By Arkadiy I. Manevich
Probably the most very important positive factors of nonlinear structures with a number of levels of freedom is the presence of inner resonances at sure kin among usual frequencies of alternative modes. This monograph is the 1st ebook committed predominantly to inner resonances in numerous mechanical structures together with these of functional value. the most function is to contemplate the interior resonances from the final viewpoint and to clarify their position in utilized nonlinear dynamics by utilizing an effective method in keeping with introducing the complicated illustration of equations of movement (together with the a number of scale method). thought of listed below are self reliant and nonautonomous discrete two-degree-of-freedom structures, endless chains of debris, and non-stop structures, together with round jewelry and cylindrical shells. particular consciousness is paid to the case of one-to-one inner resonance in structures with cubic and quadratic nonlinearities. Steady-state and nonstationary regimes of movement, interplay of the interior and exterior resonances at pressured oscillations, and bifurcations of steady-state modes and their balance also are studied.