Abstract：Peridynamics (PD) is a new continuum mechanics formulation, which is in the form of integro-differential equations. Moreover, PD has a length scale parameter which allows to analyze nonlocal phenomenon and problems that cannot be represented by classical continuum mechanics. Since its introduction, many research interests have been received especially in recent years. However, it is quite computational expensive for PD to model and analyze engineering structures in three dimensional. Hence, it is important to develop simplified PD formulations for beam like structures. In this study, vibration analysis of beam structure in PD is carried out. First, based on the Euler beam theory, a two-degree ordinary state based PD model is derived for beam structure, the method for assembling density matrix and micromodulus matrix is also explained, and then the approach to apply boundary condition is given based on Taylor series expansion and local boundary conditions. The vibration characteristic of beam with three different boundary conditions is studied and compared with the finite element results of local beam to verify the accuracy of the model and method, the influence of the PD length scale parameter on the natural frequencies is analyzed. It is found that when the density of material points is small, the non-locality of PD beam model is weak, and the PD results are closed to the finite element results. As the density of material points gradually increases, the non-locality of PD beam increases and the natural frequency decreases. When length scale parameter approaches zero, the frequency of PD beam converges to the finite element solution of local beam. Results show that the PD beam model and free boundary conditions proposed in this paper can effectively analyze the vibration characteristics of the beam, and provide means to analyze the dynamic characteristics of beam structures in PD.
2021, Vol. 42 
