Structural elements of modern machines and devices mainly consist of multilayer cylindrical polymeric materials. The study of energy dissipation in such materials is an important problem. At present, the basic equations and relations derived in the theory of deformable solids do not take into account the dissipative (or viscous) nature of fibers, or they cannot be taken into account in theories where viscosity is the same throughout the material and affects the dynamic state of the mechanical system. Based on the theory proposed in the book, the problems of minimizing (or maximizing) the energy dissipation generated in many physical and mechanical processes and their control (passive and active) can be solved.The study of wave propagation taking into account dissipative inhomogeneous properties of materials is of great practical importance. They are mainly used in geophysics, where the seismic resistance of underground structures is studied. Reduction of vibrations in machines and prevention of resonances arising in them has been an urgent problem at all times.
Safarov Ismail Ibrokhimovich is a Doctor of Physical and Mathematical Sciences and a Professor at the Department of Higher Mathematics of the Tashkent Chemical-Technological Institute, Uzbekistan. He has published more than 150 scientific works in scientific journals, and more than 200 in collections of foreign and republican scientific conferences. He is also the author of 20 monographs. Teshaev Muhsin Khudoyberdiyevich is a Doctor of Physical and Mathematical Sciences and Chief Researcher at the Bukhara Branch of the Institute of Mathematics, named after V.I. Romanovskii of the Academy of Sciences of the Republic of Uzbekistan. He has published more than 100 scientific works in scientific journals, and more than 150 in collections of foreign and republican scientific conferences. He is the author of 12 monographs.Usmonov Botir Shukurillaevich is a Professor and Doctor of Technical Sciences. In 1995 he defended his candidate's (PhD) thesis, and in 2022 his doctoral (DSc) thesis. He has published more than 70 scientific works in Uzbekistani and foreign scientific journals, and more than 100 in collections of foreign and republican scientific conferences. He is the author of 3 monographs.
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