Acoustic resonance associated with vibrations of an array of plates in a subsonic flow

The acoustic resonance effect occurring in the vibrations of an array of profiles (cascade) in a gas flow has been studied by a number of authors [1–8]. Relying on assumptions of a heuristic nature [1, 2, 7, 8] and using rather crude models [4, 6], they have derived criteria governing the acoustic resonance regimes and given the effect a certain physical interpretation. However, many problems of a physical bearing with regard to the quantitative and qualitative principles of the effect have been left unresolved. For a more complete and rigorous solution of the problem the author has previously [9, 10] analyzed the natural modes of a gas flowing past an array of plates It was determined that in the array domain the vibrational modes of the gas are localized in the vicinity, of the array and the eigenvalues are determined by the characteristic dimensions of the interstitial channel (as an open resonator). Also, the eigenfrequences were determined for the gas in the flow plane with the array absent [9]. Under spatial periodic conditions, such that the flow in the plane can be considered as a certain model of flow in an annular duct, these eigenfrequencies concurred with those obtained earlier in [1, 2, 4–6]. The results of [9, 10] are used in the present study as a basis for investigating certain laws and relations governing the unsteady aerodynamic characteristics of arrayed profiles in or close to regimes such that the gas can execute natural vibrations in the array domain and in an annular duct in the absence of the array.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 139–144, September–October, 1972.