On determination of vibration characteristics of a beam with a closing crack in bending vibrations

Strength of Materials

Volumn 32, Issue 3, 2000, Pages 211-224

  Matveev, V V ^a   Bovsunovskii, A P ^a  

^a PISARENKO INSTITUTE OF PROBLEMS OF STRENGTH   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL APPROACH; BENDING VIBRATIONS; DAMAGE DIAGNOSTICS; DISPLACEMENT WAVES; ENERGY CRITERION; MOMENT OF INERTIA; STRAIN DISTRIBUTIONS; VIBRATION CHARACTERISTICS;

INVERSE PROBLEMS; VIBRATION ANALYSIS;

CRACKS;

EID: 33747178025     PISSN: 00392316     EISSN: 15739325     Source Type: Journal    
DOI: 10.1007/BF02509848     Document Type: Article

References (25)

1. P. G. Kirshmer, "The effect of discontinuities on the natural frequency of beams,"Proc. ASTM,44, 897-904 (1944).
2. W. T. Thomson, "Vibration of slender bars with discontinuities in stiffness,"J. Appl. Mech.,16, 203-207 (1949).
3. H. J. Petroski, "Simple static and dynamic models for the cracked elastic beams,"Int. J. Fract.,17, No. 4 R71-R76 (1981).
4. P. Gudmundson, "Eigenfrequency changes of structures due to cracks, notches or other geometrical changes,"J. Mech. Phys. Solids 30, No. 5, 339-353 (1982). (Pubitemid 13508172)
5. V. M. Chushko, "The dependence of natural vibration frequency of a beam on the crack size," in:Strength of Materials and Structural Elements under Loading at Sonic and Ultrasonic, Frequencies [in Russian], Naukova Dumka, Kiev (1983), pp. 249-253.
6. A. Joshi and B. S. Madhusudhan, "A unified approach to free vibration of locally damaged beams having various homogeneous, boundary conditions,"J. Sound Vibration,147, No. 3, 475-488 (1991). (Pubitemid 21683753)
7. W. M. Ostachowich and M. Krawczuk, "Analysis of the effects of cracks on the natural frequencies of a cantilever beam,"J. Sound Vibration,150, No. 2, 191-201 (1991).
8. M. L. Kikidis and C. A. Papadopoulos, "Slenderness ratio effect on cracked beams,"J. Sound Vibration,155, No. 1, 1-11 (1992).
9. M.-H. Shen and C. Pierre, "Free vibrations of beams with a single-edge crack,"J. Sound Vibration,170, No. 2, 237-259 (1994).
10. V. A. Karasev and A. B. Roitman,Operation Development of Machines. Vibrodiagnostic Methods [in Russian] Mashinostroenie, Moscow (1986).
11. V. P. Golub, V. P. Butseroga, and A. D. Pogrebnyak, "Investigation of fatigue crack kinetics by the differential compliance method,"Prikl. Mekh.,31, No. 12, 66-74 (1995).
12. N. P. Plakhtienko and S. A. Yasinskii, "On second-order resonance in vibration of a beam with a cross crack,"Probl. Prochn., No. 3, 56-63 (1995).
13. V. V. Matveev, "On the efficiency of the method of spectral vibrodiagnostics of the fatigue damage of structural elements. Part 1. Longitudinal vibrations. Analytical solution,"Probl. Prochn., No. 6, 5-20 (1997).
14. V. V. Matveev and A. P. Bovsunovskii, "On the efficiency of the method of spectral vibrodiagnostics of the fatigue damage of structural elements. Part 2. Bending vibrations. Analytical solution,"Probl. Prochn., No. 6, 9-22 (1998).
15. A. B. Roitman, A. A. Pylov, and N. B. Aleksandrova, "Longitudinal vibrations of a crosscracked cantilever beam. Part 1. Small vibrations, "Probl. Prochn., No. 2, 23-34 (1999).
16. A. Ibrahim, F. Ismail, and H. K. Martin, "Modeling of the dynamics of a continuous beam including nonlinear fatigue crack,"Int. J. Anal., Exp. Modal Analysis,2, No. 2, 76-82 (1987).
17. R. D. Adams P. Cawley, C. J. Pye, and B. J. Stone, "A vibration technique for nondestructively assessing the integrity, of structures,"J. Mech. Eng. Sci.,20, No. 2, 93-100 (1978). (Pubitemid 9393443)
18. Ya. G. Panovko,Fundamentals of Applied Theory of Elastic Vibrations [in Russian], Mashgiz, Moscow (1957).
19. G. S. Pisarenko,Vibration of Mechanical Systems Taking into Account the Imperfect Elasticity of the Material [in Russian] Naukova Dumka, Kiev (1970).
20. J. Rise in: G. Libovitz (Ed.),Mathematical Techniques in Fracture Mechanics, Vol. 2,Fracture [Russian translation], Mir, Moscow (1975), pp. 204-335.
21. G. P. Cherepanov,Brittle Fracture, Mechanics [in Russian], Nauka, Moscow (1974).
22. I. I. Blekhman (Ed.),Vibration in Engineering. Handbook. Vol. 2.Vibration of Nonlinear Mechanical Systems [in Russian], Mashinostroenie Moscow (1979).
23. A. V. Bovsunovskii, "On determination of the natural frequency of transverse and longitudinal vibration of a cracked beam. Part 2. Experimental and calculation results,"Probl. Prochn., No. 3, 45-53 (1999).
24. D. Wendtland,Änderung der Biegeeigenfrequenzen einer Idealisierten Schaufel durch Risse Ph.D. Thesis, University of Karlsruhe (1972).
25. A. P. Bovsunovskii, "Mechanical hysteresis loop shape for metallic material under harmonic stresses below the fatigue limit. Part 2. Experimental technique and results"Probl. Prochn., No. 3, 119-130 (1997).