Abstract
The stability and nonlinear vibration of a composite laminated plate with simply supported boundary conditions in subsonic compressible airflow subjected to transverse periodic external excitation are investigated. The equation of motion of the plate is established by using the von Karman’s nonlinear plate theory. The linear potential flow theory considering the compressibility of the airflow is adopted to formulate the aerodynamic model. The nonlinear ordinary differential equation of motion of the plate is obtained by applying the assumed mode method. The critical divergence velocity and the flutter velocity of the plate are obtained by analyzing the natural frequencies of the linear system. The effects of the ply angle and the compressibility of the airflow on the critical divergence velocities and the flutter velocities of the plate are investigated. For the nonlinear system, the displacement time response of the plate subjected to accelerating airflow and transverse harmonic excitation is presented to investigate the vibration properties. The effects of the subsonic airflow on the resonance properties of the system are analyzed from the amplitude frequency curves of the plate under different flow velocities. From the study, it can be seen that with the flow velocity increasing, the natural frequencies of the plate decreases and the plate may exhibit instability of the divergence or flutter type. With the ply angle increasing from 0° to 90°, the critical divergence velocity increases and then decreases, and the flutter velocity decreases. The critical divergence velocity and the flutter velocity of the plate obtained from the compressible aerodynamic model are smaller than those obtained from the incompressible model. When the plate is in instability of divergence type, the plate vibrates with smaller amplitude around a non-zero point of equilibrium, and when the plate is in instability of flutter type, the plate vibrates with larger amplitude around a non-zero point of equilibrium. When the flow velocity exceeds the divergence velocity, the amplitude frequency curve of the plate is an irregular curve with larger vibration amplitudes and the plate may be in a chaotic motion state.
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References
Dugundji J, Dowell EH, Perkin B (1963) Subsonic flutter of panels on continuous elastic foundations. AIAA J 5(1):1146–1154
Rosenberg GS, Youngdahl CK (1962) A simplified dynamic model for the vibration frequencies and critical coolant flow velocity for reactor parallel plate fuel assemblies. Nucl Sci Eng 13:91–102
Smissaert GE (1969) Static and dynamic hydroelastic instabilities in MTR-Type fuel elements part II. Theoretical investigation and discussion. Nucl Eng Des 9(1):105–122
Kim G, David DC (1995) Hydrodynamic instabilities in flat-plate-type fuel assemblies. Nucl Eng Des 158(1):1–17
Weaver DS, Unny TE (1970) The hydroelastic stability of a flat plate. J Appl Mech 37(1):823–827
Dowell EH (1967) Nonlinear oscillations of a fluttering plate. II. AIAA J 5(10):1856–1862
Kornecki A, Dowell EH, O’brien J (1976) On the aeroelastic instability of two-dimensional panels in uniform incompressible flow. J Sound Vib 47(2):163–178
Yao G, Li FM (2013) Chaotic motion of a composite laminated plate with geometric nonlinearity in subsonic flow. Int J Non Linear Mech 50:81–90
Li P, Yang YR, Zhang ML (2011) Melnikov’s method for chaos of a two-dimensional thin panel in subsonic flow with external excitation. Mech Res Commun 38(7):524–528
Yao G, Li FM (2015) Nonlinear vibration of a two-dimensional composite laminated plate in subsonic air flow. J Vib Control 21(4):662–669
Tubaldi E, Amabili M (2013) Vibrations and stability of a periodically supported rectangular plate immersed in axial flow. J Fluids Struct 39:391–407
Gibbs SC, Sethna A, Wang I, Tang D, Dowell E (2014) Aeroelastic stability of a cantilevered plate in yawed subsonic flow. J Fluids Struct 49:450–462
Michelin S, Smith SGL (2009) Linear stability analysis of coupled parallel flexible plates in an axial flow. J Fluids Struct 25(7):1136–1157
Jensen P, Marcum WR (2014) Predicting critical flow velocity leading to laminate plate collapse—flat plates. Nucl Eng Des 267:71–87
Eloy C, Souilliez C, Schouveiler L (2007) Flutter of a rectangular plate. J Fluids Struct 23(6):904–919
Guo CQ, Païdoussis MP (2000) Stability of rectangular plates with free side-edges in two-dimensional inviscid channel flow. J Appl Mech 67:171–176
Tang L, Païdoussis MP (2007) On the instability and the post-critical behaviour of two-dimensional cantilevered flexible plates in axial flow. J Sound Vib 305(1–2):97–115
Zhao W, Païdoussis MP, Tang L, Liu M, Jiang J (2012) Theoretical and experimental investigations of the dynamics of cantilevered flexible plates subjected to axial flow. J Sound Vib 331(3):575–587
Doaré O, Michelin S (2011) Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency. J Fluids Struct 27(8):1357–1375
Younesian D, Norouzi H (2015) Frequency analysis of the nonlinear viscoelastic plates subjected to subsonic flow and external loads. Thin Walled Struct 92:65–75
Schouveiler L, Eloy C (2009) Coupled flutter of parallel plates. Phys Fluids 21(8):301–327
Dowell EH (1975) Aeroelasticity of plates and shells. Noordhoff International Publishing, Leyden
Païdoussis MP (2003) Fluid-structure interactions: slender structures and axial flow, vol 2. Elsevier/Academic Press, London
Acknowledgments
This research is supported by the China Postdoctoral Science Foundation (No. 2015M581345), and the National Natural Science Foundation of China (Nos. 11172084 and 11572007).
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Yao, G., Li, FM. Stability and vibration properties of a composite laminated plate subjected to subsonic compressible airflow. Meccanica 51, 2277–2287 (2016). https://doi.org/10.1007/s11012-016-0367-5
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DOI: https://doi.org/10.1007/s11012-016-0367-5