Influence of nonlinear distribution CNT and variable viscoelastic foundation on wave propagation in composite beams

Djaloul Zarga, Mokhtar Nebab, Hassen Ait Atmane and Hadji Lazreg

Abstract

In this study, the propagation of waves in beams reinforced with carbon nanotube-reinforced composites (CNTRCs) resting on a variable viscoelastic foundation is examined. The novelty of this work lies in addressing CNTRC beams resting on a spatially variable viscoelastic foundation, a problem that has received limited attention in the literature despite its practical significance. The reinforcement is provided by single-walled carbon nanotubes (SWCNTs), distributed in various configurations of uniaxially aligned material. Particular attention is given to the uniform distribution (UD) of reinforcement, which is analyzed to evaluate the effects of non-linear (NL) variation in CNT distribution. The governing equations of motion for the CNTRC beam are derived through the application of the First-Order Shear Deformation Theory (FSDT) in conjunction with Hamilton's principle. The beam is considered to be functionally graded (FG) and is modeled as resting on a three-parameter viscoelastic foundation, incorporating a Winkler spring interconnected with a Pasternak shear layer. Moreover, the viscoelastic behavior of the foundation is included, and the spatial variability of the Winkler foundation stiffness along the beam length is represented using linear, sinusoidal, and parabolic distributions. Analytical solutions in the form of dispersion relations are obtained to determine the wave frequencies and phase velocities. The influence of different CNT distribution configurations on wave propagation characteristics is demonstrated. Furthermore, the effects of CNT volume fraction, foundation stiffness parameters, and the damping coefficient on the dynamic response of the system are systematically investigated. Overall, this study advances the understanding of wave propagation in CNTRC beams by explicitly incorporating both non-linear CNT distribution and spatially variable viscoelastic foundations, offering insights not captured in previous beam models.

Key Words

carbon nanotube; FG-CNT beams; viscoelastic foundation; wave propagation

Address

Djaloul Zarga: Department of Civil Engineering, Faculty of Technology, University of M'Hamed BOUGARA Boumerdes, Algeria Mokhtar Nebab: Department of Civil Engineering, Faculty of Technology, University of M'Hamed BOUGARA Boumerdes, Algeria/ Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria Hassen Ait Atmane: Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria/ Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali of Chlef, Algeria Hadji Lazreg: Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam/ Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Tiaret, Algeria

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