Free vibration analysis of multiple cracked frames using dynamic stiffness method

Abstract

Cracks are the most common type of structural damage in many engineering structures, introducing the local change in stiffness of structural elements and changing the dynamic properties of the structure. Therefore, it is of great importance to detect and locate the existing structural damage in its early phase to prevent crack propagation. In the paper, free vibration analysis of beams and frames with multiple cracks has been carried out. First, the dynamic stiffness matrix of beam element with multiple cracks based on Bernoulli-Euler theory has been derived. Using the developed model, extensive free vibration study of multiple-cracked frame structures has been conducted. Original Matlab code has been developed for the derivation of natural frequencies and plot of mode shapes. After the validation of the model against the existing data from the literature, several benchmark examples are provided. As expected, increasing size and number of cracks lead to decrease of natural frequencies due to the local stiffness degradation.