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Based on the classical molecular-dynamics (MD) simulations, the vibrational behavior of cross-linked functionalized carbon nanotubes (CNTs) with polyethylene (PE) chains is studied under the applied mechanical tensile and compressive strains. So, different distribution patterns, namely mapped and wrapped distribution patterns are chosen. According to the results, it is seen that natural frequency of cross-linked functionalized CNTs reduces in which this reduction increases by increasing the weight percentage of attached chain. Under tensile strain, it is observed that the frequency of functionalized CNTs increases. Moreover, it is observed that the frequency shifts rise by increasing the applied tensile strain. By contrast, the compressive strain results in higher reductions in natural frequency of functionalized CNTs which considerably rises by increasing the applied strain. Moreover, it is shown that as the weight percentage of cross-linked functionalized CNTs increases, the sensitivity of the frequency shift to the applied tensile and compressive strains decreases and increases, respectively.

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