Modal Analysis of Monolithic and Jointed Type Cantilever Beams with Non-Uniform Section

Modal analysis of non-uniform bolted structures are of significance in modeling many complex mechanical structures. There are vast literatures available related with the analytical as well as numerical modeling of bolted joint. However, most of the analytical model discuss about the modeling of first mode of uniform structures with single bolted joint. In this paper, we present the modeling of single as well as bolted non-uniform beams using approximate mode shapes. To develop the model, we first carry out experiments to measures the modal frequencies and shapes of the test structures. Subsequently, we also do numerical modeling of non-uniform beams in ANSYS to verify the validity of the Euler-Bernoulli beam theory in developing the analytical models. Finally, using the Euler-Bernoulli beam theory, we obtain the analytical values of frequencies using the approximate the mode shapes. The analytical results are found to be closer to the experimental results with a maximum percentage error of about 15 %. The model presented in the paper can be extended to the mechanical structures with many non-uniform sections with or without bolted joints.