Resonance vibrations of a gyroscopic rotor with linear and nonlinear damping and nonlinear stiffness of the elastic support in interaction with a non-ideal energy source

Dynamic modeling of a non-ideal gyroscopic rotor system with nonlinear damping and nonlinear rigidity of an elastic support

“…These system parameters were chosen in accordance with various design parameters of the centrifuge used experimental studies. 20,39 The values of the parameters C 3 = 0.1, μ 1 , μ 3 , u 1 , u 2 are chosen in the course of numerical experimentation, as well as the values of μ 1 and μ 3 , taking into account those values at which hopping effects disappear, in accordance with the rest of the known design parameters necessary to create effective vibration isolation for the gyroscopic rotor. In calculations using equations (25) and (26), the control parameters were taken u 1 ∈ ( 1 . 1 , 1 . 5 ) and depending on the type of engine u 2 = 1 . 245 from correct physical considerations.…”

“…Iskakov et al 39 considered the effect of joint linear and nonlinear cubic damping on the dynamics of a gyroscopic rigid unbalanced rotor with a nonlinear rigidity of elastic support and a nonideal energy source is considered. It is proven that the combined linear and nonlinear cubic damping of elastic support can more effectively suppress the maximum amplitude and amplitude after resonant oscillations, eliminate abrupt phenomena, significantly reduce the amplitude of the oscillation frequency, and significantly narrow the unstable area until it is completely eliminated.…”

Resonant vibrations of a non-ideal gyroscopic rotary system with nonlinear damping and nonlinear stiffness of the elastic support

“…Experimental studies in [1] , [2] , [3] confirmed that the restoring and damping properties of viscoelastic materials should be described in nonlinear models and it was found that rubber insulators have both nonlinear stiffness and nonlinear damping. Subsequently, nonlinear shock absorbers began to be studied both by analytical and numerical methods, as well as by experimental methods [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] .…”

“…In it, the vibration of the rotor with a flexible support containing springs or rubber sheets with rotor vibration with a rigid support base is compared in the experimental single-disk rotor system supported by ball bearings at both ends. The works [11] , [12] , [13] , [14] , [15] are devoted to the study of the combined effect of linear and nonlinear cubic damping on resonance and behind it stationary and non-stationary oscillations, and on the stability of the movement of a gyroscopic rigid rotor with linear rigidity and nonlinear cubic rigidity of an elastic support. In the case of a rigid nonlinear characteristic of an elastic support, it is proved that if linear viscous damping merely shifts the lower boundary of the instability region towards high rotation speeds, then nonlinear cubic damping narrows this region on all sides until it is completely eliminated [12] , [13] , [14] .…”

“…In [ 12 , 13 ], it was experimentally confirmed that joint linear and nonlinear cubic damping of an elastic support made of rubber material can significantly reduce the vibration level of the rotor not only in the resonance region of the main harmonic and beyond it, but also eliminates vibrations of significant magnitude with jumping effects in the range of high shaft rotation speeds. It is known that quadratic nonlinearity of damping has a weak effect on the amplitude of the response of the gyroscopic rotor to suppress its vibration and on its stability [ 18 , 19 ].…”