Abstract
The dynamics and stability of an axially moving plate interacting with surrounding axial airflow are investigated. The dynamic model of the axially moving plate is established based on the Kirchhoff–Love plate theory and the linear potential flow model. The natural frequencies of the plate under different moving velocities and airflow velocities are calculated by solving the generalized eigenvalue problems of the dynamic system, from which the stability of the plate is analyzed. The effects of the surrounding airflow and the length to width ratio of the plate on the critical divergence velocity and the flutter velocity are discussed. From the simulation, it can be seen that with the flow velocity increasing, the natural frequencies of the plate decrease and then couple, resulting in the plate losing stability of the divergence and flutter types. With the length to width ratio of the plate increasing, the critical divergence velocity and the flutter velocity of the plate decrease. The critical divergence velocity and flutter velocity of the plate in surrounding airflow are lower than those in vacuum, which indicates that it is necessary to consider the effects of the surrounding airflow when analyzing the stability of the axially moving plate.
Similar content being viewed by others
References
Wickert JA, Mote CD (1988) Current research on the vibration and stability of axially moving materials. Shock Vib 20:3–13
Özkaya E, Pakdemirli M (2000) Vibrations of an axially accelerating beam with small flexural stiffness. J Sound Vib 234(3):521–535
Öz HR (2001) On the vibrations of an axially traveling beam on fixed supports with variable velocity. J Sound Vib 239(3):556–564
Kim J, Cho J, Lee U, Park S (2003) Modal spectral element formulation for axially moving plates subjected to in-plane axial tension. Comput Struct 81(20):2011–2020
Jakšić N (2009) Numerical algorithm for natural frequencies computation of an axially moving beam model. Meccanica 44(6):687–695
Banichuk N, Jeronen J, Neittaanmäki P, Tuovinen T (2010) On the instability of an axially moving elastic plate. Int J Solids Struct 47(1):91–99
Huang JL, Su RKL, Li WH, Chen SH (2011) Stability and bifurcation of an axially moving beam tuned to three-to-one internal resonances. J Sound Vib 330(3):471–485
Hu Y, Hu P, Zhang J (2015) Strongly nonlinear subharmonic resonance and chaotic motion of axially moving thin plate in magnetic field. J Comput Nonlinear Dyn 10(2):021010–021010–12
Koivurova H, Pramila A (1997) Nonlinear vibration of axially moving membrane by finite element method. Comput Mech 20(6):573–581
Shin C, Chung J, Kim W (2005) Dynamic characteristics of the out-of-plane vibration for an axially moving membrane. J Sound Vib 286(4–5):1019–1031
Hatami S, Azhari M, Saadatpour MM (2007) Free vibration of moving laminated composite plates. Compos Struct 80(4):609–620
Zhou YF, Wang ZM (2008) Vibrations of axially moving viscoelastic plate with parabolically varying thickness. J Sound Vib 316(1–5):198–210
Wang L, Hu Z, Zhong Z (2010) Dynamic analysis of an axially translating plate with time-variant length. Acta Mech 215(1–4):9–23
Yang XD, Chen LQ, Zu JW (2011) Vibrations and stability of an axially moving rectangular composite plate. J Appl Mech 78(1):1–26
Saksa T, Banichuk N, Jeronen J, Kurki M, Tuovinen T (2012) Dynamic analysis for axially moving viscoelastic panels. Int J Solids Struct 49(23–24):3355–3366
Marynowski K (2012) Dynamic analysis of an axially moving sandwich beam with viscoelastic core. Compos Struct 94(9):2931–2936
Ghayesh MH, Amabili M (2013) Three-dimensional nonlinear planar dynamics of an axially moving Timoshenko beam. Arch Appl Mech 83(4):591–604
Duan YC, Wang JP, Wang JQ, Liu YW, Shao F (2014) Theoretical and experimental study on the transverse vibration properties of an axially moving nested cantilever beam. J Sound Vib 333(13):2885–2897
Niemi J, Pramila A (1987) FEM-analysis of transverse vibrations of an axially moving membrane immersed in ideal fluid. Int J Numer Meth Eng 24(12):2301–2313
Wang L, Ni Q (2008) Vibration and stability of an axially moving beam immersed in fluid. Int J Solids Struct 45(5):1445–1457
Li HY, Li J, Liu YJ (2015) Internal resonance of an axially moving unidirectional plate partially immersed in fluid under foundation displacement excitation. J Sound Vib 358:124–141
Bauchau OA, Craig JI (2009) Structural analysis with applications to aerospace structures. Springer, New York
Al-Qaisia AA, Hamdan MN (2013) On nonlinear frequency veering and mode localization of a beam with geometric imperfection resting on elastic foundation. J Sound Vib 332(19):4641–4655
Li FM, Song ZG (2014) Aeroelastic flutter analysis for 2D Kirchhoff and Mindlin panels with different boundary conditions in supersonic airflow. Acta Mech 225(12):3339–3351
Hatami S, Ronagh HR, Azhari M (2008) Exact free vibration analysis of axially moving viscoelastic plates. Comput Struct 86(17–18):1738–1746
Acknowledgments
This research is supported by the National Natural Science Foundation of China (51135003, U1234208), the National Basic Research Program of China (2014CB046303) and the Key National Science and Technology Special Project of China (2013ZX04011011).
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Yao, G., Zhang, YM. Dynamics and stability of an axially moving plate interacting with surrounding airflow. Meccanica 51, 2111–2119 (2016). https://doi.org/10.1007/s11012-016-0365-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-016-0365-7