Novel implementation of homogenization method to predict effective properties of periodic materials

Representative volume element （RVE） method and asymptotic homogenization （AH） method are two widely used methods in predicting effective properties of pe- riodic materials. This paper develops a novel implementa- tion of the AH method, which has rigorous mathematical foundation of the AH method, and also simplicity as the RVE method. This implementation can be easily realized using commercial software as a black box, and can use all kinds of elements available in commercial software to model unit cells with rather complicated microstructures, so the model may remain a fairly small scale. Several examples were car- fled out to demonstrate the simplicity and effectiveness of the new implementation.

Theoretical and Experimental Investigation of Flexural Vibration Transfer Properties of High-Pressure Periodic Pipe

According to the theory of phononic crystals, the hydraulic pipeline is designed to be a periodic structure composed of steel pipes and hoses to suppress the vibration of the hydraulic system with band gaps. We present theoretical and experimental investigations into the flexural vibration transfer properties of a high-pressure periodic pipe with the force on the inner pipe wall by oii pressure taken into consideration. The results show that the vibration attenuation of periodic pipe decreases along with the elevation of working pressure for the hydraulic system, and the band gaps in low frequency ranges move towards high frequency ranges. The periodic pipe has good vibration attenuation performance in the frequency range below 1000 Hz and the vibration of the hydraulic system is effectively suppressed. A11 the results are validated by experiment. The experimental results show a good agreement with the numerical calculations, thus the flexural vibration transfer properties of the high- pressure periodic pipe can be precisely calculated by taking the fluid structure interaction between the pipe and oil into consideration. This study provides an effective way for the vibration control of the hydraulic system.

Periodic, Irrational and Transcendental Numbers in the Factorial Series

The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial series and the factorial system is that the factorial series does not set an upper bound at a given place after the radix point, while in the factorial system (i – 1) is the maximal possible value for ri after the radix point. I give an extended definition of periodic numbers, and show the relationship between periodic and irrational numbers. I prove the transcendence of e by means of the factorial series and the factorial number system.

MODELING AND ANALYSIS OF A COUPLED RIGID_FLEXIBLE SYSTEM

Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of failing to account for the effects of dynamic stiffening, conventional methods based on the linear theories can lead to erroneous results in many practical applications. In this paper, the idea of 'centrifugal potential field', which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established. Based on this equation, first it is proved that the elastic motion of the system has periodic property, then by using Frobenius' method its exact solution is obtained. The influences of large overall rigid motion on the elastic vibration mode shape and frequency are analysed through the numerical examples.

Effect of Multi-Pass Equal Channel Angular Pressing on the Microstructure and Mechanical Properties of a Heterogeneous Mg_(88)Y_8Zn_4 Alloy

The microstructure evolutions and mechanical properties of a heterogeneous Mg88Y8Zn4（in at.%） alloy during multi-pass equal channel angular pressing（ECAP） were systematically investigated in this work.The results show that four phases,i.e.α-Mg,18 R long period stacking ordered（LPSO） phase,Mg24Y5 and Y-rich phase,are present in cast alloy.During ECAP,dynamic recrystallization（DRX） occurs and the diameter of DRXedα-Mg grains decreases to 0.8 μm.Moreover,precipitation of lamellar 14 H LPSO structure is developed withinα-Mg phase.Both the refinement of α-Mg grains and precipitation of 14 H LPSO contribute to the increase in micro-hardness from 98 HV to 135 HV for α-Mg.In addition,a simplified model describing the evolution of 18 R LPSO phase is established,which illustrates that 18 R undergoes a four-step morphological evolution with increasing strains during ECAP,i.e.original lath → bent lath → cracked lath → smaller particles.Compression test results indicate that the alloy has been markedly strengthened after multi-pass ECAP,and the main reason for the significantly enhanced mechanical properties could be ascribed to the DRXed α-Mg grains,newly precipitated 14 H lamellas,18 R kinking and refined 18 R particles.