RESEARCH ON MECHANICAL CHARACTERISTICS OF TWO-DIMENSIONAL ABSOLUTE NODAL COORDINATE SHEAR BEAM ELEMENT BASED ON MODAL ANALYSIS (MT)

With the help of theoretical analysis and numerical simulation, the modal parameters of the two-dimensionally low-order beam elements and high-order beam elements based on the absolute nodal coordinate formulation were studied. The analytical solution of the first-order thickness natural frequency of low-order and high-order beam elements considering the Poisson effect was derived. Based on the generalized characteristic equation, four natural frequencies and natural modes of bending, axial, shear and thickness of the shear beam element based on the absolute nodal coordinate formulation were obtained. Taking a simply supported beam structure as an example, the effects of the polynomial displacement field of the shear beam element on the four natural frequencies and natural modes of bending, axial, shear and thickness were analyzed. The results show that the polynomial displacement field of the shear beam element needs to introduce both the horizontal and vertical high-order terms x~2 and y~2. They mainly affect the bending and axial modal parameters, but have little effect on the shear and thickness modal parameters, and first-order thickness natural frequencies of the lower-order and higher-order beam elements is relatively close to the derived analytical solutions of first-order thickness natural frequencies.