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Second-order approximation of angle-ply composite laminated thin plate under combined excitations
Authors:M. Sayed  A.A. Mousa
Affiliation:1. Department of Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt;2. Department of Basic Engineering Sciences, Faculty of Engineering, Menoufia University, Shebin El-Kom, Egypt;3. Department of Mathematics and Statistics, Faculty of Science, Taif University, El-Taif, P.O. Box 888, Saudi Arabia;1. Department of Chemistry, University of Sargodha, Sargodha 40100, Pakistan;2. Key Laboratory of Superlight Material and Surface Technology, Ministry of Education, Harbin Engineering University, 150001, China;3. Key Laboratory of Functional Materials and Devices for Special Environments of CAS, Xinjiang Technical Institute of Physics & Chemistry of CAS, Xinjiang Key Laboratory of Electronic Information Materials and Devices, 40-1 South Beijing Road, Urumqi 830011, China;1. Department of Chemistry, Xavier University of Louisiana, 1, Drexel Dr., New Orleans, LA 70125, United States;2. Department of Cell and Molecular Biology, Tulane University, 6400 Freret Street, 2000 Percival Stern Hall, New Orleans, LA 70118, United States;3. College of Pharmacy, Xavier University of Louisiana, 1, Drexel Dr., New Orleans, LA 70125, United States;4. Ogden College of Science and Engineering, Western Kentucky University, 1906 College Heights Boulevard #11075, Bowling Green, KY 42101-1075, United States;1. Department of Chemistry, Bialystok University of Technology, Wiejska 45A, Poland;2. Department of Agricultural - Food and Forestry Engineering, Bialystok University of Technology, Wiejska 45A, Poland;3. Department of Sanitary Biology and Biotechnology, Bialystok University of Technology, Wiejska 45A, Poland
Abstract:The influence of the quadratic and cubic terms on non-linear dynamic characteristics of the angle-ply composite laminated rectangular plate with parametric and external excitations is investigated. The method of multiple time scale perturbation is applied to solve the non-linear differential equations describing the system up to and including the second-order approximation. All possible resonance cases are extracted and investigated at this approximation order. Two cases of the sub-harmonic resonances cases (Ω2 ? 2ω1 and Ω2 ? 2ω2) in the presence of 1:2 internal resonance ω2 ? 2ω1 are considered. The stability of the system is investigated using both frequency response equations and phase-plane method. It is quite clear that some of the simultaneous resonance cases are undesirable in the design of such system as they represent some of the worst behavior of the system. Such cases should be avoided as working conditions for the system. Some recommendations regarding the different parameters of the system are reported. Comparison with the available published work is reported.
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