Vibrations in engineering and technology

Bovsunovsky Anatoliy Petrovich – Doctor of Technical Sciences, Professor, Professor of Department of Machines and Apparatus for Food and Pharmaceutical Production, National University of Food Technologies (Volodymyrska str., 68, Kyiv, Ukraine, 01601: e-mail: apbovsunovsky@gmail.com).

Surace Cecilia – Philosophy Doctor, Professor, Department of Structural Geotechnical and Building Engineering, Politecnico di Torino (Сorso Duca degli Abruzzi 24, Torino, Italy,10129; e-mail: cecilia.surace64@gmail.com).

The problems of vibration diagnostics based on the change of natural frequencies of structures are connected with the influence of ambient and operational factors (temperature, humidity, wind, heavy traffic etc.) on the natural frequencies. In some cases, this effect is comparable with the effect of damage itself and reliable diagnostics of damage becomes problematic. To solve this problem, the use of the ratio change between natural frequencies of different mode shapes is proposed as a characteristic of damage. The study has demonstrated that this ratio is unaffected by the environmental and operational factors. Application of the proposed method is illustrated using the example of Z24 reinforced concrete bridge. As the characteristic feature of the reinforced concrete structures damage is the occurrence of multiple cracks, in the analytical model, apart from the size and location of the cracks, the possibility of several locally located cracks was taken into account.The analytical study was performed to calculate the mode shapes and natural frequencies of damaged multi-span beam-like structure. The results reveal that, in order to identify local damage of subcritical size, natural frequency data of at least four modes of vibration are necessary. The eigenfrequencies obtained experimentally in the study of the Z24 bridge were used to confirm that the change in the eigenfrequency ratio can be used to diagnose relatively small local defects in complex structures. At this the reliability of such vibration diagnostics is much higher than based on the change of natural frequencies and mode shapes, since the change in the ratio of natural frequencies does not depend on the environmental conditions and operating conditions of the structure.

1. Krämer C., De Smet C.A.M., De Roeck G. (1999). Z24 bridge damage detection. Proc. of IMAC XVII, Kissimmee, Florida, USA, 1023–1029.

2. Moser P., Moaveni B. (2011). Environmental effects on the identified natural frequencies of the Dowling Hall Footbridge. Mechanical systems and signal processing, 25, 2336–2357.

3. Cross E.J., Koo K.Y., W.Brownjohn J.M., Worden K. (2013). Long-term monitoring and data analysis of the Tamar Bridge. Mechanical systems and signal processing, 35, 16–34.

4. Samir N. Shoukry, Gergis W. William, Mourad Y. Riad. (2009).Effect of moisture and temperature on the mechanical properties of concrete. Proc. of the SEM Annual Conference, Albuquerque, New Mexico, USA, 1–9.

5. Farrar C.R., Doebling S.W., Cornwell P.J. (1997). Variability of modal parameters measured on the Alamosa Canyon Bridge. Proc. of the 15^th IMAC, Orlando, Florida, USA, 257–263.

6. Peeters B., De Roeck G. (2001). One-year monitoring of the Z24-bridge: environmental effects versus damage events. Earthquake engineering and structural dynamics, 30, 2, 149–171.

7. Kim C., Jung D., Kim N. (2003). Effect of vehicle weight on natural frequencies of bridges measured from traffic-induced vibration. Earthquake engineering, 2, 1, 109–115.

8. Farrar C.R., Worden K. (2013). Structural health monitoring: a machine learning perspective. John Wiley & Sons, Ltd.

9. Sinou J.J. (2007). Damage assessment based on the frequencies’ ratio surfaces intersection method for the identification of the crack depth, location and orientation. Structural durability and health monitoring, 3, 3, 134–162.

10. Maeck J., De Roeck G. (2003). Description of Z24 benchmark. Mechanical systems and signal processing, 17, 1, 127–131.

11. Ananiev I.V. (1946). Spravochnik po raschiotu sobstvennyh kolebaniy uprugih system [Handbook for calculation of natural vibrations of elastic systems]. Moscov-Leningrad: Gostekhteorizdat. [in Russian].  

12. Reynders E., De Roeck G. (2014). Vibration-based damage identification: the Z24 bridge benchmark. Berlin-Heidelberg: Springer.

13. Fracture mechanics of concrete: Structural application and numerical calculation. (1985) / editors G.C. Sih, A. Di Tommaso. Netherlands: Springer.

14. Stress intensity factors handbook. In 3 vol. Vol. I. (1987) / editor Y.Murakami. Japan: Pergamon Press.

15. Reynders E., De Roeck G.  (2010). A local flexibility method for vibration-based damage localization and quantification. Journal of sound and vibration, 329, 12, 2367–2383.