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<p>This paper investigates the free vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) joined conical-cylindrical (JCC) shells. Artificial springs are adopted to simulate boundary conditions. Based on Donnell’s thin shell theory, the strain energy and kinetic energy of the FG-CNTRC JCC shells are formulated. Displacement admissible functions are expressed in terms of Chebyshev polynomials, and the modal frequency equations are derived via Rayleigh-Ritz method. Convergence and accuracy of the present model are verified. A comprehensive parametric study is performed to examine the effects of the gradient index, carbon nanotube volume fraction, spring stiffness coefficients, shells thickness, semi-cone angle, and temperature on the structural vibration characteristics. Numerical results indicate that within the volume fraction exponent range of 0 to 5, the X-type CNTs distribution has amore significant effect on the modal frequencies, while the O-type distribution exhibits the least influence; the axial spring stiffness coefficient affects the structural frequencies more remarkably than other spring components; an in shells thickness enhances the structural stiffness, leading to an almost linear increase in frequencies; an rise in temperature reduces elastic modulus and stiffness of structure, resulting in a decrease in frequencies.</p>

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Analysis of free vibration characteristics of carbon nanotubes reinforced functionally graded conical-cylindrical joined shells

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Runhao Wan,
  • Wenguang Liu,
  • Pan Guo,
  • Xuyang Cai

摘要

This paper investigates the free vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) joined conical-cylindrical (JCC) shells. Artificial springs are adopted to simulate boundary conditions. Based on Donnell’s thin shell theory, the strain energy and kinetic energy of the FG-CNTRC JCC shells are formulated. Displacement admissible functions are expressed in terms of Chebyshev polynomials, and the modal frequency equations are derived via Rayleigh-Ritz method. Convergence and accuracy of the present model are verified. A comprehensive parametric study is performed to examine the effects of the gradient index, carbon nanotube volume fraction, spring stiffness coefficients, shells thickness, semi-cone angle, and temperature on the structural vibration characteristics. Numerical results indicate that within the volume fraction exponent range of 0 to 5, the X-type CNTs distribution has amore significant effect on the modal frequencies, while the O-type distribution exhibits the least influence; the axial spring stiffness coefficient affects the structural frequencies more remarkably than other spring components; an in shells thickness enhances the structural stiffness, leading to an almost linear increase in frequencies; an rise in temperature reduces elastic modulus and stiffness of structure, resulting in a decrease in frequencies.