Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time(HB-AFT) domain technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

Harmonic Balance Methods:A Review and Recent Developments

The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to complex symbolic operations.Many variants have been developed to improve the HB method,among which the time domain HB-like methods are regarded as crucial improvements because of their fast computation and simple derivation.So far,there are two problems remaining to be addressed.i)A dozen of different versions of HB-like methods,in frequency domain or time domain or in hybrid,have been developed;unfortunately,misclassification pervades among them due to the unclear borderlines of different methods.ii)The time domain HB-like methods suffer from non-physical solutions,which have been shown to be caused by aliasing(mixture of the high-order into the low-order harmonics).Although a series of dealiasing techniques have been developed over the past two decades,the mechanism of aliasing and the final solution to dealiasing are still not well known to the academic community.This paper aims to provide a comprehensive review of the development of HB-like methods and enunciate their principal differences.In particular,the time domain methods are emphasized with the famous aliasing phenomenon clearly addressed.

Energy Decay of Solutions to a Nondegenerate Wave Equation with a Fractional Boundary Control

In this paper,we study the energy decay rate for a one-dimensional nondegenerate wave equation under a fractional control applied at the boundary.We proved the polynomial decay result with an estimation of the decay rates.Our result is established using the frequency-domain method and Borichev-Tomilov theorem.

Study of Unforced Unsteadiness in Centrifugal Pump at Partial Flow Rates

In order to explore the unforced unsteadiness of centrifugal pumps,a 2-D frequency domain imaging display technology was used to study the development of these unsteady flow structures at partial flow conditions.The results showed that,the unsteady flow field was not only affected by rotor and stator interaction,but also appeared an unforced unsteadiness with fundamental frequency of St≈0.23 around the impeller throat area.Moreover,as the flow rates decreased,this unsteady flow structure gradually weakened and disappeared.When the flow rate was reduced to 0.6 times of design flow rate,another two unforced unsteady flow structures with characteristic frequencies of St≈0.0714 and St≈0.12 began to appear in the same area.Therefore,with the operating condition smaller than design flow rate,the internal flow became more and more complex.In addition to the forced unsteadiness,the unforced unsteadiness which is not connected with the blade passage frequency became more and more obvious.