# The response for lightly damped systems may not be

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Unformatted text preview: Typical Force Windows Response (Exponential) Windows Response (exponential) windows are used to minimize the leakage error for lightly damped systems by attenuating the response so that it decays to zero within the observation period. Normally, for lightly damped systems, a window that attenuates to 1-5 percent at the end of the response is appropriate. For heavily damped systems, a window that is similar to the decay of the system will attenuate any noise. (5-72) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + Exponential Window (10%) 1 0.8 Amplitude 0.6 0.4 0.2 0 −0.2 0 0.2 0.4 0.6 Time: (0−T) 0.8 1 Exponential Window (5%) 1 0.8 Amplitude 0.6 0.4 0.2 0 −0.2 0 0.2 0.4 0.6 Time: (0−T) 0.8 1 Exponential Window (1%) 1 0.8 Amplitude 0.6 0.4 0.2 0 −0.2 0 0.2 0.4 0.6 Time: (0−T) 0.8 1 Figure 5-40. Typical Response Windows (5-73) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + Response (Exponential) Windows Correction The windows that are added to the force and response signals must be corrected. Primarily, the response (exponential) window may add signiﬁcant damping to the resultant frequency response function. This can only be corrected after the modal damping for each mode is found. • h pq (t) = Σ A pqr eλ t r=1 r 2N • e β t h pq (t) = e β t e β t h pq (t) = e β t h pq (t) = 2N 2N r=1 Σ A pqr e λ r t r • Σ A pqr e β t eλ t r=1 Σ r=1 2N • A pqr e(λ r + β )t = Σ A pqr eλ t r=1 ˆr 2N ˆ • λr • σr ˆ • σr • ωr = σ r + j ω r = (σ r + β ) + j ω r ˆ ˆ = σr + β = σr − β ˆ = ωr ˆ 5.4 Structural Testing Conditions The test condition for any modal analysis test involves several environmental factors as well as appropriate boundary conditions. First of all, the temperature, humidity, vacuum, and gravity effects must be properly considered to match with previous analysis models or to allow the experimentally determined model to properly reﬂect the system. In addition to the environmental concerns, the boundary conditions of the system under test are very important. Traditionally, modal analysis tests have been performed under the assumption that the test boundary conditions can be made to conform to one of four conditions: (5-74) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + • • • • Free-free boundary conditions (Impedance is zero). Fixed boundary conditions (Impedance is inﬁnite) Operating boundary conditions (Impedance is correct). Arbitrary boundary conditions (Impedance is known). It should be obvious that, except in very special situations, none of these boundary conditions can be practically achieved. Instead, practical guidelines are normally used to evaluate the appropriateness of the chosen boundary conditions. For example, if a free-free boundary is chosen, the desired frequency of the highest rigid body mode should be a factor of ten below the ﬁrst deformation mode of the system under test. Likewise, for the ﬁxed boundary test, the desired...
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