Stability of nonlinear vibrations of plate protected from vibrations

Abstract This work is devoted to solving the problem of the stability of nonlinear vibrations of the plate, which is protected from vibrations under the influence of kinematic excitations. A dynamic absorber is taken as an object to protect against vibrations. The dissipative properties of the plate material and the damping element of dynamic absorber are expressed by the Pisarenko-Boginich model of the hysteresis type. An analytical expression of the stability conditions was obtained using Lyapunov’s first approximation method. A system of differential equations of normal form is obtained for nonlinear vibration of a plate with dynamic absorber, a characteristic equation is constructed, and it is shown on the basis of the Hurwitz criterion that the negativity of the real part of its roots ensures the stability of nonlinear vibrations of the protected plate.

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