Effect of Notch Depth & Location on Modal Natural Frequency of Cantilever Beams

Abstract

The dynamic characteristics of a beam with breathing notch is studied in this paper. A systematic approach has been adopted in the present investigation to develop theoretical expressions for evaluation of natural frequencies and mode shapes. A simple elastic cantilever beam with breathing notch located at different position is considered for the dynamic analysis. The notch depth and its location are the main parameters for the vibration analysis of beams. The notch depth and its position may affect the natural frequency. Hence, it is essential to study the effect of notch depth and its location on modal natural frequency of the beam for the decent performance and its safety. This paper emphasis on the examination of these changes, which are useful for identification of notch location. The cantilever beam made of mild steel is selected for the study. In this work the comprehensive analysis of cantilever beam with & without notch has been done using analytical analysis and finite element method (FEM) and experimentally. An experimental set up was developed in which a cantilever beam with notch was excited by a hammer and the response was obtained using an accelerometer. The method presented describes the relation between the modal natural frequency with notch depth and its location. This paper contains the study of dynamic properties of cantilever beams subjected to free vibration under the influence of notch at different points along the length.