The propagation of quasi-shear waves along the layers of a prestressed composite material is described using the three-dimensional linearized theory of elasticity. The composite consists of two alternating layers that are free to slip relative each other. The dispersion equation is analyzed numerically. The effect of the prestresses on the wave velocity is studied Keywords: laminated composite material, three-dimensional linearized theory of elasticity, prestresses, slip, quasi-shear waveIntroduction. Dynamic processes in prestressed bodies, including layered materialsá are studied in numerous papers in periodicals [7, 8, 11-14, etc.], their results being summarized in a number of monographs [4-6, etc.]. Moreover, these results are also reviewed in [1,3,10]. Various aspects of prestresses in dynamic problems (wave propagation, motion of punches and loadsá etc.) are addressed in [11-14, etc.]. Solving such problems and studying dynamic processes in real bodies are of importance because elastic bodies, including layered materials, usually have initial (residual) stresses of various nature. Members of modern structures made of laminated composites are in most cases subject to dynamic loads.The propagation of plane waves in prestressed periodically laminated composites with perfectly bonded layers was studied in [4,7,8]. Similar problems in the absence of prestresses were solved in [2,15]. In reality, the bonding of layers is often imperfect. This issue was addressed in [9] where the method of study of elastic waves in prestressed laminates [4] was extended to the case of imperfect bonding.We will use this method to study wave propagation in a composite consisting of two alternating layers that are free to slip relative to each other. The dispersion equation for quasishear waves will be analyzed numerically, and the effect of prestresses on their velocity will be examined.
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