Abstract
The dynamics of a mechanical system consisting of a parallel-connected main elastic element, an external disturbance compensator having a nonlinear force characteristic, and a viscous friction damper sprung by a linear spring are studied. The resulting system of differential equations describing the behavior of the system has one and a half degrees of freedom and has specific properties depending on the ratio of stiffness of the main spring and the spring suspension of a viscous friction damper. It is established that a single nonlinear system with one and a half degrees of freedom has either one or two harmonics. In the general solution of the system of differential equations, there are always two harmonics in the above-resonance zone, one of which is always equal to the disturbance frequency, and the second one is sufficiently close to the frequency k0. In the linear conservative case and the absence of suspension of the viscous friction damper, the natural frequency of the displacement of the system k0 =14.046 s-1.
Highlights
It is known that the introduction of an object into the standard vibration protection scheme consisting of an elastic element and an oscillation damper of the second disturbance transmission channel in which it is inverted, i.e. a compensating device, allows providing high parameters of its dynamic properties [1]
The following notations are introduced in the figure: m- mass of the protected object, Cstiffness of the main elastic element, Cd-stiffness of spring connected in series with the viscous friction damper, - viscous friction coefficient of the system, q - load displacement, - kinematic external disturbance, Q( ) = a1 +a3 3 - power characteristic of the compensator of the external disturbance (Figure 2), = z – - deflection of the suspension
The following fact is obvious: the angle of the phase shift between the displacements of the load exists, and to move the suspension point of the damper relative to the external disturbance, it can be considered equal to zero. This statement will allow us to carry out further analytical studies of the mechanical system under consideration, which is quite similar to the Duffing equation [2,3,4,5,6], which has jumping amplitude of oscillation
Summary
It is known that the introduction of an object into the standard vibration protection scheme consisting of an elastic element and an oscillation damper of the second disturbance transmission channel in which it is inverted, i.e. a compensating device (compensator), allows providing high parameters of its dynamic properties [1]. To protect the hydraulic damper from shock effects, an additional elastic element is used between it and the base. The assessment of the influence of the stiffnessof an elastically suspended damper on the dynamics of such a system has not been fully studied
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
