A hybrid method for analysing stationary random vibration of structures with uncertain parameters

Liu, Fan; Zhao, Yan

doi:10.1016/j.ymssp.2021.108259

Cited by 13 publications

(6 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As the expansion coefficients are calculated, the approximate probability distributions of the CPSD and CSD of the system can be obtained by calculating the sample values of these responses using Equations. ( 26) and (27). In this numerical example, 10 6 samples were generated for each polynomial base, and the corresponding sample values of CPSD and CSD were calculated using Equations ( 26) and (27).…”

Section: Single-degree-of-freedom Systemmentioning

confidence: 99%

“…( 26) and (27). In this numerical example, 10 6 samples were generated for each polynomial base, and the corresponding sample values of CPSD and CSD were calculated using Equations ( 26) and (27). The probability distribution of the displacement CPSD at 𝜔 = 3.4 rad∕s and 𝑡 = 15 s is shown in Figure 5.…”

Section: Single-degree-of-freedom Systemmentioning

confidence: 99%

“…In the PDD method, the values of 𝑅 and 𝑃 are 1 and 2, respectively, whereas the 𝑚 value is maintained at 5. A total of 10 5 samples are generated for each polynomial base, and the corresponding sample values of CPSD and CSD are calculated using Equations ( 26) and (27), and the approximate probability distributions can be obtained. Figure 14 shows the probability distribution of the acceleration CPSD when 𝑡 = 8 s and 𝜔 = 7.0 rad∕s is shown.…”

Section: 2mentioning

confidence: 99%

“…Because of the advantages of PSD for describing random vibration, extending the random vibration analysis of deterministic structures and developing the analysis of the CPSD and conditional standard deviation (CSD) of structures with uncertain parameters can better meet the theoretical and engineering requirements. In previous research by the authors, the PDD combined with the pseudo excitation method (PEM) for analysing stationary random vibration of stochastic structures has been proposed 27 . In fact, the statistical characteristics of many random loads demonstrate time‐dependent evolution characteristics.…”

Section: Introductionmentioning

confidence: 99%

“…In previous research by the authors, the PDD combined with the pseudo excitation method (PEM) for analysing stationary random vibration of stochastic structures has been proposed. 27 In fact, the statistical characteristics of many random loads demonstrate time-dependent evolution characteristics. Such characteristics are generally modelled using an evolutionary PSD function.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Nonstationary random vibration analysis of structures with uncertain parameters based on a polynomial dimensional decomposition

Liu

Zhao

2022

Earthq Engng Struct Dyn

Self Cite

View full text Add to dashboard Cite

Based on polynomial dimensional decomposition (PDD), a novel method for analysing nonstationary random vibration of structures with uncertain parameters is proposed in this paper. The uncertain structural parameters are assumed to be independent random variables, with certain types of probability distributions; thus, the nonstationary random vibration responses of the structures become stochastic functions of these uncertain parameters. A dimensional decomposition and Fourier expansion were applied to calculate the statistical characteristics of the nonstationary random vibration responses of the structures. To calculate the conditional power spectral density (CPSD) and conditional standard deviation (CSD) of the nonstationary random vibration responses, CPSD and CSD were explicitly expressed using expansion coefficients and polynomial basis. Subsequently, the probability distributions of the structural responses can be effectively calculated in terms of these explicit expressions. Dimension-reduction integration and Gauss numerical integration were applied to calculate expansion coefficients. The validity of the proposed method was verified by numerical examples, including a single-degree-of-freedom system and a multi-degree-offreedom system (reinforced concrete shear wall). The results indicate that the proposed method is as accurate as Monte Carlo simulation (MCS), whereas the proposed method requires considerably smaller number of nonstationary random vibration analyses than MCS. Moreover, the nonstationary random vibration analysis of a long-span cable-stayed bridge demonstrates that the proposed method is feasible for quantifying the uncertainties of the nonstationary random vibration responses of complex engineering structures with uncertain parameters.

show abstract

Section: Single-degree-of-freedom Systemmentioning

confidence: 99%

Section: Single-degree-of-freedom Systemmentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations