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<p>Currently, existing Rayleigh Beam elastic theory models for nanobeams not only fail to account for the influence of foundation deformation on the beam but also neglect the length interactions between atomic lattices. Consequently, they cannot accurately reflect the beam’s true mechanical properties. Therefore, the primary objective of this manuscript is to propose a novel computational method that precisely reveals the true mechanical behavior of globally coupled beams. First, this method successfully incorporates foundation deformation effects. By employing a global coupling mechanism that accounts for length interactions between atomic lattices, it establishes a nonlocal Rayleigh nanobeam vibration model on elastic foundations and provides a degeneracy verification method for the model. Second, by applying the Laplace transform to convert the model from the time domain to the frequency domain, and employing Hasselmann’s complex modal synthesis method, the spatial state transfer function of this vibration model in the frequency domain, along with its analytical solutions and verification of solution degeneracy, have been successfully derived. Finally, the mechanism of global coupling was revealed constitutively through the beam’s material point. The effects of nonlocal factors, geometric factors, and ground beam stiffness parameters on the vibration frequency and amplitude of the Rayleigh nonlocal nanobeam on an elastic foundation were analyzed. Analysis indicates that nonlocal effects dominate system frequency regulation. Their influence on the frequency of Rayleigh nonlocal nanobeams on low-order elastic foundations far exceeds that of higher-order effects, with response sensitivity increasing at higher orders. Amplitude fluctuations intensify as the factor strengthens. Geometric factors and ground beam stiffness parameters exert minor effects on beam frequencies. These findings provide crucial guidance for nanobeam applications in biosensors, cell-material surface interactions, and disease diagnosis and treatment.</p>

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Analysis of the influence of nonlocal factors on the vibration of Rayleigh nonlocal nanobeams on elastic foundations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月29日

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  • Kun Zhao,
  • Guobing Wang,
  • Zhanwu Zhou,
  • Lei Wang

摘要

Currently, existing Rayleigh Beam elastic theory models for nanobeams not only fail to account for the influence of foundation deformation on the beam but also neglect the length interactions between atomic lattices. Consequently, they cannot accurately reflect the beam’s true mechanical properties. Therefore, the primary objective of this manuscript is to propose a novel computational method that precisely reveals the true mechanical behavior of globally coupled beams. First, this method successfully incorporates foundation deformation effects. By employing a global coupling mechanism that accounts for length interactions between atomic lattices, it establishes a nonlocal Rayleigh nanobeam vibration model on elastic foundations and provides a degeneracy verification method for the model. Second, by applying the Laplace transform to convert the model from the time domain to the frequency domain, and employing Hasselmann’s complex modal synthesis method, the spatial state transfer function of this vibration model in the frequency domain, along with its analytical solutions and verification of solution degeneracy, have been successfully derived. Finally, the mechanism of global coupling was revealed constitutively through the beam’s material point. The effects of nonlocal factors, geometric factors, and ground beam stiffness parameters on the vibration frequency and amplitude of the Rayleigh nonlocal nanobeam on an elastic foundation were analyzed. Analysis indicates that nonlocal effects dominate system frequency regulation. Their influence on the frequency of Rayleigh nonlocal nanobeams on low-order elastic foundations far exceeds that of higher-order effects, with response sensitivity increasing at higher orders. Amplitude fluctuations intensify as the factor strengthens. Geometric factors and ground beam stiffness parameters exert minor effects on beam frequencies. These findings provide crucial guidance for nanobeam applications in biosensors, cell-material surface interactions, and disease diagnosis and treatment.