Search results for "Restoring force"
showing 5 items of 5 documents
A New Look at the Stochastic Linearization Technique for Hyperbolic Tangent Oscillator
1998
Abstract Stochastic linearization technique is reconsidered for oscillator with restoring force in form of hyperbolic tangent. We show that a subtle error was made in the previously known procedure for derivation of the linearized system parameters. Two new error-free procedures, namely, those based on minimization of mean square difference between (a) restoring force or (b) potential energy of the original non-linear system and their linear counterparts, are suggested. The results of numerical analysis are shown.
Linear theory of the Rayleigh–Taylor instability at a discontinuous surface of a relativistic flow
2017
We address the linear stability of a discontinuous surface of a relativistic flow in the context of a jet that oscillates radially as it propagates. The restoring force of the oscillation is expected to drive a Rayleigh-Taylor instability (RTI) at the interface between the jet and its cocoon. We perform a linear analysis and numerical simulations of the growth of the RTI in the transverse plane to the jet flow with a uniform acceleration. In this system, an inertia force due to the uniform acceleration acts as the restoring force for the oscillation. We find that not only the difference in the inertia between the two fluids separated by the interface but also the pressure at the interface h…
Nonlinear vibrations and hysteresis of micromachined silicon resonators designed as frequency-out sensors
1987
Experimental observation of nonlinear vibrations and hysteresis of micromachined silicon resonators is reported. The experimental results are explained using a simple model in which the restoring force acting in the resonator contains a small cubic term. The effects will impose a limit to the maximum amplitude which can be excited while still maintaining reliability of these devices as frequency-out sensors.
Optimal tuning of tuned liquid column damper systems in random vibration by means of an approximate formulation
2014
Passive control devices are often added to slender and flexible systems in order to increase their structural safety. Several types of devices have been proposed in order to reduce the dynamic responses of different kind of structural systems. Among them, the tuned liquid column damper (TLCD) proved to be very effective in reducing vibration of various type of structures by means of a combined action which involves the motion of the liquid mass within the tube. The restoring force, in particular, is produced by the force of gravity acting on the liquid and the damping effect is generated by the hydrodynamic head losses that arise during the motion of the liquid inside the TLCD. Since the in…
On stiffness and damping of vibro-impact dynamics of backlash
2021
We consider the instantaneous stiffness and damping of the vibro-impact in a backlash pair. Opposed to the existing and mostly used models of the backlash, we address the problem of contact and separation, and the associated force propagation within a mechanical pair, from a viewpoint of the vibro-impact dynamics. We discuss the impact forces with the coefficient of restitution as a principal factor which shapes the transient backlash response.We show that a common approach to modeling the backlash by means of a dead-zone in a restoring force is unsuitable for correctly capturing the mechanical impact. We exemplary demonstrate a qualitative accord between an experimental backlash response a…