In the enormous and still poorly mastered gap between the macro level,\nwhere well developed continuum theories of continuous media and engineering\nmethods of calculation and design operate, and atomic, subordinate\nto the laws of quantum mechanics, there is an extensive meso-hierarchical\nlevel of the structure of matter. At this level unprecedented previously products\nand technologies can be artificially created. Nano technology is a qualitatively\nnew strategy in technology: it creates objects in exactly the opposite\nwayâ??large objects are created from small ones [1]. We have developed a new\nmethod for modeling acoustic monitoring of a layered-block elastic medium\nwith several inclusions of various physical and mechanical hierarchical structures\n[2]. An iterative process is developed for solving the direct problem for\nthe case of three hierarchical inclusions of l, m, s-th ranks based on the use of\n2D integro-differential equations. The degree of hierarchy of inclusions is determined\nby the values of their ranks, which may be different, while the first\nrank is associated with the atomic structure, the following ranks are associated\nwith increasing geometric sizes, which contain inclusions of lower\nranks and sizes. Hierarchical inclusions are located in different layers one\nabove the other: the upper one is abnormally plastic, the second is abnormally\nelastic and the third is abnormally dense. The degree of filling with inclusions\nof each rank for all three hierarchical inclusions is different. Modeling is carried\nout from smaller sizes to large inclusions; as a result, it becomes possible\nto determine the necessary parameters of the formed material from acoustic\nmonitoring data.
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