Abstract
In this paper, the quasi-P wave propagation in epoxy/lead composites is studied by the differential method with polarization stress and polarization momentum. The corresponding differential equations are numerically solved by the fourth-order Runge–Kutta method, and the dynamic effective modulus and density are obtained. Correctness of the results obtained by the differential method is verified by comparing with the results obtained by the self-consistent method as well as experiments. Results show that the dynamic effective modulus L 1133 and L 3333 increase with the increase of aspect ratio δ , whereas L 1111 and L 1122 decrease with the increase of δ . The phase velocity ratio of the quasi-P wave propagation in the composites tends to 1 when the dimensionless wave number is large, and the dynamic effective density and modulus obtained are not isotropic when δ ≠ 1 . It is believed that the differential method can be a choice for solving dynamic effective properties of heterogeneous composites.
Highlights
In daily life, epoxy/lead composites have attracted more and more attention and been applied in many fields [1,2,3] since epoxy resins have the advantages of being green and degradable. e actual working environment of these composites is complex and changeable, especially in the case of nondestructive testing carried out on the composites with wave propagation
We study the possibility of analyzing the dynamic effective properties of two-phase particulate reinforced composites using the differential method. e quasi-P wave propagation in epoxy/lead composites is considered
Material properties are same with the matrix when calculating the phase velocity of the matrix material, and material properties are taken as dynamic effective properties when calculating phase velocity of the composite. e matrix is epoxy, and inclusion is lead
Summary
Epoxy/lead composites have attracted more and more attention and been applied in many fields [1,2,3] since epoxy resins have the advantages of being green and degradable. e actual working environment of these composites is complex and changeable, especially in the case of nondestructive testing carried out on the composites with wave propagation. Nemat-Nasser used the dynamic equivalent inclusion method to construct the dynamic effective constitutive relation in the case of periodic layered elastic composite by introducing eigenstress and eigenvelocity [8]. Sigalas and Soukoulis analyzed and studied the propagation of elastic waves in periodic layered composite by the transfer matrix method [10]. Garcıa-Pablos et al firstly analyzed and studied the frequency band structure of elastic wave propagation in composites by the using finitedifference time-domain method, and verified the calculated results by comparing with experimental results [15]. Kafesaki and Economou used the multiple scattering method to analyze and calculate the frequency band of elastic wave propagation in three-dimensional periodic composites [16]. Hussein analyzed the calculation of phononic crystal, photonic crystal, and electronic band structure, respectively, by means of the reduced Bloch mode expansion [18]
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