Vibration, Stability, and Resonance of Angle-Ply Composite Laminated Rectangular Thin Plate under Multiexcitations

摘要

An analytical investigation of the nonlinear vibration of a symmetric cross-ply composite laminated piezoelectric rectangular plate under parametric and external excitations is presented. The method of multiple time scale perturbation is applied to solve the nonlinear differential equations describing the system up to and including the second-order approximation. All possible resonance cases are extracted at this approximation order. The case of 1:1:3 primary and internal resonance, where Ω_3 ≌ω_1, ω_2 ≌ω_1, and ω_3 ≌ 3ω_1, is considered. The stability of the system is investigated using both phase-plane method and frequency response curves. The influences of the cubic terms on nonlinear dynamic characteristics of the composite laminated piezoelectric rectangular plate are studied. The analytical results given by the method of multiple time scale is verified by comparison with results from numerical integration of the modal equations. Reliability of the obtained results is verified by comparison between the finite difference method (FDM) and Runge-Kutta method (RKM). It is quite clear that some of the simultaneous resonance cases are undesirable in the design of such system. Such cases should be avoided as working conditions for the system. Variation of the parameters μ_1, μ_2, α_7, β_8, ω_1,ω_2, f_1, f_2 leads to multivalued amplitudes and hence to jump phenomena. Some recommendations regarding the different parameters of the system are reported. Comparison with the available published work is reported.