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 diversity. the subsequent themes are mentioned in nice detail:
Vibrations of deterministic linear mechanical dynamic platforms uncovered to mechanical random so much and or enforced movement (acceleration); Vibrations of deterministic linear mechanical dynamic structures uncovered to random acoustic rather a lot (sound pressures; Random vibration of statistically outlined mechanical platforms and a lot utilizing Statistical power research (SEA); Non-linear buildings excited to random (white noise) mechanical lots analyzed through the use of the Fokker-Planck-Kolgomorov (FPK) equation.
The thought of random vibration is strongly regarding the layout of spacecraft constructions and is illustrated with basic and tougher labored examples; each one part ends with posed difficulties; frequently solutions are supplied.
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Extra info for Random Vibrations in Spacecraft Structures Design: Theory and Applications
Example text
Dx = L 2 L3 The natural frequency associated with the assumed mode sin( πx L ) will be fn = π 2 EI . 73 × 103 Nm2 . The bending beam is manufactured from an Al-alloy with a Young’s modulus E = 70 × 109 Pa. The cross section of the beam is a square tube with a height (width) h and h . Calculate the associated h and t from the required a wall thickness t = 20 second moment of area I. The second moment of area of the cross section is I= h4 . 133 mm. The constant running load q, has a white noise PSD Wq = 20 000 N2 /Hz and has been derived from the acoustic loads.
Fig. 12. 4 Deterministic Linear Dynamic Systems 43 At first the natural frequency fn will be calculated and after that the modal damping ratio ζ. The mean value of the displacement x(t) is μx = μkF = 0. 02. 955 × 10−4 m. 9690. 0310. We now study an example where a continuous beam loaded with a running load q will be converted to a SDOF system, using the assumed mode approach. Example. 5 kg/m must have a minimum natural frequency fn = 125 Hz. The beam is illustrated in Fig. 13. Calculate the required bending stiffness EI.
0310. We now study an example where a continuous beam loaded with a running load q will be converted to a SDOF system, using the assumed mode approach. Example. 5 kg/m must have a minimum natural frequency fn = 125 Hz. The beam is illustrated in Fig. 13. Calculate the required bending stiffness EI. To do so the deflection w(x, t) of the beam will be written as πx w(x, t) = sin η(t), L where η(t) is called the generalized coordinate or modal participation. Calculate the generalized mass mg and stiffness kg .
