PSI - Issue 19

Giovanni M. Teixeira et al. / Procedia Structural Integrity 19 (2019) 175–193 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 9. Truck chassis being excited at 12 loading channels.

The input PSD matrix and transfer functions need to be consistently defined in regards to units, type of load and its magnitudes. Fig. 10 provides an example (G=9800mm/s2) of units consistency using the [mm-t-s] system.

Fig. 10. Consistent units in the linear transformation. The stress PSD G σ (f), as derived in Eq. 13, is a scalar function of frequency and consequently can be directly used in the equation below to calculate the spectral moments:

  f m f G f df max 0     n n

(15)

There is a wide range of PDFs available in the literature (Quigley, J. et al. (2016)) that are appropriate for the various narrow and broad band scenarios, Gaussian and non-Gaussian loads, stationary and non-stationary conditions. As an example, the PDF proposed by Dirlik, T. (1985) is written as follows:

  R 0 1 D D Z S = e e D Ze Q R 2 m p           2 2 2 -Z Q -Z -Z 1 2 2R 2 3 2

(16)

It is dependent on several parameters (Equations 17) that are basically combinations of the four spectral moments (m 0 , m 1 , m 2 , m 4 ).