Use of the elastic-and-rigid-combined beam element for dynamic analysis of a two-dimensional frame with arbitrarily distributed rigid beam segments

This paper presents an elastic-and-rigid-combined beam element such that the dynamic characteristics of a hybrid beam and a two-dimensional frame composed of any number of elastic and rigid beam segments can be easily determined. First of all, the displacements for the two nodes of a rigid beam segment are determined in terms of the displacements of its centre of gravity (c.g.). Next, the mass and stiffness matrices for the elastic-and-rigid-combined beam element are derived using the above-mentioned nodal displacements of the rigid beam segment and those of the two adjacent elastic beam elements. Furthermore, for the transformation of state variables of last elastic-and-rigid-combined (or three-node) beam element between the local and global co-ordinate systems, a new transformation matrix is also presented. Finally, the overall property matrices of the entire vibrating system are determined with the conventional assembly technique of finite element method (FEM) and its natural frequencies and associated mode shapes are determined with the standard approach. Some important factors, such as length of rigid beam segment, position for the centre of gravity (c.g.) of rigid beam segment, and total number of rigid beam segments in the entire vibrating system, are investigated. Numerical results reveal that the above-mentioned parameters have significant influence on the dynamic characteristics of the structure with arbitrarily distributed rigid beam segments.