Nonlinear dynamic response and time-delay feedback vibration control of multilayer beams on compressible clayey foundations subjected to moving concentrated loads

Roger Eno
Laboratory for Mechanics and Materials (LMEMA), Department of Civil Engineering, National Higher Polytechnic School of Douala, University of Douala, Douala P.O. Box 2701, Cameroon
Guillaume Hervé Poh'sié
Department of Civil Engineering, Higher Institute of Advanced Technologies (ISTA), University Institute of the Gulf of Guinea (IUG), Douala P.O. Box 12489, Cameroon; Department of Mechanical Engineering, College of Technology, University of Buea, Buea P.O. Box 63, Cameroon; Department of Civil Engineering, National Higher Polytechnic School of Yaoundé, University of Yaoundé I, Yaoundé P.O. Box 8390, Cameroon
Hermann Joel Ouandji Boutcheng
Department of Physics, Faculty of Science, University of Buea, Buea P.O. Box 63, Cameroon
Ekoum Ewandjo Nkoue
Laboratory for Mechanics and Materials (LMEMA), Department of Civil Engineering, National Higher Polytechnic School of Douala, University of Douala, Douala P.O. Box 2701, Cameroon
Dianorre Tokoue Ngatcha
Laboratory for Mechanics and Materials (LMEMA), Department of Civil Engineering, National Higher Polytechnic School of Douala, University of Douala, Douala P.O. Box 2701, Cameroon
Joseph Mousi Bikoun
Laboratory for Mechanics and Materials (LMEMA), Department of Civil Engineering, National Higher Polytechnic School of Douala, University of Douala, Douala P.O. Box 2701, Cameroon; Department of Civil Engineering, Advanced Teacher Training College for Technical Education (ENSET), University of Douala, Douala P.O. Box 1872, Cameroon
Fabien Kenmogne
Department of Civil Engineering, Advanced Teacher Training College for Technical Education (ENSET), University of Douala, Douala P.O. Box 1872, Cameroon
Séverin Nguiya
Laboratory for Geophysics (LG), National Higher Polytechnic School of Douala, University of Douala, Douala P.O. Box 2701, Cameroon

Article ID: 4372

Keywords: moving concentrated load; multilayer beam; interlayer coupling; modal mismatch; dynamic control

Abstract

This study investigates the nonlinear vibration behaviour of multilayer beams resting on a compressible elastic foundation and subjected to a moving concentrated load. The objective is to analyse the combined effects of geometric nonlinearity, interlayer elastic coupling, foundation compressibility, and moving-load excitation on the dynamic response of the structure. An analytical formulation based on the Lagrangian formalism is developed, incorporating kinetic energy, bending energy, foundation stiffness, interlayer coupling, and nonlinear stretching effects. The proposed formulation captures the structural dynamics through coupled Duffing-type nonlinear modal interactions, while accounting for damping and moving-load excitation. A Fourier-Galerkin modal reduction is employed to derive a reduced-order temporal system, whose equilibrium states and stability characteristics are investigated. Numerical simulations performed using Fourier modal decomposition and a fourth-order Runge-Kutta scheme reveal complex dynamic behaviours, including multistability, resonance amplification, quasi-periodic oscillations, and branch-jump phenomena induced by nonlinear interactions and parameter sensitivity. To mitigate excessive vibrations, a time-delay feedback controller is introduced and applied to all modal coordinates. The delayed control law yields a transcendental characteristic equation, from which explicit stability conditions are established in terms of the feedback gain and time delay. Numerical results demonstrate that the proposed controller effectively suppresses nonlinear vibration amplification, reduces oscillation amplitudes, and improves the dynamic stability of the system. The proposed framework provides a comprehensive nonlinear beam-foundation interaction model combined with delay-based vibration control, contributing to the analysis and stabilization of multilayer structural systems subjected to moving loads on deformable foundations.

Published

2026-08-16

How to Cite

Eno, R., Poh’sié, G. H., Boutcheng, H. J. O., Nkoue, E. E., Ngatcha, D. T., Bikoun, J. M., Kenmogne, F., & Nguiya, S. (2026). Nonlinear dynamic response and time-delay feedback vibration control of multilayer beams on compressible clayey foundations subjected to moving concentrated loads. Advances in Differential Equations and Control Processes, 33(3). https://doi.org/10.59400/adecp4372

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Vol. 33 No. 3 (2026): In Progress

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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