DEFORMATION DUE TO TIME HARMONIC SOURCES IN MICROPOLAR THERMOELASTIC MEDIUM POSSESSING CUBIC SYMMETRY WITH TWO RELAXATION TIMES

The response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated. Fourier transform is employed and the transform is inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution are compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases are also deduced.

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） do- main 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.

时域谐波平衡求解器中非物理解出现根源探析

The time domain harmonic balance method is an attractive reduced order method of analyzing unsteady flow for turbomachines. However, the method can admit non-physical solutions. Non-physical solutions were encountered from a three-blade-row compressor configuration in a time domain harmonic balance analysis. This paper aims to investigate the root cause of the non-physical solutions. The investigation involves several strategies, which include increasing the number of harmonics, increasing the number of time instants, including scattered modes,including the rotor-rotor interaction, and the use of a new method-the approximate time domain nonlinear harmonic method. Numerical analyses pertinent to each strategy are presented to reveal the root cause of the non-physical solution. It is found that the nonlinear interaction of unsteady flow components with different fundamental frequencies is the cause of the non-physical solution. The non-physical solution can be eliminated by incorporating extra scattered modes or using the approximate time domain nonlinear harmonic method.

Elastodynamic analysis at an interface of viscous fluid/thermoelastic micropolar honeycomb medium due to inclined load

In this paper, the effect of angle inclination at the interface of a viscous fluid and thermoelastic micropolar honeycomb solid due to inclined load is investigated. The inclined load is assumed to be a linear combination of normal load and tangential load. Laplace transform with respect to time variable and Fourier transform with respect to space variable are applied to solve the problem. Expressions of stresses, temperature distribution, and pressures in the transformed domain are obtained by introducing potential functions. The numerical inversion technique is used to obtain the solution in the physical domain. The frequency domain expressions for steady state are also obtained with appropriate change of variables. Graphic representations due to the response of different sources and changes of angle inclination are shown. Some particular cases are also discussed.

Spatio-temporal patterns of satellite-derived grassland vegetation phenology from 1998 to 2012 in Inner Mongolia, China

Spatio-temporal variations of vegetation phenology, e.g. start of green-up season（SOS） and end of vegetation season（EOS）, serve as important indicators of ecosystems. Routinely processed products from remotely sensed imagery, such as the normalized difference vegetation index（NDVI）, can be used to map such variations. A remote sensing approach to tracing vegetation phenology was demonstrated here in application to the Inner Mongolia grassland, China. SOS and EOS mapping at regional and vegetation type（meadow steppe, typical steppe, desert steppe and steppe desert） levels using SPOT-VGT NDVI series allows new insights into the grassland ecosystem. The spatial and temporal variability of SOS and EOS during 1998–2012 was highlighted and presented, as were SOS and EOS responses to the monthly climatic fluctuations. Results indicated that SOS and EOS did not exhibit consistent shifts at either regional or vegetation type level; the one exception was the steppe desert, the least productive vegetation cover, which exhibited a progressive earlier SOS and later EOS. Monthly average temperature and precipitation in preseason（February, March and April） imposed most remarkable and negative effects on SOS（except for the non-significant impact of precipitation on that of the meadow steppe）, while the climate impact on EOS was found to vary considerably between the vegetation types. Results showed that the spatio-temporal variability of the vegetation phenology of the meadow steppe, typical steppe and desert steppe could be reflected by the monthly thermal and hydrological factors but the progressive earlier SOS and later EOS of the highly degraded steppe desert might be accounted for by non-climate factors only, suggesting that the vegetation growing period in the highly degraded areas of the grassland could be extended possibly by human interventions.

Periodic response analysis of a misaligned rotor system by harmonic balance method with alternating frequency/time domain technique

A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Periodic solutions are obtained through harmonic balance method with alternating frequency/time domain(HB-AFT) technique, and then compared with the results of numerical simulation. Good agreement confirms the feasibility of HB-AFT scheme. Moreover, the Floquet theory is adopted to analyze motion stability of the system when rotor runs at different speed intervals. A simple strategy to determine the monodromy matrix is introduced and two ways towards unstability are found for periodic solutions: the period doubling bifurcation and the secondary Hopf bifurcation. The results obtained will contribute to the global response analysis and dynamic optimal design of rotor systems.