Nonlinear Vibration of a Stiffened Plate Considering the Existence of Initial Stresses
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This paper presents a study on the nonlinear dynamic behavior of a stiffened plate with the existence of initial stresses. A stiffened plate is assumed to be composed of a plate and some stiffeners, which are treated separately. The plate is analyzed based on Thin Plate Theory, while the stiffeners are considered as geometrically nonlinear Euler-Bernoulli beams. The equations of both kinetic energies and strain energies of the plate and stiffeners are established. After that, the dynamic equilibrium equations for the stiffened plate are derived according to Lagrange equation. The nonlinear frequency for single-mode result is obtained through Elliptic function, and the accuracy of the analytical solution is verified through comparison with Ansys finite element method. In addition, homotopy analysis method is used to solve 3:1 internal resonance of the stiffened plate. With parametric analysis being conducted, the investigation on how initial stresses influence the nonlinear dynamic properties is carried out. Some useful nonlinear dynamic properties and conclusions are obtained, and thees can provide references for engineering application.
Keywordsstiffened plates initial stresses nonlinear vibration frequency internal resonance
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- Chia, C. Y. (1980). Non-linear analysis of plates, McGraw-Hill, New York, NY, USA.Google Scholar
- Duc, N. D., Cong, P. H., Tuan, N. D., Tran, P., Anh, V. M., and Quang, V. D. (2016). “Nonlinear vibration and dynamic response of imperfect eccentrically stiffened shear deformable sandwich plate with functionally graded material in thermal environment.” Journal of Sandwich Structures & Materials, Vol. 18, No. 4, pp. 445–473, DOI: 10.1177/1099636215602142.CrossRefGoogle Scholar
- Hoseini, S. H., Pirbodaghi, T., Asghari, M., Farrahi G. H., and Ahmadian, M. T. (2008). “Nonlinear free vibration of conservative oscillators with inertia and static type cubic nonlinearities using homotopy analysis method.” Journal of Sound and Vibration, Vol. 316, Nos. 1–5, pp. 263–273, DOI: 10.1016/j.jsv.2008.02.043.CrossRefGoogle Scholar