000021722 001__ 21722
000021722 005__ 20170622131301.0
000021722 04107 $$aeng
000021722 046__ $$k2017-06-15
000021722 100__ $$aLurie, Konstantin
000021722 24500 $$aON WAVE PROPAGATION THROUGH REGULAR AND IRREGULAR MATERIAL FORMATIONS WITH PROPERTIES PERIODIC IN SPACE-TIME

000021722 24630 $$n6.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000021722 260__ $$bNational Technical University of Athens, 2017
000021722 506__ $$arestricted
000021722 520__ $$2eng$$aHeterogeneous material structures assembled in space and time – dynamic materials (DM) – have shaped a novel material concept that finds applications to various problems, especially to material optimization in continuum dynamics. The specifics of DM resides in their universal feature to be thermodynamically open systems. To secure the temporal variability of material properties, a non-stop exchange of mass/momentum/energy should be maintained between the DM formation and the environment. Mathematically, the DM concept is expressed through linear hyperbolic equations with variable coefficients. When such coefficients (material properties) take at each point of space-time one out of two admissible systems of values, then we speak about “two materials” that may be distributed in space-time to form two types of layouts. One of them, termed regular, is characterized by the absence of collisions between the characteristics of the same family on the interfaces separating two different materials. Another type of a layout, termed irregular, allows for such collisions. This talk will offer examples illustrating both types of DM. The first (regular) case is given by a checkerboard structure assembled from two distinct materials and doubly periodic in space and time. When the structural parameters fall into certain continuous intervals, the waves traveling through this structure accumulate energy that is pumped into them by an external agent at the moments of temporal property switching. Another (irregular) example allows for a collision of characteristics, which may become necessary in the context of optimal design in dynamics. Physically speaking, the collision of characteristics means the rise of discontinuities in solutions of the dynamic equations. But when the equations are originally assumed linear (which is a part of the DM concept), then this property remains in effect only through a regular case. Contrary to that, in the irregular situation, one expects the appearance of non-linearity of some sort, generated by the physics of material collisions. Transformation of energy that accompanies such collisions may become irreversible, and, as a consequence, the problem may acquire features typical for a standard entropy situation. In this talk, there will be suggested a reasonable model that introduces a special dynamic scenario by assuming that the colliding elementary masses cling together to form clots – the moving finite masses. We require conservation of momentum through collisions to describe the subsequent motion of the clots. This requirement is implemented as a part of the concept of totally inelastic impact; through such collisions, the kinetic energy is lost (Carnot theorem), and the expected irreversibility follows. Technically, the original continuity equation becomes complemented with two additional ODEs governing the formation and the motion of clots; the extended system then exposes a substantial non-linearity that makes the optimization problem well-posed.

000021722 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000021722 653__ $$a

000021722 7112_ $$aCOMPDYN 2017 - 6th International Thematic Conference$$cRhodes Island (GR)$$d2017-06-15 / 2017-06-17$$gCOMPDYN2017
000021722 720__ $$aLurie, Konstantin
000021722 8560_ $$ffischerc@itam.cas.cz
000021722 8564_ $$s118058$$uhttps://invenio.itam.cas.cz/record/21722/files/17631.pdf$$yOriginal version of the author's contribution as presented on CD, section: [MS05] Periodicity-induced effects and methods in structural dynamics
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000021722 962__ $$r21500
000021722 980__ $$aPAPER