式表明, 该系统输出功率谱可用激励强度的多项式函数来表示, 其结果为研究激励强度对非线性系统输出功率谱的影响提供了有效途径.

     

    Abstract: Volterra series is a powerful mathematical tool fornonlinear system analysis, which is essentially an extension of theconvolution operation from linear systems to nonlinear systems. In thisstudy, based on the Volterra series, an analytical expression is derived tocalculate the power spectrum density (PSD) for the output of nonlinearsystems subjected to Gaussian white noise excitation. This expressionreveals that the PSD of the nonlinear system can be expressed as polynomialfunction of the input intensity. This expression provides an efficient wayto study the effect of the input intensity of a Gaussian white noiseexcitation on the PSD of nonlinear system output.

     

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