Elastic wave dispersion and attenuation caused by multiple types of disc-shaped inclusions

Abstract

Purpose The purpose of this paper is to numerically investigate time-harmonic elastic wave propagation with the analysis of effective wave velocities and attenuation coefficients in a three-dimensional elastic composite consisting of infinite matrix and uniformly distributed soft, low-contrast and absolutely rigid disc-shaped micro-inclusions. Design/methodology/approach Within the assumptions of longitudinal mode of a propagating wave as well as dilute concentration and parallel orientation of inclusions in an infinite elastic matrix, Foldy’s dispersion relation is applied for introducing a complex and frequency-dependent wavenumber of homogenized structure. Then, the effective wave velocities and attenuation coefficients are directly defined from the real and imaginary parts of wavenumber, respectively. Included there a far-field forward scattering amplitude by a single low-contrast inclusion given in an analytical form, while for the other types of single scatterers it is determined from the numerical solution of boundary integral equations relative to the displacement jumps across the surfaces of soft inclusion and the stress jumps across the surfaces of rigid inclusion. Findings On the frequency dependencies, characteristic extremes of the effective wave velocities and attenuation coefficients are revealed and analyzed for different combinations of the filling ratios of involved types of inclusions. Anisotropic dynamic behavior of composite is demonstrated by the consideration of wave propagation in perpendicular and tangential directions relatively to the plane of inclusions. Specific frequencies are revealed for the first case of wave propagation, at which inclusion rigidities do not affect the effective wave parameters. Originality/value This paper develops a micromechanical study that provides a deeper understanding of the effect of thin-walled inclusions of diversified rigidities on elastic wave propagation in a three-dimensional composite. Described wave dispersion and attenuation regularities are important for the non-destructive testing of composite materials by ultrasonics.

Vibration of orthotropic doubly curved panel with a set of inclusions of arbitrary configuration with different types of connections with the panel

“…The parameters of approximation are as follows: K = 50, S (1) = S (2) = 20, ε 1 = ε 2 = ε = b 2 π S (2) m. Such method of generalized summation is used:…”

“…In both cases the simplest form of vibration takes place and the vibration frequency substantially influences the amplitude of the deflection of the panel and the displacements of the inclusions. On the lower frequency range the sharp increase of the amplitude of the deflection of the 2π = 35 Hz: solid curve form (1) =m (2) = 50 kg, dashed curve form (1) =m (2) = 100 kg, dotted curve for m (1) =m (2) = 150 kg. 2π = 100 Hz: solid curve form (1) =m (2) = 50 kg, dashed curve form (1) =m (2) = 100 kg, dotted curve for m (1) =m (2) = 150 kg.…”

“…In Fig. 6, the non-symmetrical case is considered, when inclusions have different masses m (1) = 50 kg,m (2) = 100 kg, are subjected to different external forces P = 0.5 m.…”

“…The vibration of shells and plates with the attached masses or the concentrated masses at the points received much attention among researchers. There are also works known in literature dealing with the dynamic problems for the 3-D infinite elastic body with the inclusions [1][2][3][4][5]. However, to the author's knowledge, there is a scarcity of published materials regarding vibration of the finite curved panels carrying the massive inclusions of some shape penetrating the panel through all its thickness.…”

Dynamic interaction of a thin metallic inclusion with a piezoceramic matrix

“…Ці умови є наслідком механічних або математичних припущень, або ж їх отримують за допомогою асимптотичних методів. Огляди літератури, де використовують механічні і математичні гіпотези, можна знайти в працях [4,[9][10][11]. Тонкі п'єзоелектричні неоднорідності у пружній матриці розглядали в публікаціях [5,12,15,16].…”