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Fig. 2. Coupled plates used in numerical simulations (all dimensions are in m).

Figure 2 Coupled plates used in numerical simulations (all dimensions are in m).

Related Figures (11)

Fig. 1. Probability density functions of participation factors for coupled RR plates: (a) pdf of self-terms Wy? and (b) pdf of cross-terms yw? il corresponding to immediate neighbours. important. Observations from numerical simulations suggest that wy? has a bimodal probability distribution. A typical example for the coupled rectangular (RR) plates considered below is shown in Fig. la. The locations of the peaks depend on the connection strength of the joint between the subsystems. The reason for this is that each mode tends to be more-or-less localised within one particular subsystem rather than being spread uniformly across the system. Finally, the cross-mode participation factors have zero mean and probability distributions that appear more Gaussian in distribution—an example is shown in Fig. |b.
Fig. 1. Probability density functions of participation factors for coupled RR plates: (a) pdf of self-terms Wy? and (b) pdf of cross-terms yw? il corresponding to immediate neighbours. important. Observations from numerical simulations suggest that wy? has a bimodal probability distribution. A typical example for the coupled rectangular (RR) plates considered below is shown in Fig. la. The locations of the peaks depend on the connection strength of the joint between the subsystems. The reason for this is that each mode tends to be more-or-less localised within one particular subsystem rather than being spread uniformly across the system. Finally, the cross-mode participation factors have zero mean and probability distributions that appear more Gaussian in distribution—an example is shown in Fig. |b.
Physical and geometric properties (SI units) for plates | and 2 Table 1
Physical and geometric properties (SI units) for plates | and 2 Table 1
Fig. 3. Example transfer mobility for RR plate. vetoed. LOW UNM MHLOUCIULE FHOUGE OVEILUP UPPPONUTLALLOTS JOR £4 Lit 7 At low modal overlap the EICs in Eq. (8) are dominated by the self terms, i.e. those (in the numerator) for which k =j. For moderate M, nearest-neighbour mode interactions start to become important (i.e. those terms for which k = 7+1). Low and moderate M approximations for the EICs, and hence for the ACLFs, can be made by including only these few terms. Fig. 5 shows one example, for which the approximations can be seen to be good for M<0.3 or 0.7 respectively, or thereabouts. One consequence of this is that for low or
Fig. 3. Example transfer mobility for RR plate. vetoed. LOW UNM MHLOUCIULE FHOUGE OVEILUP UPPPONUTLALLOTS JOR £4 Lit 7 At low modal overlap the EICs in Eq. (8) are dominated by the self terms, i.e. those (in the numerator) for which k =j. For moderate M, nearest-neighbour mode interactions start to become important (i.e. those terms for which k = 7+1). Low and moderate M approximations for the EICs, and hence for the ACLFs, can be made by including only these few terms. Fig. 5 shows one example, for which the approximations can be seen to be good for M<0.3 or 0.7 respectively, or thereabouts. One consequence of this is that for low or
ig. 4. Variation of apparent coupling loss factor with modal overlap: (a) 500 Hz centre frequency, (b) 1500 Hz centre frequency — .R, DD, - . . PP,- ++ ee eee damping loss factor.
ig. 4. Variation of apparent coupling loss factor with modal overlap: (a) 500 Hz centre frequency, (b) 1500 Hz centre frequency — .R, DD, - . . PP,- ++ ee eee damping loss factor.
Fig. 5. Apparent coupling loss factor for PP plates, 1500 Hz centre frequency: — moderate and - — - — - — - — low modal overlap approximations.
Fig. 5. Apparent coupling loss factor for PP plates, 1500 Hz centre frequency: — moderate and - — - — - — - — low modal overlap approximations.
Fig. 6. Convergence of 95 percentile of #,, as a function of normalised standard deviation of local natural frequencies, various modal overlap, RR plates, centre frequency 1500 and 100 Hz bandwidth.
Fig. 6. Convergence of 95 percentile of #,, as a function of normalised standard deviation of local natural frequencies, various modal overlap, RR plates, centre frequency 1500 and 100 Hz bandwidth.
Fig. 7. ACLF #,, for RR plates at 1500 Hz, frequency bandwidth 400 Hz, from CMS/perturbation approach: mean ACLF, — - — - — S and 95 percentile ACLF.
Fig. 7. ACLF #,, for RR plates at 1500 Hz, frequency bandwidth 400 Hz, from CMS/perturbation approach: mean ACLF, — - — - — S and 95 percentile ACLF.
onservative compared with the perturbation and random centre frequency selection approaches (see Figs. 8b ind 10a). This may be due to the fact that these statistics are estimated from a relatively small sample of modes large enough to estimate mean and variance with some confidence, perhaps, but not distributions anc -orrelations).
onservative compared with the perturbation and random centre frequency selection approaches (see Figs. 8b ind 10a). This may be due to the fact that these statistics are estimated from a relatively small sample of modes large enough to estimate mean and variance with some confidence, perhaps, but not distributions anc -orrelations).
‘ig. 10. ACLF 7; for RR plates at 1500 Hz, frequency bandwidth 50 Hz: (a) random centre frequency selection and (b) sampling from srobability distribution; CLF, mean ACLF, — - — - — 5 and 95 percentile ACLF.
‘ig. 10. ACLF 7; for RR plates at 1500 Hz, frequency bandwidth 50 Hz: (a) random centre frequency selection and (b) sampling from srobability distribution; CLF, mean ACLF, — - — - — 5 and 95 percentile ACLF.
‘ig. 11. ACLF 7. at 1500Hz, frequency bandwidth 50Hz from CMS/perturbation approach: (a) DD plates and (b) PP plates; CLF, mean ACLF, — - — - — 5 and 95 percentile ACLF.
‘ig. 11. ACLF 7. at 1500Hz, frequency bandwidth 50Hz from CMS/perturbation approach: (a) DD plates and (b) PP plates; CLF, mean ACLF, — - — - — 5 and 95 percentile ACLF.
Related topics:
EngineeringFinite Element Analysis (FEA)Sound and VibrationStatistical Energy AnalysisConfidence Limit
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