A new six-degrees of freedom model designed for a composite plate through PPF controllers

• Published in: Applied Mathematical Modelling 2020-12, Vol.88, p.604-630
• Main Authors: Bauomy, H.S., EL-Sayed, A.T.
• Format: Article
• Language: English
• Subjects: Composite structures; Controllers; Current goal; Degrees of freedom; Different composite structures; Dynamic stability; Dynamical systems; Frequency response; Mathematical analysis; Mathematical models; Multiple scale; Nonlinear control; Nonlinear dynamics; Nonlinear equations; Nonlinear response; Numerical prediction; Perturbation methods; Piezoelectric composite plate; Piezoelectricity; PPF; PPF and NSC; Vibration control
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2020.06.067

•Positive position feedback (PPF) controllers added to a composite plate with mixed excitations.•A new six degrees of freedom model simulating nonlinear vibrations of the plate are proposed.•Perturbation technique is applied to have the solutions of the main system.•Numerical outcomes show that PPF methods have big effects on reducing vibrations of the amplitudes.•Numerical solution be an excellent harmony with steady-state amplitude using frequency response curves. The idea of this manuscript is to convert nonlinear positive position feedback (PPF) controllers with symmetric cross-ply composite piezoelectric laminated plates among mixed excitations. A new six degrees of freedom model simulating nonlinear vibrations (NVs) of a composite plate has proposed. The perturbation technique has used to study the transient and steady-state response of nonlinear dynamic equations that presented the main system. The stability of the system via frequency response curves (FRCs) and force response curves (FRCs) have discussed and calculated. The effect on every coefficient's system has considered numerically. A comparison has been made between PPF controller and another control Nonlinear Saturation Control (NSC) to show the amount of vibration reduction produced by the system using PPF control is better than that NSC. Numerical outcomes show that PPF methods have big effects on reducing vibrations of the amplitudes. Then, the predictions from numerical simulations are in excellent harmony with frequency response curves. Lastly, the comparison with newly available papers has been reported.