An exact solution for the natural frequencies and mode shapes for a beam elastically constrained at its ends and to which a rigid mass is elastically mounted is obtained. The attached mass can both translate and rotate. The general solution is obtained using the Laplace transform with respect to the spatial variable and yields the exact solutions to several previously published simpler configurations that were obtained using approximate methods. Numerous numerical results are presented for the natural frequency coefficients that extend previously reported results and that show the transition between various limiting cases. In addition, values are presented for the lowest two natural frequency coefficients for a beam that is clamped at both ends and is carrying a two dof spring-mass system. Representative mode shapes at selected values of the system’s parameters are also given.
Besides cost issue, the charging infrastructures popularization and charging safety assurance are two major concerns for promoting electric vehicles (EVs). Several pilot-run programs, such as in the U.S., Europe, Japan, China, and Taiwan as well, enforce the safety compliance of EVs and infrastructures as an implementation policy. To be part of the players, it is essential to have the comprehensive understanding of the standard differences among IEC, SAE/UL, GB and JEVS. The way to compile the issued standards in different regions, however, is time consuming and may get limited helpful hints until tried and tested. Based on above-mentioned standards, this study summarized an overview in aspects of construction, function, performance and safety for charging equipments. To facilitate as a competent safety design, key requirements of electrical safety were presented. These crucial design rules included functional requirements, constructional requirements, personal protection against electric shock, insulation coordination, electromagnetic compatibility and charging control. The rationale and compliance requirements were highlighted to assist as design guidelines. In addition, learning from the past is always a good approach to build confidence to comply with the safety requirements. Based on the standards-follow most IEC and some SAE/UL-for pilot-run project in Taiwan, a case study of an AC charging stand provided the safety faults encountered and solutions in designing a new product that can meet safety requirements effectively. With these design guidelines and the case study, this paper provided a solid basis of safety design for electric vehicle charging equipments.
The effects on the onset of chatter by the dynamic interaction of the workpiece and its method of support, the turret, the lathe bed, the cutting forces and the cutting conditions are determined. A generalized modal analysis is used to solve the four governing equations in the frequency domain. It is found that there are four dimensionless quantities that couple the equations, the most important being N0, the ratio of the static stiffness of the workpiece to the translational stiffness of the turret. The dimensionless critical depth of cut Hc and corresponding chatter frequency coefficient Ωc2 are determined as a function of N0 for two feed rates, several surface speeds, and for two workpiece boundary conditions; cantilevered and clamped-hinged. It is shown that the magnitudes of Hc and Ωc2 are oscillatory as a function of N0, and the occurrence of their peak values is proportional to the surface speed of the workpiece to the fourth power. It is found that for the parameters selected the effect of the dynamic response of the lathe bed is to increase by 7 percent the values of N0 at which the peak values of Hc occur. It is also found that the value of the equivalent viscous damping of the system and the magnitude of the real part of the cutting force coefficient govern the magnitudes of Hc and Ωc2 as a function of N0.
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