Improved FEM natural frequency calculation for structural frames by local correction procedure

Abstract

The accurate calculation of natural frequencies is important for vibration and earthquake analyses of structural frames. For this purpose, it is necessary to discretize each beam or column of the frame into one or more smaller elements. The required number of elements per member increases when the frame’s modal shapes have wavelengths similar to the beam lengths. This paper presents a method that reduces the number of elements needed for a precise calculation. This is achieved by implementing a straightforward local correction to the kinetic and elastic energy of certain elements, resulting in a substantial decrease in error. The validity of this method is demonstrated through a range of examples, from simple canonical cases to more realistic ones. Additionally, the paper discusses the unique features of this method and examines its relationship with other approaches.