Principal axes of M-DOF structures Part I:Static loading

This paper is the first in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynamic response of structures to enable better design of structures and control modification devices/systems. Under idealized design conditions, the structural responses are obtained by using single direction input ground motions in the direction of the intended control devices/systems, and by assuming that the responses of the structure is decoupleable in three mutually perpendicular directions. This standard practice has been applied to both new and retrofitted structures using various seismic protective systems. Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects - of which torsion is a component) of the dynamic response of structures. In order to quantify such effects, it is necessary to examine the principal axes of structures under both static and dynamic loading. This first paper deals with quantitative definitions of principal axes and “cross effects” of three-dimensional structures under static load by using linear algebra. It shows theoretically that, for three-dimensional structures, such principal axes rarely exist. Under static loading conditions, the cross effect is typically small and negligible from the viewpoint of engineering applications. However, it provides the theoretical base for subsequent quantification of the response couplings under dynamic loads, which is reported in part II of this series.

Principal axes of M-DOF structures PartⅡ:Dynamic loading

This paper is the second in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads.The primary purpose of this series is to understand the magnitude of the dynamie response of structures to enable better design of structures and response modification devices/systems.Under idealized design condi- tions,the structural responses are obtained by using single directinn input ground motions in the direction of the intended response modification devices/systems,and by assuming that the responses of the structure is deconpleable in three mutual- ly perpendicular directions.This standard practice has been applied to both new and retrofitted structures using various seis- mic protective systems.Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects of which torsion is a component)of the dynamic response of structures.In order to quantify such effects,it is necessary to examine the principal axes of structures under both static and dynamic loading.In this twn-part series,the first paper is concerned with static loading,which provides definitions and fundamental formulations,with the conclusion that cross effects of a statically loaded M-DOF structure resulting from the lack of principal axes are of insignificant magnitude. However,under dynamic or earthquake loading,a relatively small amount of energy transferred across perpendicular direc- tions is accumulated,which may result in significant enlargement of the structural response.This paper deals with a formu- lation to define the principal axes of M-DOF structures under dynamic loading and develops quantitative measures to identify cross effects resuhing from the non-existence of principal axes.

A theoretical method based on Fourier spectrum analysis for the focusing performances of the X-ray compound refractive lenses

It is important to predict the intensity distribution in focusing plane for designing the X-ray compound refractive lenses. On the basis of analyzing the structure of X-ray compound lenses and comparing it with Praunhofer diffraction system, it is concluded that the X-ray focusing system can be regarded as a kind of Praunhofer diffraction system. Therefore, a method based on Fourier spectrum analysis is presented to predict the intensity distribution in the focusing plane for the X-ray lenses. A brief analysis on the relationship between the parameters of X-ray lenses and their focusing performance is also given in this paper.

Accelerating the Construction of New Development Pattern and the Paths of Manufacturing Transformation and Upgrading

This paper reviews the basic implications and policy orientation of the new development pattern and the impacts of constructing the new development pattern on the manufacturing transformation and upgrading,based on which the choice of manufacturing transformation and upgrading paths is further discussed under the new development pattern.This paper holds that the paths of manufacturing transformation and upgrading need to be adjusted and expanded under the conditions of constructing the new development pattern.The main ideas are as follows.Restructuring the manufacturing industry chain with the large domestic market as the main guide,creating the good environment conducive to independent innovation,coordinating the regional layout for the overall high-quality manufacturing development,optimizing the business environment and enhancing the vitality and driving force of the manufacturing’s development,relying on the Belt and Road Initiative(BRI)for a higher level of international circulation.The theoretical bases for adjusting and expanding the paths of manufacturing transformation and upgrading are:embracing the new requirements with domestic circulation as the mainstay,the characteristics with the mutual reinforcement of domestic and international circulations,and promoting the manufacturing’s high-quality development and the medium and high-speed growth.