Abstract
On the basis of an analysis of the asymptotics of higher approximations to solutions of a differential equation of longitudinal vibrations of a macroelastic body whose nonlinearity is explained by the hysteresis and “breathing” of the damaged material in the process of its cyclic deformation under conditions of tension-compression, we estimate the applicability of the spectral characteristics of strain cycles of the body under conditions of its natural or resonance vibrations to the diagnostics of fatigue damage of structural elements. It is shown that if nonlinearity is explained solely by the hysteresis of the material, then even the most representative first higher odd harmonics revealed in the vibration spectrum have very small amplitudes and the analysis of their variations is, in fact, similar to the analysis of the variations of the logarithmic decrement of vibrations (regarded as an integral characteristic of the dissipative properties of the material of the investigated element) but has lower resolution. At the same time, the discontinuities of the material appearing in the process of strain cycling are characterized by formation of numerous microcracks or a macrocrack and result in more clear detection of the representative constant component and even harmonics (mainly the second and fourth ones) in the spectrum of strain cycles of a vibration-insulated structural element in the process of its natural or resonance vibrations. These characteristics may serve as sensitive and efficient parameters for detection of fatigue damage to the material.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. S. Ivanova and V. F. Terent'ev,The Nature of Fatigue in Metals [in Russian], Metallurgiya, Moscow (1975).
F. M. Mednikov and M. L. Nechaevskii,A Method for the Evaluation of the Degree of Fatigue Damage to Materials, Inventor's Certificate 1499168 USSR, MKI N 01 N 3/32,Otkryt. Izobret., No. 29, p. 169 (1989).
N. G. Shul'zhenko, G. B. Ovcharova, and V. P. Biletchenko, “Analysis of the characteristics of vibrations of a multiple-seated rotor with a transverse crack under small static strains,”Probl. Prochn., No. 2, pp. 92–96 (1996).
N. G. Shul'zhenko and G. B. Ovcharova, “Vibrations of a multiple-seated rotor with a transverse crack,” in: Proc. Intern. Conf on the Dynamics of Rotor Systems [in Russian], Podol'e Techological University, Khmelnitskii, pp. 75–76 (1996).
G. S. Pisarenko, A. P. Yakovlev, and V. V. Matveev,Vibration-Absorbing Properties of Structural Materials. Handbook [in Russian], Naukova Dumka, Kiev (1971).
V. V. Matveev,Damping of Vibrations of Deformed Bodies [in Russian], Naukova Dumka, Kiev (1985).
G. S. Pisarenko,Vibrations of Elastic Systems with Dissipation of Energy in the Material [in Russian], Izd. Akad. Nauk Ukr. SSR, Kiev (1955).
G. S. Pisarenko,Dissipation of Energy in the Process of Mechanical Vibration [in Russian], Izd. Akad. Nauk Ukr. SSR, Kiev (1962).
S. Kotsan'da,Fatigue Fracture of Metals [in Russian], Metallurgiya, Moscow (1976).
Grabowski, “Vibration properties of a rotor with a transverse crack,”Konstruir. Tekhnol. Mashinostr.,103, No. 1, pp. 98–104 (1980).
V. P. Butseroga, “Equipment for experimental investigation of the growth of fatigue cracks,”Probl. Prochn., No. 2, pp. 110–119 (1996).
A. N. Romanov and N. A. Makhutov, “Investigation of the process of crack propagation under high-temperature single-stage and low-cycle loading,”Zavod. Lab., No. 1, pp. 85–91 (1978).
Vibrations in Engineering. Handbook, Vol. 2: Vibrations of Nonlinear Mechanical Systems [in Russian], Mashinostroenie, Moscow (1979).
S. I. Ratner,Fracture under Repeated Loads [in Russian], Oborongiz, Moscow (1959).
A. Ya. Krasovskii,Physical Fundamentals of Strength [in Russian], Naukova Dumka, Kiev (1977).
Yu. Murakami (editor),Stress Intensity Factors. Handbook [Russian translation], Vol. 1, Mir, Moscow (1990).
V. T. Troshchenko, V. V. Pokrovskii, and A. V. Prokopenko,Crack Resistance of Metals under Cyclic Loading [in Russian], Naukova Dumka, Kiev (1987).
V. V. Matveev, “Substantiation of the application of strain criteria of high-cycle fatigue fracture of metals. Part 2: A new approach,”Probl. Prochn., No. 3, pp. 3–12 (1995).
Author information
Authors and Affiliations
Additional information
Translated from Problemy Prochnosti, No. 6, pp. 5–20, November–December, 1997.
Rights and permissions
About this article
Cite this article
Matveev, V.V. Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 1. Longitudinal vibrations, analytical solution. Strength Mater 29, 561–572 (1997). https://doi.org/10.1007/BF02767605
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02767605