Nonlinear analysis of dynamic instability of aircraft wing structure based on first order shear beam theory and differential quadratic solution method

Document Type : Original Article

Authors

1 Assistant Professor, Department of Mechanical Engineering, Khatamul-Anbiya Air Defense University, Tehran, Iran.

2 Professor, Department of Aerospace Engineering, MalekAshtar University of Technology, Tehran, Iran

Abstract

In this paper, for the first time, a nonlinear analysis of the dynamic instability of a relatively thick curved structure equivalent to a composite wing layer is performed. For this purpose, the wing structure of the aircraft is considered as a relatively thick curved beam and modelling has been done using first-order shear theory. Van Carmen's large non-linear strain relationships have been used in strain components in a curved line environment. One of the most complex instability modes is axial excitation of the curved beam under a harmonic dynamic load despite a static constant value. These static loads (positive or negative) and dynamic harmonic load coefficient have a significant relationship with static buckling load. Considering the dynamic axial load, the dynamic equations governing the system and the equations of the boundary conditions are obtained using the Hamilton principle and the method of calculating the changes, and to solve them, the generalized numerical differential squaring method is used. Also in this paper, for the first time, by solving the final algebraic nonlinear equations, the stability region of a relatively thick curved beam is determined as changes in the excitation frequency in terms of dynamic load. To determine the effects of different parameters on natural frequencies, critical buckling load and beam stability range, different modes including different linear and nonlinear kinematic models, different values of static load, length to beam thickness ratio and radius of curvature along with beam types Flat and curved composite layers have been considered. As one of the most important results, the results show that considering different combinations of fibbers, the amount of curvature as well as the geometric nonlinearity of the material is important and will have a great impact on the predicted responses for the dynamic instability region.

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References

[1] Chen, L. W., Lin, C. Y., and Wang, C. C., (2002), “Dynamic stability analysis and control of a composite beam with piezoelectric layers”, Composite Structures, 56(1), pp. 97-109.
[2] Chen, L. Q., Yang, X. D., and Cheng, C. J., (2004), “Dynamic stability of an axially accelerating viscoelastic beam”, European Journal of Mechanics-A/Solids, 23(4), pp. 659-666.
[3] Aristizabal-Ochoa, J. D., (2007), “Static and dynamic stability of uniform shear beam-columns under generalized boundary conditions”, Journal of Sound and Vibration, 307(1-2), pp. 69-88.
[4] Chandrashekhara, K., Krishnamurthy, K., and Roy, S., (1990), “Free vibration of composite beams including rotary inertia and shear deformation”, Composite Structures, 14(4), pp. 269-279.
[5] Wang, X., Zhu, X., and Hu, P., (2015), “Isogeometric finite element method for buckling analysis of generally laminated composite beams with different boundary conditions”, International Journal of Mechanical Sciences, 104, pp. 190-199.
[6] Emam, S. A., and Nayfeh, A. H., (2009), “Postbuckling and free vibrations of composite beams”, Composite Structures, 88(4), pp. 636-642.
[7] Kiral, B. G., Kiral, Z., and Ozturk, H., (2015), “Stability analysis of delaminated composite beams”, Composites Part B: Engineering, 79, pp. 406-418.
[8] Karaagac, C., ÖZTÜRK, H., and Sabuncu, M., (2007), “Lateral dynamic stability analysis of a cantilever laminated composite beam with an elastic support”, International Journal of Structural Stability and Dynamics, 7(03), pp. 377-402.
[9] Chand, R. R., Behera, P. K., Pradhan, M., and Dash, P., (2019), “Study of Static and Dynamic Stability of an Exponentially Tapered Revolving Beam Exposed to a Variable Temperature Grade under Axial Loading”, International Journal of Acoustics and Vibration, 24(3), pp. 504-510.
[10] Rafiee, M., He, X. Q., and Liew, K. M., (2014), “Non-linear dynamic stability of piezoelectric functionally graded carbon nanotube-reinforced composite plates with initial geometric imperfection”, International Journal of Non-Linear Mechanics, 59, pp. 37-51.
[11] Singha, M. K., and Daripa, R., (2009), “Nonlinear vibration and dynamic stability analysis of composite plates”, Journal of Sound and Vibration, 328(4-5), pp. 541-554.
[12] Sahmani, S., and Bahrami, M., (2015), “Size-dependent dynamic stability analysis of microbeams actuated by piezoelectric voltage based on strain gradient elasticity theory”, Journal of Mechanical Science and Technology, 29(1), pp. 325-333.
[13] Lim, C. W., Wang, C. M., and Kitipornchai, S., (1997), “Timoshenko curved beam bending solutions in terms of Euler-Bernoulli solutions”, Archive of Applied Mechanics, 67(3), pp. 179-190.
[14] Wang, J., Shen, H., Zhang, B., and Liu, J., (2018), “Studies on the dynamic stability of an axially moving nanobeam based on the nonlocal strain gradient theory”, Modern Physics Letters B, 32(16), pp. 1850167.
[15] Pavlović, I., Pavlović, R., Ćirić, I., and Karličić, D., (2015), “Dynamic stability of nonlocal Voigt–Kelvin viscoelastic Rayleigh beams”, Applied Mathematical Modelling, 39(22), pp. 6941-6950.
[16] Saffari, S., Hashemian M., and Toghraie, D., (2017), “Dynamic stability of functionally graded nanobeam based on nonlocal Timoshenko theory considering surface effects”, Physica B: Condensed Matter, 520, pp. 97-105.
[17] Vatan Can, S., Cankaya, P., Ozturk, H., and Sabuncu, M., (2020), “Vibration and dynamic stability analysis of curved beam with suspended spring–mass systems”, Mechanics Based Design of Structures and Machines, pp. 1-15.
[18] Ansari, R., and Gholami, R., (2015), “Dynamic stability of embedded single walled carbon nanotubes including thermal effects”, Iranian Journal of Science and Technology Transactions of Mechanical Engineering, 39, pp. 153-161.
[19] Zamanzadeh, M., Rezazadeh, G., Jafarsadeghi-Poornaki, I., and Shabani, R., (2013), “Static and dynamic stability modeling of a capacitive FGM micro-beam in presence of temperature changes”, Applied Mathematical Modelling, 37(10-11), pp. 6964-6978.
[20] Fu, Y., Wang, J., and Mao, Y., (2012), “Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment”, Applied Mathematical Modelling, 36(9), pp. 4324-4340.
[21] Zheng, X., Zhang, J., and Zhou, Y., (2005), “Dynamic stability of a cantilever conductive plate in transverse impulsive magnetic field”, International Journal of Solids and Structures, 42(8), pp. 2417-2430.

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History

  • Receive Date: 12 February 2022
  • Revise Date: 20 June 2022
  • Accept Date: 01 July 2022

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