A probability density function of stress amplitude applicable to power spectral density curves of structural random vibration response

• Published in: International journal of fatigue 2024-09, Vol.186, p.108408, Article 108408
• Main Authors: Wu, Shao-Dong, Shang, De-Guang, Shi, Feng-Tian, Zhao, Bo-Cheng
• Format: Article
• Language: English
• Subjects: Broadband signal; Monte Carlo method; Power spectral density; Probability density function; Random vibration
• ISSN: 0142-1123; 1879-3452
• DOI: 10.1016/j.ijfatigue.2024.108408

•The rainflow distribution was divided into three regions based on the value of zero-order spectral moment of power spectral density curve.•Each region of the rainflow distribution was fitted using Rayleigh or exponential functions, respectively.•A probability density function combining two Rayleigh functions and an exponential function was proposed. The power spectral density curves of the random vibration response of a plate specimen with different spectral width coefficients were obtained by selecting different frequency ranges, and the probability distributions of the stress amplitudes were obtained by applying Monte Carlo method and rainflow counting method. Each probability distribution was divided into three segments by the corresponding zero-order spectral moment value, and each segment was fitted using either a Rayleigh function or an exponential function. Finally, a probability density function of stress amplitude was proposed by combining two Rayleigh functions and an exponential function. The proposed probability density function can be used to obtain the stress amplitude probability distribution for the power spectral density curves of structural random vibration response with any bandwidth, and the accuracy of the proposed function was verified based on the response data of a specimen of 7075-T651 aluminum alloy material under the action of six typical power spectral curves.