Analysis of the Effect of Nonlocal Factors on the Vibration of Euler-Bernoulli Beams

Currently, the Euler-Bernoulli beam theory relies mainly on the classical continuous medium and local elasticity theories in vibration analysis, but fails to take into account the length interactions between atomic lattices, which makes it difficult to accurately reflect the mechanical properties of beams. Therefore, the goal of this study is to develop a novel method to accurately calculate the mechanical properties of beams. The method is used in combining the Eringen nonlocal theory and extending the Euler-Bernoulli beam theory to construct a nonlocal physical model of beams applicable to arbitrary loads and to verify its degradation. The model is solved by the Nigam-Jennings method, and the effects of nonlocal factors and beam parameters on its self-oscillation frequency and deformation are explored. It is found that the effect of the nonlocal factors on the vibration frequency is negligible after the beam length reaches a certain threshold, while the effect of the nonlocal factors on the vibration frequency and amplitude is significantly enhanced when the vibration mode order increases.