Download Theory and Application of Statistical Energy Analysis by Richard H. Lyon PDF

By Richard H. Lyon

This updated moment version offers a accomplished exam of the speculation and alertness of Statistical power research (SEA) in acoustics and vibration. entire with examples and information taken from actual difficulties this specific e-book additionally explores
the impression of desktops on SEA and emphasizes computing device established SEA calculations. as well as a dialogue of the connection among SEA and different methods utilized in reaction estimation, idea and alertness of Statistical strength Anlaysis, Second
Edition, explores the elemental relationships among version and wave descriptions of systems.

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It will not always be as convenient as it is in this case, but the ordering by some parameter is a necessary condition to allow us to do the counting at all. When the ordering indices form a lattice as shown in Fig. 7, then each lattice point corresponds to an area AAk = π2/Αρ in the wavenumber plane where Ap = Lx L2 is the area of the plate. As we increase the wavenumber from On the average, this will include ktok + Ak, we include a new area ^kAk. ^KkAlAAk new modes. 10) which we term the modal density in wavenumber.

19) We see that Δ is very nearly the total damping of the two resonators. This result also emphasizes the importance of resonant interaction between the resonators because the average in Eq. 18) is dominated by integration over the bandwidth Δ. The average power flow is TiS'o {Πί2) " = ΤΓΤΠΓ (31 20) · and S. 21) with λ^[μ1ω2+{γ2+2μκ) where we assumed μ2 « 1 and Α/ω « 1. 22) Energy Sharing by Coupled Systems 59 The average interaction, therefore, is equivalent to a white noise source acting on resonator 2 of spectral density S'e .

This tendency toward energy equality is an example of "equipartition of energy", a principle that is well known in statistical mechanics. 3 of this chapter, we have discussed modal and wave descriptions of finite systems. These two ways of describing the motion are in most cases fully equivalent to each other, but that does not mean that the choice of description is arbitrary. Certain aspects of structural vibration are much more readily interpreted in one description than in the other. The effect of damping at the boundaries of a plate is readily described by wave reflection processes, but its description in modal terms is extremely complicated and tedious.

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