Damped vibration analysis of a two-degree-of-freedom discrete system

A simple step‐by‐step procedure, including several novel techniques discussed in the Appendices, is given for minimizing ac phase noise in typical interferometric systems such as two‐beam interferometers, holographic setups, four‐wave mixers, etc. Special attention is given to index of refraction fluctuations, direct mechanical coupling, and acoustic coupling, whose importance in determining ac phase noise in interferometric systems has not been adequately treated. The minimization procedure must be carried out while continuously monitoring the phase noise which can be done very simply by using a photodiode measurement of the interferometer output. Supplementary measurements using a microphone and accelerometer will also be helpful in identifying the sources of phase noise. Emphasis is placed on new techniques or new modifications of older techniques which will not usually be familiar to most workers in optics. Thus, the necessity of eliminating the effects of index of refraction fluctuations which degrad...

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The minimization of ac phase noise in interferometric systems

In terms of the traditional dynamic vibration absorber (DVA), the vibration damping effect improves with the mass ratio of DVA increasing, and the vibration level of target system is effectively controlled in the case that the mass ratio of DVA is large. This characteristic restricts the application of DVA to the track because of the limited available space. This study proposes one type of DVA with negative stiffness (NSDVA) applied to floating slab track to reduce the track vibration under the condition of small mass ratio and presents a design methodology of NSDVA attached on flexible system. Firstly, the mechanical model of floating slab with NSDVA is simplified to a two-degree-of-freedom system, and theoretical expressions of NSDVA’s optimal parameters, i.e., ratio of frequency, damping and stiffness are deduced according to the fixed-point expansion theory and stability condition. Secondly, with the combination of the multi-modal control theory and the finite element method, optimal parameters of NSDVA applied to a multi-degree of freedom (MDOF) system are calculated. 3-D finite element model of floating slab-NSDVA is built in ABAQUS software, and the modal analysis of floating slab is conducted to determine the target modal and equivalent mass. Compared with the traditional Voigt type DVA, the NSDVA adopted in this paper is proved to be more effective to reduce the both floating slab and rail vibration level. The design methodology of NSDVA attached to a MDOF system presented in this paper is feasible.

H.R. Srirangarajan

Papers

Voigt dynamic vibration absorber