PSI - Issue 19

Zhu Li et al. / Procedia Structural Integrity 19 (2019) 528–537 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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2. Computational Modeling Approach

The proposed modeling approach is schematically shown in Fig. 1. The modeling approach is based on the discretization concept that time varying response PSDs for a given structure can be computed from a time-varying input PSD function on the basis of discretization of the input PSD. The time-varying input PSD is formed by three swept narrowbands superimposed on one stationary wideband. The time varying input PSD can be decomposed into u number of finite discrete PSD positions and corresponding response PSDs can be computed from all discrete PSD positions. Each response PSD position is further divided into v number of narrow frequency band of PSD segments; The PSD segments are divided sufficiently narrow frequency bandwidth to assume that the process is narrowband one. Therefore, the stress distribution of each narrowband PSD segment can be characterized by the probability density function of a Rayleigh distribution. Different PSD narrowband segments can be associated with different Rayleigh distributions. The fatigue damage for each PSD narrowband segment can be then determined by the stress life curve (S-N curve) on the basis of Palmgren –Miner’s rule . Finally, the total fatigue damage for each PSD position can be determined by summation of damage values of each narrowband segment. In order to calculate the Fatigue Damage Index (FDI) for all PSD position, the modeling procedure is repeated for each PSD position of the complete evolutionary response PSD.

Fig. 1. Schematic representation of computational modeling approach.

2.1. Input Power Spectrum Density

Many machine systems experience complex random vibrations due to service operational conditions. Several standards such as MIL-STD 810 and AECTP 400, were developed to represent actual operational loading conditions experienced by machine systems such as helicopters, tracked vehicles, and jet engines [19]. The AECTP 400 mechanical environmental tests are obtained from field test data of various vehicle types. A subset of AECTP 400 standard, the B1 tracked vehicle test spectrum, describes a wideband random vibration superimposed by three sweeping high-amplitude narrowbands [19]. The B1 test spectrum is used for the modeling approach proposed in this paper because it accurately represents the complex vibration environment that is experienced by tracked vehicles. The B1 spectrum consists of three swept narrowbands and one stationary wideband random PSD. The first narrowband sweeps from 20 Hz to 170 Hz, the second one sweeps from 40 Hz to 340 Hz, and the third one sweeps from 60 Hz to 510 Hz. The sweep rate is defined within the range of one-half to one octave per minute. Table 1 shows the simplified sweep rate values (1 Hz/sec, 2 Hz/sec, and 3 Hz/sec for first, second, and third narrowbands, respectively) that are assumed to reduce the computational intensity of the model.