We discuss an approximate analytical method for calculating the main parameter of nonlinearity of vibration of an elastic body with a closing crack, which is simulated by a single-degree-of-freedom system with an asymmetric bilinear characteristic of the restoring force, under a strong 2nd-order superharmonic resonance.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. V. Matveev, “Approximate analytical determination of vibrodiagnostic parameters of non-linearity of elastic bodies due to the presence of a closing crack. Part 1. Available and proposed methods of solution,” Strength Mater., 36, No. 4, 333–344 (2004).
V. V. Matveev and O. A. Bovsunovskii, “Approximate analytical determination of vibrodiagnostic parameters of a cracked elastic body under subharmonic resonance. Part 1. Weak resonance,” Strength Mater., 40, No. 2, 180–191 (2008).
V. V. Matveev and O. A. Bovsunovskii, “Approximate analytical determination of vibrodiagnostic parameters of a cracked elastic body under subharmonic resonance. Part 2. Strong resonance,” Strength Mater., 40, No. 3, 283–291 (2008).
V. V. Matveev and A. P. Bovsunovskii, “Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 3. Analytical and numerical determination of natural frequencies of longitudinal and bending vibrations of beams with transverse cracks. Solution,” Strength Mater., 31, No. 4, 341–350 (1999).
V. V. Matveev and O. E. Boginich, “Vibrodiagnostic parameters of fatigue damage in rectangular plates. Part 1. A procedure of determination of damage parameters,” Strength Mater., 36, No. 6, 549–557 (2004).
V. V. Matveev and O. E. Boginich, “Vibrodiagnostic parameters of fatigue damage in rectangular plates. Part 3. Through-the-thickness and surface semi-elliptical cracks,” Strength Mater., 38, No. 5, 466–480 (2006).
V. V. Matveev, “Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 1. Longitudinal vibrations, analytic solution,” Strength Mater., 29, No. 6, 561–572 (1997).
V. V. Matveev, “Approximate analytical determination of vibrodiagnostic parameters of non-linearity of elastic bodies due to the presence of a closing crack. Part 2. Determination of diagnostic parameters in principal and 2-nd order superharmonic resonances,” Strength Mater., 36, No. 5, 449–462 (2004).
Author information
Authors and Affiliations
Additional information
Translated from Problemy Prochnosti, No. 4, pp. 5 – 19, July – August, 2010.
Rights and permissions
About this article
Cite this article
Matveev, V.V., Boginich, O.E. Approximate analytical determination of vibrodiagnostic parameters of the presence of a crack in an elastic body under superharmonic resonance. Strength Mater 42, 363–373 (2010). https://doi.org/10.1007/s11223-010-9225-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11223-010-9225-1