Abstract
The subject of the paper is an application of the non-destructive vibration method for identifying the location of two cracks occurring in a beam. The vibration method is based on knowledge of a certain number of vibration frequencies of an undamaged element and the knowledge of the same number of vibration frequencies of an element with a defect. The analyzed beam, with a variable cross-sectional area, has been described according to the Bernoulli-Euler theory. To determine the values of free vibration frequencies the analytical solution, with the help of the Green’s function method, has been used.
Highlights
The beams, whose geometry and/or material properties change along their length, are important for instance in the design of aircraft, robot arms and tall buildings, where they are used both to reduce weight or volume, and to increase strength and stability
The relative error defines the difference between the assumed positions of cracks (L1a, L2a) and the values calculated in the identification process (L1d, L2d):
The identification of the location of two symmetrical cracks occurring in the cantilever beam with a variable cross-sectional area has been done
Summary
The beams, whose geometry and/or material properties change along their length, are important for instance in the design of aircraft, robot arms and tall buildings, where they are used both to reduce weight or volume, and to increase strength and stability. In these types of objects even minor damage can cause structural failure and even catastrophe. In the case of three-dimensional graphs (knowledge of the first three vibration frequencies), it is possible to identify two parameters of one damage (e.g. position and depth of gap [9]) or, as will be shown in this paper, one parameter (position of defects) of two cracks. The governing differential equation of motion of i-th system’s segment is:
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call