Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of ideal fluid, the coupling dynamic equations of rigid tank, elastic appendages and liquid fuel are de...Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of ideal fluid, the coupling dynamic equations of rigid tank, elastic appendages and liquid fuel are derived using H-O principle. In the case of pitch excitation, the modified potential function and wave height function are introduced to describe the moving boundary of fluid, then Galerkin＇s method is used to discretize the dynamic equations into ordinary differential equations. The natural frequencics of the coupling system are formulated in liquid depth, the length of the tank, etc. The formulae are confirmed by numerical simulations, which also show that the effects of liquid and elastic appendages on the attitude angular of rigid.展开更多
In this paper, a series of chiral non-symmetrical liquid crystals （nBA-chol） consisting of a cholesteryl ester moiety as chiral entity and a biphenyl aromatic core with different terminal alkyl chain has been synthe...In this paper, a series of chiral non-symmetrical liquid crystals （nBA-chol） consisting of a cholesteryl ester moiety as chiral entity and a biphenyl aromatic core with different terminal alkyl chain has been synthesized and investigated for their liquid crystalline properties. Effects of numbers of methylene units in the terminal alkyl chain on the phase transition temperatures and on the temperature-dependent pitch lengths of the chiral liquid crystals have been studied. The long terminal alkyl chain tends to exhibit smectic A mesophases. The pitch lengths of the cholesteric mesophases of the chiral liquid crystals decrease with increasing temperature and with increasing numbers of methylene units in the terminal alkyl chain, respectively.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10302013 and 10572022)
文摘Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of ideal fluid, the coupling dynamic equations of rigid tank, elastic appendages and liquid fuel are derived using H-O principle. In the case of pitch excitation, the modified potential function and wave height function are introduced to describe the moving boundary of fluid, then Galerkin＇s method is used to discretize the dynamic equations into ordinary differential equations. The natural frequencics of the coupling system are formulated in liquid depth, the length of the tank, etc. The formulae are confirmed by numerical simulations, which also show that the effects of liquid and elastic appendages on the attitude angular of rigid.
基金Financial support from National Natural Science foundation(No.20674005)National High Technology"863"Program of China(No.2006AA03Z108)National Science and Technology Supporting Item(No.2006BAI03A09)
文摘In this paper, a series of chiral non-symmetrical liquid crystals （nBA-chol） consisting of a cholesteryl ester moiety as chiral entity and a biphenyl aromatic core with different terminal alkyl chain has been synthesized and investigated for their liquid crystalline properties. Effects of numbers of methylene units in the terminal alkyl chain on the phase transition temperatures and on the temperature-dependent pitch lengths of the chiral liquid crystals have been studied. The long terminal alkyl chain tends to exhibit smectic A mesophases. The pitch lengths of the cholesteric mesophases of the chiral liquid crystals decrease with increasing temperature and with increasing numbers of methylene units in the terminal alkyl chain, respectively.
