Abstract
The actual plate structures are not as ideal as the general theoretical analysis. They are potentially subjected to imperfections, significantly influencing their instability behaviors when they vibrate in fluids. On the one hand, the possible imperfections come from the structure itself, and on the other hand, they come from the mismatch between theoretical and experimental modelings. The lack of influence analysis of imperfections will lead to many deviations in our understanding of the structure’s mechanical properties and the experimental results. This brief note presents a numerical study on the instability of a plate with two types of imperfections: the crack defect and imperfect edge-support, and reveals the influence of these imperfections on the plate instability behaviors when the plate is subjected to a steady axial airflow. The crack defect is modeled as an all-over part-through crack in the plate and the imperfect edge-support as elastic end support with transversal and rotational springs. For the uncracked plate, the elastic end support allows the coexistence of the flutter and divergence instability. The rotational spring plays a vital role in the distributions of instability regions and the transition of two instability types. The plate exhibits more complicated instability behaviors with the effect of both crack and elastic end support. There will be transitions between instability regions, and the instability transition processes between different instability types are more diversified.
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References
Raghunathan RS, Kim HD, Setoguchi T (2002) Aerodynamics of high-speed railway trains. Prog. Aerosp. Sci. 38:469–514
Li P, Yang YR, Xu W, Chen G (2020) Imperfect bifurcations in an initially curved plate loaded by incompressibale axial flow. Nonlinear Dyn. 99:1379–1402
Li P, Wang ZX, Zhang DC, Yang YR (2021) On bifurcations and chaos of a focred rectangular plate with large deflection loaded by subsonic airflow. Thin-walled Struct 161:107421. https://doi.org/10.1016/j.tws.2020.107421
Dowell EH (1975) Aeroelasticity of plates and shells. Noordhoff International Publishing, Leyden
Dowell EHA (2015) modern course in aeroelasticity, fifth revised and, enlarged. Springer Cham Heidelberg New York Dordrecht London
Païdoussis MP (2004) Fluid-structure interactions. Slender structures and axial flow, vol 2, 1st edn. Elsevier Academic Press, London
Watanabe Y, Suzuki S, Sugihara M, Sueoka Y (2002) A experimental study of paper flutter. J Fluids Struct 16:529–542
Watanabe Y, Isogai K, Suzuki S, Sugihara M (2002) A theoretical study of paper flutter. J Fluids Struct 16:543–560
Allen JJ, Smits AJ (2001) Energy harvesting eel. J Fluids Struct 15:629–640
de Breuker R, Abdalla MM, Gürdal Z (2008) Flutter of partially rigid cantilevered plates in axial flow. AIAA J 46:936–946
Dugundji J, Dowell EH, Perkin B (1963) Subsonic flutter of panels on continuous elastic foundations. AIAA J 5:1146–1154
Ishii T (1965) Aeroelastic instabilities of simply supported panels in subsonic flow. Los Angeles, AIAA Paper, Meeting of the AIAA, pp. 765–772
Shahrokh A, Ellen CH (1979) The stability of partially rigid two-dimensional surfaces in uniform incompressible flow. J Sound Vib 65:339–351
Kornecki A, Dowell EH, O‘Brien J (1974) On the aeroelastic instability of two-dimensional panels in uniform incompressible flow. J Sound Vib 47:163–178
Wang Q, Koh CG (2003) Regions of flutter and bucking instability for a cracked beam. AIAA J 41:2302–2304
Beloiu DM, Ibrahim RA, Pettit CL (2005) Influence of boundary conditions relaxation on panle flutter with compressive in-plane loads. J Fluids Struct 21:743–767
Li P, Yang YR (2014) On the stability and chaos of a plate with motion constraints in subsonic flow. Int J Non-Linear Mech 59:28–36
Li P, Li ZW, Dai CD, Yang YR (2018) On the non-linear dynamics of a forced plate with boundary conditions correction in subsonic flow. J Appl Model 64:15–46
Li P, Li ZW, Dai CD, Yang YR (2018) Non-linear limit cycle flutter of a plate with Hertzian contact in axial flow. J Fluids Struct 81:131–160
Li P, Liang S, Zhang DC, Zhu YZ, Yang YR (2019) The instability of a plate fixed at both ends in an axial flow revisited: an application of the DQ-BE method. J Eng Math 118:43–61
Caddemi S, Caliò I (2009) Exact closed-form solution for the vibration modes of the Euler-Bernoulli beam with multiple open cracks. J Sound Vib 327:473–489
Caddemi S, Caliò I (2012) The influence of the axial force on the vibration of the Euler-Bernoulli beam with an arbitrary number of cracks. Arch Appl Mech 82:827–839
Yang ZC, Xia W (2010) Analytical models, numerical solutions and advances in the study of panel flutter. Adv Mech 40(1):81–97 (in Chinese)
Kornecki A (1973) On the character of instability of certain aeroelastic systems. AIAA J 40:616–617
Sundararajan C (1976) Influence of an elastic end support on the vibration and stability of Beck‘s column. Int J Mech Sci 18:239–241
Simitses GJ, Hodges DW (2006) Fundamentals of structureal stability. Elsevier Academic Press, London
Shih YS, Wu GY (2002) Effect of vibration on fatigue crack growth of an edge crack for a rectangular plate. Int J Fatigue 24:557–566
Paulus M, Dasgupta A (2012) Semi-empirical life model of a cantilevered beam subjected to random vibration. Int J Fatigue 45:82–90
Strganac TW, Kim YI (1996) Aeroelastic behavior of composite plates subject to damage growth. J Aircraft 33:638–73
Wang K, Inman DJ (2007) Crack-induced effects on aeroelasticity of an unswept composite wing. AIAA J 45:542–551
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant Nos: 12072298; 11772273). The authors are grateful to the anonymous reviewers whose comments helped immensely in writing this paper.
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Li, P., Zhu, Y., Zhang, D. et al. A numerical study of instability transition of a beam-like plate with imperfections loaded by a steady axial airflow. Meccanica 57, 507–521 (2022). https://doi.org/10.1007/s11012-021-01455-8
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DOI: https://doi.org/10.1007/s11012-021-01455-8