Download Random Vibrations in Spacecraft Structures Design: Theory by J. Jaap Wijker PDF

By J. Jaap Wijker

This ebook treats the random mechanical and acoustical vibrations of deterministic and statistical dynamic structures, within the high and low frequency variety. the subsequent themes are mentioned in nice detail:

Vibrations of deterministic linear mechanical dynamic platforms uncovered to mechanical random quite a bit and or enforced movement (acceleration); Vibrations of deterministic linear mechanical dynamic structures uncovered to random acoustic a lot (sound pressures; Random vibration of statistically outlined mechanical structures and quite a bit utilizing Statistical strength research (SEA); Non-linear buildings excited to random (white noise) mechanical lots analyzed through the use of the Fokker-Planck-Kolgomorov (FPK) equation.

The idea of random vibration is strongly regarding the layout of spacecraft buildings and is illustrated with easy and tougher labored examples; every one part ends with posed difficulties; frequently solutions are supplied.

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05, Q = 10. 1 g2 /Hz. Calculate the rms acceleration of the SDOF system. 53Grms . 3 Multi-Inputs and Single Output (MISO) In Fig. 15 a SDOF system is shown with both an enforced acceleration u ¨(t) at the base and a direct force F (t). The PSD function of the response x(t) will be calculated. 4 Deterministic Linear Dynamic Systems 53 Fig. 15. 163) or x ¨(t) + 2ζωn x(t) ˙ + ωn2 x(t) = 2ζωn u(t) ˙ + ωn2 u(t) + The PSD function of q(t) with f (t) = Sqq (ω) = 2ζωn ω 2 + ωn ω F (t) m F (t) = q(t). 165) where Sf f (ω) = WFmF2(ω) the PSD function of f (t), Su¨u¨ (ω) the PSD function of the enforced acceleration u ¨(t) and Sf u¨ (ω) = Su∗¨f (ω) the cross PSD function of f (t) and u ¨(t) and is in general a complex valued function.

159) now becomes E{¨ x2 (t)} = Rx¨x¨ (0) = = Su¨ 2π ∞ −∞ |H(ω)|2 (2ζωn ω)2 + ωn4 dω ωn Su¨ π (1 + 4ζ 2 ) ≈ fn QWu¨ . 146). 155), the expectation of the mean square of the displacement x(t) can be found: ωn Su π (1 + 4ζ 2 ) ≈ fn QWu . 161) E{x2 (t)} = Rxx (0) = 4ζ 2 The PSD function of the enforced acceleration u ¨(t) is given by Wu¨u¨ (f ) = (2πf )4 Wuu (f ), so that the expectation of the displacement x(t) may be expressed as E{¨ x2 (t)} E{x2 (t)} = . 162) (2πf )4 Example. 05, Q = 10. 1 g2 /Hz.

52) Sxx (ω) has the following properties: • Sxx (ω) = Sxx (−ω) • Sxx (ω) ≥ 0. The spectral moment mi of a stationary random process X(t) is defined as [154] ∞ 1 |ω|i Sxx (ω)dω. 55) |ω|4 Sxx (ω)dω. 57) m0 where γ1 is the central frequency and has a geometrical meaning of being the centroid of the spectral distribution Sxx (ω), and γ2 has the geometrical meaning of the radius of gyration of Sxx (ω) about the origin. 3 Random Process 27 where the range of δ is 0 ≤ δ < ∞. For a harmonic process, m1 = ω0 m0 and m2 = ω02 m0 , δ = 0, hence small values of δ indicate a narrow band process.

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