Exploring the vibration stability of a plate protected from vibrations under influence of harmonic excitations

This study investigates the stability of joint nonlinear stationary vibrations of a hysteresis-type elastic dissipative characteristics plate and dynamic absorber under harmonic excitation. The research focuses on a mechanical system consisting of an elastic plate and a dynamic absorber designed to protect the structure from vibrations. The elastic-dissipative relationships of both the plate and the absorber are formulated based on the Pisarenko-Boginich hypothesis, which makes it possible to account for the internal resistance forces typical of hysteresis-type materials. Using the harmonic linearization method, analytical solutions to the system’s nonlinear differential equations were obtained. The derived expressions describe the dependence of the vibration amplitude and frequency on the interaction between the plate and the dynamic absorber. The stability of the stationary vibration modes of the system was examined by means of the vertical tangents method. The analytical results demonstrate that elastic plates with hysteresis-type dissipation exhibit effective vibration damping within specific frequency ranges of excitation. This implies that such materials can significantly reduce the amplitude of steady-state vibrations when appropriately tuned with a dynamic absorber. The findings of this research provide valuable insights for the design and optimization of vibration protection systems. The obtained stability conditions were numerically analyzed depending on the plate material and the dissipative properties of the dynamic absorber damping element. Relevant conclusions were drawn and recommendations were given. The change in the stability field was analyzed and the active parameters in this were determined.