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Steel and Composite Structures Volume 48, Number 3, August 2023 , pages 335-351 DOI: https://doi.org/10.12989/scs.2023.48.3.335 |
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Nonlinear vibration and primary resonance of multilayer functionally graded shallow shells with porous core |
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Kamran Foroutan and Liming Dai
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| Abstract | ||
| This research studies the primary resonance and nonlinear vibratory responses of multilayer functionally graded shallow (MFGS) shells under external excitations. The shells considered with functionally graded porous (FGP) core and resting on two types of nonlinear viscoelastic foundations (NVEF) governed by either a linear model with two parameters of Winkler and Pasternak foundations or a nonlinear model of hardening/softening cubic stiffness augmented by a Kelvin–Voigt viscoelastic model. The shells considered have three layers, sandwiched by functionally graded (FG), FGP, and FG materials. To investigate the influence of various porosity distributions, two types of FGP middle layer cores are considered. With the first-order shear deformation theory (FSDT), Hooke's law, and von-Karman equation, the stress-strain relations for the MFGS shells with FGP core are developed. The governing equations of the shells are consequently derived. For the sake of higher accuracy and reliability, the P-T method is implemented in numerically analyzing the vibration, and the method of multiple scales (MMS) as one of the perturbation methods is used to investigate the primary resonance. The results of the present research are verified with the results available in the literature. The analytical results are compared with the P-T method. The influences of material, geometry, and nonlinear viscoelastic foundation parameters on the responses of the shells are illustrated. | ||
| Key Words | ||
| FG porous core; method of multiple scales; multilayer FG shallow shells; nonlinear viscoelastic foundation; P-T method; primary resonance | ||
| Address | ||
| Kamran Foroutan and Liming Dai: 1)Sino-Canada Research Centre of Nonlinear Dynamics and Noise Control of Xiamen University of Technology and the University of Regina, Xiamen University of Technology, China 2)Industrial Systems Engineering, University of Regina, Regina, SK, S4S 0A2, Canada | ||