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Published in: Strength of Materials 5/2021

03-12-2021

Boundary Effect on Forming the Natural Frequency Spectrum of Flexural Vibrations of Beams with Local Surface Defects

Authors: A. P. Zinkovskii, I. G. Tokar

Published in: Strength of Materials | Issue 5/2021

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Abstract

The authors present the results of calculation investigations on the determination of the mechanisms of the boundary effect for the beam with a constant rectangular cross section on the formation of the natural frequency spectrum of flexural vibrations in the presence of an open edge fatigue crack on the beam surface. For various boundary conditions of the beam fixation, variations of the first-mode flexural vibration natural frequencies at different locations of the above surface defect (modeled by a 1 mm-wide groove with variable depth) along the beam length are established. The analysis of the obtained dependencies revealed that the beam with both free edges contained a segment where the natural frequency of flexural vibrations of the damaged beam was no less than the intact beam frequency. Moreover, there is stress symmetry about the beam middle, which undergoes the maximum frequency variation due to damage. Meanwhile, in the beam with two rigidly fixed edges, the maximal variations of the natural flexural frequencies of the damaged beam occurred at some distance from these edges, namely at 0.025 and 0.975 relative lengths. When the defect/groove was located in the middle of the beam, the damaged beam’s natural frequency varied less (almost twice). Moreover, the data symmetry about the beam middle was observed in the dependencies (0.25 and 0.75), where the natural frequencies of the damaged and intact beams were the same. In the beam with one rigidly fixed end, the smallest value of the natural frequency of the damaged beam vibrations is observed near the fixed edge. With the groove shift from the edge, the vibration frequency increases, reaching or even exceeding that of the intact beam with increased relative length value. For the beam with one or two rigidly fixed edges, the identical dependencies in the direction of one or two axes were obtained. Therefore, for the beam boundary conditions implying one or two free edges, there were segments with the natural frequencies of vibrations of the damaged beam exceeding those of the intact beam. On the contrary, for the boundary conditions of the beam with fixed ends, the above values are equal only locally, i.e., within a very narrow beam segment.
Literature
1.
go back to reference I. A. Birger and B. F. Balashov, Structural Strength of Materials and Parts of Gas-Turbine Engines [in Russian], Mashinostroenie, Moscow (1981). I. A. Birger and B. F. Balashov, Structural Strength of Materials and Parts of Gas-Turbine Engines [in Russian], Mashinostroenie, Moscow (1981).
2.
go back to reference S. P. Timoshenko, D. H. Young, and W. Weaver, Vibration Problems in Engineering, Wiley, Chichester. (1974). S. P. Timoshenko, D. H. Young, and W. Weaver, Vibration Problems in Engineering, Wiley, Chichester. (1974).
3.
go back to reference I. A. Birger and B. F. Schorr, Dynamics of Aircraft Gas-Turbine Engines [in Russian], Mashinostroenie, Moscow (1981). I. A. Birger and B. F. Schorr, Dynamics of Aircraft Gas-Turbine Engines [in Russian], Mashinostroenie, Moscow (1981).
4.
go back to reference A. A. Inozemtsev and V. L. Sandratskii, Gas-Turbine Engines [in Russian], JSC Aviadvigatel (2006). A. A. Inozemtsev and V. L. Sandratskii, Gas-Turbine Engines [in Russian], JSC Aviadvigatel (2006).
5.
go back to reference V. V. Matveev, Damping Vibrations of Deformable Bodies [in Russian], Naukova Dumka, Kiev (1985). V. V. Matveev, Damping Vibrations of Deformable Bodies [in Russian], Naukova Dumka, Kiev (1985).
6.
go back to reference Yu. A. Nozhnitskii, “Development of key (critical) technologies for creating a new generation of gas-turbine engines,” in: New Technological Processes and Reliability of GTE (Scientific and Technical Collection) [in Russian], Issue 1: Blisks and Blinks of Turbomachines, TsIAM, Moscow (2000), pp. 5–34. Yu. A. Nozhnitskii, “Development of key (critical) technologies for creating a new generation of gas-turbine engines,” in: New Technological Processes and Reliability of GTE (Scientific and Technical Collection) [in Russian], Issue 1: Blisks and Blinks of Turbomachines, TsIAM, Moscow (2000), pp. 5–34.
8.
go back to reference A. N. Petukhov, Fatigue Resistance of GTE Parts [in Russian], Mashinostroenie, Moscow (1993). A. N. Petukhov, Fatigue Resistance of GTE Parts [in Russian], Mashinostroenie, Moscow (1993).
9.
go back to reference M. Sh. Nikhamkin, L. V. Voronov, I. P. Konev, and I. V. Semenova, “Foreign object damage and stress concentration in compressor blades,” in: Reliability and Durability of Structural Machines [in Russian], Issue 31 (2008), pp. 126–135. M. Sh. Nikhamkin, L. V. Voronov, I. P. Konev, and I. V. Semenova, “Foreign object damage and stress concentration in compressor blades,” in: Reliability and Durability of Structural Machines [in Russian], Issue 31 (2008), pp. 126–135.
10.
go back to reference E. V. Martsenyuk, A. I. Garkusha, and V. S. Chigrin, “Influence of the defect type ‘dents’ on the frequency characteristics of compressor blades,” Aviats.-Kosm. Tekh. Tekhnol., No. 8 (85), 61–65 (2011). E. V. Martsenyuk, A. I. Garkusha, and V. S. Chigrin, “Influence of the defect type ‘dents’ on the frequency characteristics of compressor blades,” Aviats.-Kosm. Tekh. Tekhnol., No. 8 (85), 61–65 (2011).
11.
go back to reference I. G. Tokar’ and A. P. Zinkovskii, “Influence of the parameters of a local defect in a regular system on the range of eigenfrequencies of vibrations and the level of vibration stresses in elements of the same type,” Strength Mater., 42, No. 2, 167–174 (2010), https://​doi.​org/​10.​1007/​s11223-010-9203-7. I. G. Tokar’ and A. P. Zinkovskii, “Influence of the parameters of a local defect in a regular system on the range of eigenfrequencies of vibrations and the level of vibration stresses in elements of the same type,” Strength Mater., 42, No. 2, 167–174 (2010), https://​doi.​org/​10.​1007/​s11223-010-9203-7.
12.
go back to reference P. F. Rizos, N. Aspragathos, and A. D. Dimarogonas, “Identification of crack location and magnitude in a cantilever beam from the vibration modes,” J. Sound Vib., 138, No. 3, 381–388 (1990). CrossRef P. F. Rizos, N. Aspragathos, and A. D. Dimarogonas, “Identification of crack location and magnitude in a cantilever beam from the vibration modes,” J. Sound Vib., 138, No. 3, 381–388 (1990). CrossRef
13.
go back to reference W. M. Ostachowicz and M. Krawczuk, “Analysis of the effect of cracks on the natural frequencies of a cantilever beam,” J. Sound Vib., 150, No. 2, 191–201 (1991). W. M. Ostachowicz and M. Krawczuk, “Analysis of the effect of cracks on the natural frequencies of a cantilever beam,” J. Sound Vib., 150, No. 2, 191–201 (1991).
14.
go back to reference T. Y. Kam and T. Y. Lee, “Detection of cracks in structures using modal test data,” Eng. Fract. Mech., 42, No. 2, 381–387 (1997). CrossRef T. Y. Kam and T. Y. Lee, “Detection of cracks in structures using modal test data,” Eng. Fract. Mech., 42, No. 2, 381–387 (1997). CrossRef
15.
go back to reference Y. S. Lee and M. J. Chung, “A study on crack detection using eigenfrequency test data,” Comput. Struct., 77, No. 3, 327–342 (2000). CrossRef Y. S. Lee and M. J. Chung, “A study on crack detection using eigenfrequency test data,” Comput. Struct., 77, No. 3, 327–342 (2000). CrossRef
17.
go back to reference P. Gudmundson, “Eigenfrequency changes of structures due to cracks, notches or other geometrical changes,” J. Mech. Phys. Solids, 30, 339–353 (1982). CrossRef P. Gudmundson, “Eigenfrequency changes of structures due to cracks, notches or other geometrical changes,” J. Mech. Phys. Solids, 30, 339–353 (1982). CrossRef
18.
go back to reference Yu. S. Vorobyev and M. A. Storozhenko, “Analysis of vibrations of turbomachine blade systems with damage,” Aviats.-Kosm. Tekh. Tekhnol., No. 8 (44), 132–134 (2007). Yu. S. Vorobyev and M. A. Storozhenko, “Analysis of vibrations of turbomachine blade systems with damage,” Aviats.-Kosm. Tekh. Tekhnol., No. 8 (44), 132–134 (2007).
20.
go back to reference G. S. Pisarenko, A. P. Yakovlev, and V. V. Matveev, Strength of Materials. Handbook [in Russian], Naukova Dumka, Kiev (1975). G. S. Pisarenko, A. P. Yakovlev, and V. V. Matveev, Strength of Materials. Handbook [in Russian], Naukova Dumka, Kiev (1975).
Metadata
Title
Boundary Effect on Forming the Natural Frequency Spectrum of Flexural Vibrations of Beams with Local Surface Defects
Authors
A. P. Zinkovskii
I. G. Tokar
Publication date
03-12-2021
Publisher
Springer US
Published in
Strength of Materials / Issue 5/2021
Print ISSN: 0039-2316
Electronic ISSN: 1573-9325
DOI
https://doi.org/10.1007/s11223-021-00335-6