Based on the Reynolds equation with Reynolds boundary conditions,the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings.By doing so,a profile of nonlinear oil film force of single-pad journal bearings is established.According to the structure of combination journal bearings,nonlinear oil film force of combination journal bearing is obtained by retrieval,interpolation and assembly techniques.As for symmetrical flexible Jeffcott rotor systems supported by combination journal bearings,the nonlinear motions of the center of the rotor are calculated by the self-adaptive Runge-Kutta method and Poincaré mapping with different rotational speeds.The numerical results show that the system performance is slightly better when the pivot ratio changes from 0.5 to 0.6,and reveals nonlinear phenomena of periodic,period-doubing,quasi-periodic motion,etc.
Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson-θ-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincaré map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.
The stretchable sensor wrapped around a foldable airfoil or embedded inside of it has great potential for use in the monitoring of the structural status of the foldable airfoil.The design methodology is important to the development of the stretchable sensor for status monitoring on the foldable airfoil.According to the requirement of mechanical flexibility of the sensor,the combined use of a layered flexible structural formation and a strain isolation layer is implemented.An analytical higher-order model is proposed to predict the stresses of the strain-isolation layer based on the shear-lag model for the safe design of the flexible and stretchable sensors.The normal stress and shear stress equations in the constructed structure of the sensors are obtained by the proposed model.The stress distribution in the structure is investigated when bending load is applied to the structures.The numerical results show that the proposed model can predict the variation of normal stress and shear stress along the thickness of the strain-isolation(polydimethylsiloxane)layer accurately.The results by the proposed model are in good agreement with the finite element method,in which the normal stress is variable while the shear stress is invariable along the thickness direction of strain-isolation layer.The high-order model is proposed to predict the stresses of the layered structure of the flexible and stretchable sensor for monitoring the status of the foldable airfoil.
Stretchable/flexible electronics has attracted great interest and attention due to its potentially broad applications in bio-compatible systems. One class of these ultra-thin electronic systems has found promising and important utilities in bio-integrated monitoring and therapeutic devices. These devices can conform to the surfaces of soft bio-tissues such as the epidermis, the epicardium, and the brain to provide portable healthcare functionalities. Upon contractions of the soft tissues, the electronics undergoes compression and buckles into various modes, depending on the stiffness of the tissue and the strength of the interfacial adhesion. These buckling modes result in different kinds of interfacial delamination and shapes of the deformed electronics, which are very important to the proper functioning of the bioelectronic devices. In this paper, detailed buckling mechanics of these thin-film electronics on elastomeric substrates is studied. The analytical results, validated by experiments, provide a very convenient tool for predicting peak strain in the electronics and the intactness of the interface under various conditions.
