M.Ye.Yurchenko Resonant method of determination of local inhomogeneity of elastic properties under longitudinal and bending vibrations of a bar |
Acoustic bulletin, Vol. 5 ¹ 4, (2002) |
| Inhomogeneity of elastic properties of a bar under given boundary conditions is studied in case of longitudinal and bending vibrations (direct and inverse problems). It is supposed that the material's density is a constant in the whole domain of the bar, having the given dimensions, and the inhomogeneity of elastic properties to be determined is located in the vicinity of some cross-section of the bar. When solving the inverse problem we assume values of 10-20 eigenfrequencies of longitudinal or bending vibrations to be known. To derive the solution of the inverse problems a method of approximation of the inhomogeneity function by the finite sum of terms of the Fourier series (method of the low-frequency tomography) is used. Numerical values of eigen spectra for longitudinal and bending vibration of the bar with the inhomogeneity are found. The system of algebraic equations for determination of the coefficients of the Fourier series is obtained by comparison of the frequency spectra of vibrations for a homogeneous bar and the data on eigenfrequencies of the bar having the the given defect. |
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KEY WORDS: local inhomogeneity, inverse problem, low-frequency tomography, vibration eigenfrequencies |
| TEXT LANGUAGE: Ukrainian |