On parametric oscillations of pendular and rotor systems

Different kind of parametrical phenomena in vibrating systems are presented. Nonlinear properties of rotating and pendulum dynamical systems give some interesting industrial applications. The purpose of this paper is to show the possibility to generalize the models and to find a similarity of certain physical presentations and possible analysis. The effects of non-uniform rotation of unbalanced rotor, synchronization of multiples pendulums with common vibrating base, stabilization of vertical column, auto parametrical damper etc. are included in consideratio

Dynamic stability of a flexible rod under parametric excitation

A homogeneous rod with a constant cross section, vertically mounted and cantilevered, is considered. At the unstrained state, the rod’s axis is straight. It is supposed lateral stiffness is that the rod buckles in static conditions only under gravity and its axis bends. Flexural oscillations of the rod when its base vibrates vertically are investigated. Stabilization circumstances of the rod axis rectilinearity depending on excitation parameters, internal and external damping, and rod flexibility are determined

Parametric synthesis of rod spatial vibroisolation system under arbitrarily directed external disturbance

A mathematical model of flexible-rod spatial vibroisolating suspension, describing the motion of protected object, is considered. An algorithm is proposed for solving the problem of spatial displacement of the object under the action of static forces applied in an arbitrary direction. The coefficients of stiffness matrix of the suspension are determined depending on the position of static equilibrium. It is demonstrated that, depending on the requirements by varying geometrical parameters of the rods, different dynamic properties of the suspension may be obtained

On parametric oscillations of pendular and rotor systems

Different kind of parametrical phenomena in vibrating systems are presented. Nonlinear properties of rotating and pendulum dynamical systems give some interesting industrial applications. The purpose of this paper is to show the possibility to generalize the models and to find a similarity of certain physical presentations and possible analysis. The effects of non-uniform rotation of unbalanced rotor, synchronization of multiples pendulums with common vibrating base, stabilization of vertical column, auto parametrical damper etc. are included in consideratio

Multi-cutter turning process stability analysis

This work displays results of a modelling-based investigation a process of multi-cutter turning process focusing on the stability of nominal steady-state case. The modelling is based on the new surface formation equations, on the equations of motion and on a rational fraction cutting law. The influence of the parameters of the system on the stability of the steady cut is analyzed

Features of Dynamics of Antivibration Mounts with Inertial Hydraulic Converter Subjected to Vibro-Impact Loading

Antivibration mounts with inertial hydraulic converter are widely used to protect a variety of technical systems from shock and vibration. As it follows from existing literature, models of such a mounts on the basis of mechanical and mechanical-electrical analogies instead of real hydro-mechanical system are usually used to study their dynamic properties and design. These models are not able to describe fluid dynamics in hydraulic mount, and are not suitable to study rapidly changing processes, which is especially required for effective application of the mounts at vibro-shock loading. In this work, a model of inertial hydraulic converter, which is a system of two hydraulic cylinders of unilateral operating principle, connected by a rigid hydraulic tube, is described. Dynamics of fluid in hydraulic converter is described by the Navier-Stokes equations for a compressible fluid and the equation of state of the fluid in assumption of its isentropic motion. The results of numerical simulation of antivibration mount dynamics at shock loading by using finite element package ANSYS/LS-DYNA are presented. It is found out that increasing the length of the tube and reducing the tube diameter lead to an increase in the transmitted dynamic force

Dynamic stability of a flexible rod under parametric excitation

A homogeneous rod with a constant cross section, vertically mounted and cantilevered, is considered. At the unstrained state, the rod’s axis is straight. It is supposed lateral stiffness is that the rod buckles in static conditions only under gravity and its axis bends. Flexural oscillations of the rod when its base vibrates vertically are investigated. Stabilization circumstances of the rod axis rectilinearity depending on excitation parameters, internal and external damping, and rod flexibility are determined