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Dynamics of nonlinear cantilever piezoelectric–mechanical system: An intelligent computational approach

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  • Naz, Sidra
  • Raja, Muhammad Asif Zahoor
  • Kausar, Aneela
  • Zameer, Aneela
  • Mehmood, Ammara
  • Shoaib, Muhammad

Abstract

In this study, a novel application of intelligent computing by the exploitation of a supervised neural networks (SNNs) optimized with the Levenberg–Marquardt method (LMM) is presented to study the dynamics of nonlinear cantilever piezoelectric–mechanical system (NCPMS) represented with a second-order system of ordinary differential equation. The dataset for NCPMS is created using Adams numerical solver for input and target parameters for continuous mapping of SNN model of the system. The training, testing, and validation processes are exploited for SNNs models learned by LMM to determine the solution of NCPMS for different scenarios based on variation of amplitude and phase of cantilever frequency for small- and large-time domains while keeping the tip mass, beam length, mass density, capacitance and load resistance constant. The performance of SNN to solve NCPMS is substantiated on measurement of achieved accuracy through mean squared error, error histogram illustrations and regression analyzes.

Suggested Citation

  • Naz, Sidra & Raja, Muhammad Asif Zahoor & Kausar, Aneela & Zameer, Aneela & Mehmood, Ammara & Shoaib, Muhammad, 2022. "Dynamics of nonlinear cantilever piezoelectric–mechanical system: An intelligent computational approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 88-113.
    • Handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:88-113
    DOI: 10.1016/j.matcom.2022.01.011
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    1. Wang, Jinliang & Zhang, Ran & Kuniya, Toshikazu, 2021. "A reaction–diffusion Susceptible–Vaccinated–Infected–Recovered model in a spatially heterogeneous environment with Dirichlet boundary condition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 848-865.
    2. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Wahab, Hafiz Abdul & Altamirano, Gilder Cieza & Zhang, Yu-Dong & Le, Dac-Nhuong, 2021. "Integrated intelligence of neuro-evolution with sequential quadratic programming for second-order Lane–Emden pantograph models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 87-101.
    3. Sabir, Zulqurnain & Saoud, Sahar & Raja, Muhammad Asif Zahoor & Wahab, Hafiz Abdul & Arbi, Adnène, 2020. "Heuristic computing technique for numerical solutions of nonlinear fourth order Emden–Fowler equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 534-548.
    4. Roopnarain, Ryan & Roy Choudhury, S., 2021. "Amplitude death, oscillation death, and periodic regimes in dynamically coupled Landau–Stuart oscillators with and without distributed delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 30-50.
    5. Jadoon, Ihtesham & Raja, Muhammad Asif Zahoor & Junaid, Muhammad & Ahmed, Ashfaq & Rehman, Ata ur & Shoaib, Muhammad, 2021. "Design of evolutionary optimized finite difference based numerical computing for dust density model of nonlinear Van-der Pol Mathieu’s oscillatory systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 444-470.
    6. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Sakar, Mehmet Giyas & Raja, Muhammad Asif Zahoor, 2020. "Novel design of Morlet wavelet neural network for solving second order Lane–Emden equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 1-14.
    7. Jena, Rajarama Mohan & Chakraverty, Snehashish & Baleanu, Dumitru, 2021. "SIR epidemic model of childhood diseases through fractional operators with Mittag-Leffler and exponential kernels," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 514-534.
    8. Umar, Muhammad & Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Aguilar, J.F. Gómez & Amin, Fazli & Shoaib, Muhammad, 2021. "Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4+ T-cells," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 241-253.
    9. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Khalique, Chaudry Masood & Unlu, Canan, 2021. "Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 799-812.
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