Vibration of Thermally Stressed Pretwisted Cantilever Composite Plates

Abstract

Fig. 5 Variations of the magnitude of the e ow response kk ( (u, v)kk as a function of the suction wave number ® and wave speed cr for Re= 5 ££ 10 3 ; continuous and dashed lines correspond to the symmetric and asymmetric suctions, respectively. eigensolution (TS wave) and a unique asymmetric particular solution of the inhomogeneous problem. A very large response of the e ow is possible in this case but requires a perfect tuning between the neutral TS wave and the surface suction wave. Results presented in Fig. 3 demonstrate that linear theory is inadequate in the neighborhood of (linear) neutral stability points and a nonlineartheorymustbeusedregardlessofthemagnitudeofthesuction. The nonlinear effectmay expand therangeofthe TSinstability and may initiate an instability of the type studied in Ref. 1. Figure 5 shows e ow response to surface suction for the subcritical value of Reynolds number Re = 5 £ 10 3 when all TS waves are stable. The near resonance between the TS and the surface suction waves may lower the critical Reynolds number due to the subharmonic character of the instability, provided that suction with sufe ciently large amplitude is used. IV. Conclusions The preceding results demonstrate that small suction nonuniformities may affect the e owinstability only if they contain the critical or near-critical suction waves, that is, waves with the same or almost the same wave number a and phase speed cr as the neutral TS waves. Suction waves slightly detuned with the neutral TS waves mayaffectinstabilityprovidedthattheamplitudeofsuctionnonuniformitiesislargeenough. Our conclusionscould be readilytestedin a e owwith a fewsuction slots at the wall that could emulate suction waves with the desired wave number and phase speed.