טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentDikla Elias
SubjectIdentification of Continuous Damage in Beams through
Changes in Frequencies
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Dr. Goldfeld Yiska
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

The study deals with vibration-based damage identification in beams. The objective was to develop a simple and direct identification technique by using a reduced number of unknown stiffness parameters, and based on changes in the modal frequencies only. Therefore, the stiffness distribution along the beam is represented by a polynomial function, while its coefficients are the unknown in the identification procedure. Thus, the procedure suits a continuous damage scenario, which in the case of reinforced concrete elements represents an advanced distributed cracked zone. In order to reduce the number of degrees of freedom of the analytical model, the algorithm employs the “exact” element method. The identification procedure constructs a sensitivity matrix using a reference stage of a healthy beam.

The study opens with an introduction, which presents the motivation for damage identification of beam elements, and followed by a literature survey of the available knowledge in the field, focusing on identification procedures based only on changes in modal frequencies.

The second part presents the calculation of the frequencies using the "exact element” method, which assumes that the beam properties (such as: cross section area, moment of inertia, etc.) can be described as continuous functions such as polynomial functions.

The third part describes the identification procedure. The purpose is to asses damaged zones along the beam, which cause change in the stiffness distribution. A sensitivity matrix using the frequencies of the healthy beam is constructed once for every beam, and by a given set of frequencies of a damaged condition, the coefficients of the stiffness distribution function can be evaluated. Thus, a subset of modal frequencies before and after damage is the only needed modal information. The presented procedure was validated on statically determinate and over determinate beams, and on analytical and distorted modal frequencies. In order to demonstrate its practicability, the procedure was also examined using experimental data available from the literature.

The last part describes an analytical identification procedure for local damage. The cracks were modeled locally as mass less rotational springs that are characterized by their equivalent depth. The results of the identification procedure show that the severity of the damage can be evaluated with a higher level of reliability than it location. This is due to the fact that different damage locations lead to the same modal frequencies reduction.