Mechanical vibration response of CNT-reinforced nanocomposite conical shells using the Mori–Tanaka micromechanics model and FSDT

Saira Javed; Saira Javed

doi:10.3934/math.20251298

AIMS Mathematics

2025, Volume 10, Issue 12: 29552-29581. doi: 10.3934/math.20251298

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Research article

Mechanical vibration response of CNT-reinforced nanocomposite conical shells using the Mori–Tanaka micromechanics model and FSDT

Saira Javed ^,

Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Hofuf, Al Ahsa, 31982, Saudi Arabia

Received: 18 September 2025 Revised: 22 November 2025 Accepted: 05 December 2025 Published: 15 December 2025
MSC : 70H25, 74-10, 74A05, 74H15, 74H25, 74M20

The free vibration behavior of carbon nanotube (CNT)-reinforced nanocomposite conical shells was investigated using the first-order shear deformation theory (FSDT) in conjunction with the Mori–Tanaka homogenization scheme. CNTs were incorporated into an epoxy matrix and E-glass fibers to enhance mechanical performance, particularly stiffness and damping characteristics. The effective material properties of the CNT-reinforced nanocomposite were computed using the Mori–Tanaka method, accounting for the volume fraction, orientation, and dispersion of CNTs within the matrix. A derivation of the dynamic equilibrium equations of motion for conical shells was carried out using Hamilton's principle, incorporating lateral shear deformation effects to improve accuracy for thick and moderately thick shells. An appropriate boundary condition associated with spline approximation was used to extract the natural frequencies. Ply orientation, number of layers, and shape parameters, including cone angle, length ratio, and circumferential node number, were considered to assess their influence on the frequencies. Numerical results demonstrate that matrix material significantly affects natural frequencies. Inclusion and exclusion of CNT in composites also alter the natural frequencies. These outcomes provide useful perspectives for improving the design and vibration mitigation of advanced nanocomposite conical shell structures used in aerospace, automotive, and marine engineering applications.
- carbon nanotube,
- reinforced nanocomposite,
- Mori–Tanaka model,
- matrix,
- frequency
Citation: Saira Javed. Mechanical vibration response of CNT-reinforced nanocomposite conical shells using the Mori–Tanaka micromechanics model and FSDT[J]. AIMS Mathematics, 2025, 10(12): 29552-29581. doi: 10.3934/math.20251298

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Abstract

The free vibration behavior of carbon nanotube (CNT)-reinforced nanocomposite conical shells was investigated using the first-order shear deformation theory (FSDT) in conjunction with the Mori–Tanaka homogenization scheme. CNTs were incorporated into an epoxy matrix and E-glass fibers to enhance mechanical performance, particularly stiffness and damping characteristics. The effective material properties of the CNT-reinforced nanocomposite were computed using the Mori–Tanaka method, accounting for the volume fraction, orientation, and dispersion of CNTs within the matrix. A derivation of the dynamic equilibrium equations of motion for conical shells was carried out using Hamilton's principle, incorporating lateral shear deformation effects to improve accuracy for thick and moderately thick shells. An appropriate boundary condition associated with spline approximation was used to extract the natural frequencies. Ply orientation, number of layers, and shape parameters, including cone angle, length ratio, and circumferential node number, were considered to assess their influence on the frequencies. Numerical results demonstrate that matrix material significantly affects natural frequencies. Inclusion and exclusion of CNT in composites also alter the natural frequencies. These outcomes provide useful perspectives for improving the design and vibration mitigation of advanced nanocomposite conical shell structures used in aerospace, automotive, and marine engineering applications.

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