Special issue devoted to the 14th International conference “Dynamical Systems — Theory and Applications”

Abstract

in Łódź, Poland. The content of the presented articles includes modern states and contemporary perspectives of mathematical modeling, simulation, stability, control and new mathematical methods addressed to nonlinear dynamical systems, both in theoretical aspects and practical applications.The Scientific Committee of the conference included the following well-known researchers: H. Altenbach -PREFACE distribution. Special attention is focused to deficient values in different senses, in particular to deficient values in the sense of Petrenko in the case of solutions of finite order. Moreover, the problem of small deficient functions is also considered in this study. Eventually, the estimates of deficiencies, multiplicity indices and, in the case of functions of finite order, deviations from small functions, are also presented.(6) Circular membrane with a centrally-located opening -analytical model using parameterization of the non-empty torus, by Waszczuk-Młyńska and Radkowski [6] proposed a model of circular membrane with an opening in its central part (damagesimulating opening). A novel partial differential equation of the analyzed system is computed by means of the Fourier method of separation of variables as well as applying the Bessel substitution. The correctness of the presented analytical model and the obtained results in the form of the natural frequency were verified based on the experimental tests and the numerical modeling.(7) Solving partial differential equations in computational mechanics via nonlocal numerical approaches, by Martowicz et al. [7] is addressed to solving partial differential equations for a continuum solid body by using a nonlocal formulation. The authors introduce a nonlocal finite difference scheme to show its applicability to computational mechanics. Moreover, potential areas of practical applications for the presented method are indicated. Using the proposed method, selected thermal and mechanical properties of a gas foil bearing (GFB) component and a rod-like structural part of GFB made of super alloy Inconel 625 are investigated numerically.We hope that scientific problems considered in this special issue will be interesting for readers of the Journal of Applied Mathematics and Mechanics. In here, we are very grateful to Prof. Holm Altenbach for invitation to edit this special issue. We would like also to thank all the Referees for their times, critical remarks and efforts in helping us to carry out the review process.