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

Abstract

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, whereΩ3≅ω1,ω2≅ω1, andω3≅3ω1, 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 parametersμ1,μ2,α7,β8,ω1,ω2,f1,f2leads 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.

Non-linear time delay saturation controller for reduction of a non-linear vibrating system via 1:4 internal resonance

“…The effects of different terms (quadratic and cubic) on nonlinear dynamic characteristics under mixed excitations are investigated by Sayed and Mousa [13]. An analytical analysis of the nonlinear dynamics of a symmetric cross-ply composite laminated piezoelectric plate under mixed excitations is investigated by Sayed and Mousa [14]. They verified the analytical results by multiple time scale method with the numerical results of the modal equations.…”

“…Figs. [14][15][16][17][18][19] shows that the steady state amplitude of the plant and controller (controller 1:4 internal resonance in action) at simultaneous primary and principle parametric resonance where Ω ≅ , Ω ≅ 2 in the presence of 1:4 internal resonance ≅ 4 for different values of time delays , , , for the same value of the parameters shown in Fig. 2 Fig.…”

Vibration characteristics analysis and structural improvement of natural gas venting ignition pipeline

“…The natural gas venting ignition pipeline has nonlinear vibration. The current researches on nonlinear vibration include the nonlinear vibrations of a contact-mode atomic force microscopy(AFM) model subjected to multi excitations are controlled via a time-delayed positive position feedback (PPF) controller [10], M. Sayed et al applied active control to the nonlinear dynamic beam system to eliminate its vibration [11], Ali Kandil first derived a nonlinear dynamic equation for controlling the lateral vibration of a controlled system under a constant stiffness coefficient [12], the work of N. A. Saeed et al aims to study and control the nonlinear dynamic behavior of a nonlinear asymmetric shaft system [13,14], Y. S. HAMED et al studied the nonlinear dynamics control of a contact atomic force microscope system using a time-delay proportional-differential controller [15,16]. However, the above studies have rarely studied the vibration characteristics of vented horizontal pipes and risers.…”

Active vibration suppression of a nonlinear electromechanical oscillator system with simultaneous resonance

“…Sayed and Kamel [26,27] used the saturation control of a linear controller to reduce the vibrations due to rotor blade flapping motion and they investigated the effect of different controllers on the vibrating system. Sayed et al [28][29][30][31] investigated the non-linear dynamic characteristics of the angle-ply composite laminated rectangular plate model under both parametric and external excitations. Also, they studied three cases of primary and internal resonance (1:2, 1:1, 1:1:3) and they compared the analytical results with the numerical one of the modal equations.…”