Abstract
Here, we consider the free vibration of a tapered beam modeling nonuniform single-walled carbon nanotubes, i.e., nanocones. The beam is clamped at one end and elastically restrained at the other, where a concentrated mass is also located. The equation of motion and relevant boundary conditions are written considering nonlocal effects. To compute the natural frequencies, the differential quadrature method (DQM) is applied. The influence of the small-scale parameter, taper ratio coefficient, and added mass on the first natural frequency is investigated and discussed. Some numerical examples are provided to verify the accuracy and validity of the proposed method, and numerical results are compared to those obtained from exact solution. Since the numerical results are in excellent agreement with the exact solution, we argue that DQM provides a simple and powerful tool that can also be used for the free vibration analysis of carbon nanocones with general boundary conditions for which closed-form solutions are not available in the literature.
Highlights
Materials 2021, 14, 3445. https://Carbon-based nanostructures have been intensively researched due to their outstanding properties
Here, we consider the free vibration of a tapered beam modeling nonuniform singlewalled carbon nanotubes, i.e., nanocones
Since the numerical results are in excellent agreement with the exact solution, we argue that differential quadrature method (DQM) provides a simple and powerful tool that can be used for the free vibration analysis of carbon nanocones with general boundary conditions for which closed-form solutions are not available in the literature
Summary
Carbon-based nanostructures have been intensively researched due to their outstanding properties. Still based on the nonlocal Euler–Bernoulli beam theory, the effects of taper ratio coefficient, small-scale parameter, and viscoelastic behavior on the resonant frequencies of CNCs was discussed in [30]. The influence of the small-scale parameter, taper ratio coefficient, and added mass on the first, natural, dimensionless frequency is investigated in Section 4 to assess the accuracy and validity of the proposed method. The results complement those previously reported in [35], where the convergence of the method was validated through known exact solutions.
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