In this paper, the dynamic oscillation of a rectangular thin plate under parametric and external excitations is investigated and controlled. The motion of a rectangular thin plate is modeled by coupled second-order nonlinear ordinary differential equations. The formulas of the thin plate are derived from the von Kármán equation and Galerkin's method. A control law based on negative acceleration feedback is proposed for the system. The multiple time scale perturbation technique is applied to solve the nonlinear differential equations and obtain approximate solutions up to the second-order approximations. One of the worst resonance case of the system is the simultaneous primary resonances, where . From the frequency response equations, the stability of the system is investigated according to the Routh–Hurwitz criterion. The effects of the different parameters are studied numerically. It is also shown that the system parameters have different effects on the nonlinear response of the thin plate. The simulation results are achieved using matlab 7.0 software. A comparison is made with the available published work.
Skip Nav Destination
Article navigation
July 2016
Research-Article
Active Control of a Rectangular Thin Plate Via Negative Acceleration Feedback Available to Purchase
H. S. Bauomy,
H. S. Bauomy
Department of Mathematics,
Faculty of Science,
Zagazig University,
Zagazig 44519, Egypt;
Faculty of Science,
Zagazig University,
Zagazig 44519, Egypt;
Department of Mathematics,
College of Arts and Science in Wadi Addawasir,
Prince Sattam Bin Abdulaziz University,
P.O. Box 54,
Wadi Addawasir 11991, Saudi Arabia
e-mail: [email protected]
College of Arts and Science in Wadi Addawasir,
Prince Sattam Bin Abdulaziz University,
P.O. Box 54,
Wadi Addawasir 11991, Saudi Arabia
e-mail: [email protected]
Search for other works by this author on:
A. T. EL-Sayed
A. T. EL-Sayed
Department of Basic Sciences,
Modern Academy for Engineering and
Technology,
Mokatem 11585, Egypt
e-mail: [email protected]
Modern Academy for Engineering and
Technology,
Mokatem 11585, Egypt
e-mail: [email protected]
Search for other works by this author on:
H. S. Bauomy
Department of Mathematics,
Faculty of Science,
Zagazig University,
Zagazig 44519, Egypt;
Faculty of Science,
Zagazig University,
Zagazig 44519, Egypt;
Department of Mathematics,
College of Arts and Science in Wadi Addawasir,
Prince Sattam Bin Abdulaziz University,
P.O. Box 54,
Wadi Addawasir 11991, Saudi Arabia
e-mail: [email protected]
College of Arts and Science in Wadi Addawasir,
Prince Sattam Bin Abdulaziz University,
P.O. Box 54,
Wadi Addawasir 11991, Saudi Arabia
e-mail: [email protected]
A. T. EL-Sayed
Department of Basic Sciences,
Modern Academy for Engineering and
Technology,
Mokatem 11585, Egypt
e-mail: [email protected]
Modern Academy for Engineering and
Technology,
Mokatem 11585, Egypt
e-mail: [email protected]
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 6, 2015; final manuscript received March 23, 2016; published online May 13, 2016. Assoc. Editor: Firdaus Udwadia.
J. Comput. Nonlinear Dynam. Jul 2016, 11(4): 041025 (12 pages)
Published Online: May 13, 2016
Article history
Received:
September 6, 2015
Revised:
March 23, 2016
Citation
Bauomy, H. S., and EL-Sayed, A. T. (May 13, 2016). "Active Control of a Rectangular Thin Plate Via Negative Acceleration Feedback." ASME. J. Comput. Nonlinear Dynam. July 2016; 11(4): 041025. https://doi.org/10.1115/1.4033307
Download citation file:
Get Email Alerts
Cited By
Simple Tuning for an Adaptive and Model-Free Control of Indoor Airships
J. Comput. Nonlinear Dynam (August 2025)
Global Dynamics and Multistability in a Class of Piecewise Asymmetric Oscillators
J. Comput. Nonlinear Dynam (October 2025)
Multifactor Analysis of Static and Dynamic Characteristics of Membrane Air Springs for Small Passenger Cars
J. Comput. Nonlinear Dynam (October 2025)
Study on the Fractal and Chaotic Prediction Model and Dynamics Characteristics of Friction Force During Running-in
J. Comput. Nonlinear Dynam (October 2025)
Related Articles
Primary Resonance of Dry-Friction Oscillator With Fractional-Order Proportional-Integral-Derivative Controller of Velocity Feedback
J. Comput. Nonlinear Dynam (September,2016)
Response of a Harmonically Forced Dry Friction Damped System Under Time-Delayed State Feedback
J. Comput. Nonlinear Dynam (March,2018)
Vibration Suppression of a Four-Degrees-of-Freedom Nonlinear Spring Pendulum via Longitudinal and Transverse Absorbers
J. Appl. Mech (January,2012)
Analysis of a Chaotic Electrostatic Micro-Oscillator
J. Comput. Nonlinear Dynam (January,2011)
Related Proceedings Papers
Related Chapters
Graphical Methods for Control Systems
Introduction to Dynamics and Control in Mechanical Engineering Systems
Quasi Static Approximation of Wireless Power Transfer Systems through Coupled Resonance and Improving Power Transfer Efficiency
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3
Conclusion
Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow