An overview of the research conducted in the area of linear and nonlinear vibrations of loudspeakers and revolution shells was given in the turning-point frequency range in Chapter 1. It shows that some problems conce...An overview of the research conducted in the area of linear and nonlinear vibrations of loudspeakers and revolution shells was given in the turning-point frequency range in Chapter 1. It shows that some problems concerning vibrations of shells in the turning-point range have to be further studied. The linear vibrations of truncated revolution shells with the first-order turningpoint were systematically investigated in the turningpoint range from Chapter 2 to Chapter 6, including the general solutions for the free vibration, the eigenvalues under various boundary conditions, the forced vibrations driven by an edge force or an edge displacement and some related special effects, and the applications in loudspeaker vibrations. The nonlinear autoparametric vibration was examined in Chapter 7. Main results are listed as follows.展开更多
Terrain plays a key role in landscape pattern formation, particularly in the transition zones from mountains to plains.Exploring the relationships between terrain characteristics and landscape types in terrain-complex...Terrain plays a key role in landscape pattern formation, particularly in the transition zones from mountains to plains.Exploring the relationships between terrain characteristics and landscape types in terrain-complex areas can help reveal the mechanisms underlying the relationships. In this study, Qihe River Basin, situated in the transition zone from the Taihang Mountains to the North-China Plain, was selected as a case study area. First, the spatial variations in the relief amplitudes(i.e.,high-amplitude terrain undulations) were analyzed. Second, the effects of relief amplitudes on the landscape patterns were indepth investigated from the perspectives of both landscape types and landscape indices. Finally, a logistic regression model was employed to examine the relationships between the landscape patterns and the influencing factors(natural and human) at different relief amplitudes. The results show that with increasing relief amplitude, anthropogenic landscapes gradually give in to natral landscapes. Specifically, human factors normally dominate the gentle areas(e.g., flat areas) in influencing the distribution of landscape types, and natural factors normally dominate the highly-undulating areas(e.g., moderate relief areas). As for the intermediately undulating areas(i.e.,medium relief amplitudes), a combined influence of natural and human factors result in the highest varieties of landscape types. The results also show that in micro-relief areas and small relief areas where natural factors and human factors are more or less equally active,landscape types are affected by a combination of natural and human factors.The combination leads to a high fragmentation and a high diversity of landscape patterns. It seems that appropriate human interferences in these areas can be conducive to enhancing landscape diversity and that inappropriate human interferences can aggravate the problems of landscape fragmentation.展开更多
The equations representing the free vibration of any thin shells of revolution, except the shells with constant curvature (cylindrical and spherical shell), have a simple turning point, when the frequency parameter Ω...The equations representing the free vibration of any thin shells of revolution, except the shells with constant curvature (cylindrical and spherical shell), have a simple turning point, when the frequency parameter Ω lies at a certain interval and the waves in the circumferential direction are not too many. All of their asymptotic solutions are developed, which are valid for the whole range of the shell surface and satisfy the required accuraracy of the theory of thin shells. Three categories of the generalized function Z_h (h=1, 2, 3, 4), R and J are defined, of which a singular membrane solution and four bending solutions can be expressed. Particularly, the second category of the generalized function R is first obtained which is a generalization of a new solution to the related equation. This new solution is found by modifying the Laplace transform method. The frequency equation of the truncated shells of revolution clamped at their two boundaries is finally given.展开更多
文摘An overview of the research conducted in the area of linear and nonlinear vibrations of loudspeakers and revolution shells was given in the turning-point frequency range in Chapter 1. It shows that some problems concerning vibrations of shells in the turning-point range have to be further studied. The linear vibrations of truncated revolution shells with the first-order turningpoint were systematically investigated in the turningpoint range from Chapter 2 to Chapter 6, including the general solutions for the free vibration, the eigenvalues under various boundary conditions, the forced vibrations driven by an edge force or an edge displacement and some related special effects, and the applications in loudspeaker vibrations. The nonlinear autoparametric vibration was examined in Chapter 7. Main results are listed as follows.
基金supported by the National Basic Research Program of China(Grant No.2015CB452702)the National Natural Science Foundation of China(Grant Nos.41671090&41601091)
文摘Terrain plays a key role in landscape pattern formation, particularly in the transition zones from mountains to plains.Exploring the relationships between terrain characteristics and landscape types in terrain-complex areas can help reveal the mechanisms underlying the relationships. In this study, Qihe River Basin, situated in the transition zone from the Taihang Mountains to the North-China Plain, was selected as a case study area. First, the spatial variations in the relief amplitudes(i.e.,high-amplitude terrain undulations) were analyzed. Second, the effects of relief amplitudes on the landscape patterns were indepth investigated from the perspectives of both landscape types and landscape indices. Finally, a logistic regression model was employed to examine the relationships between the landscape patterns and the influencing factors(natural and human) at different relief amplitudes. The results show that with increasing relief amplitude, anthropogenic landscapes gradually give in to natral landscapes. Specifically, human factors normally dominate the gentle areas(e.g., flat areas) in influencing the distribution of landscape types, and natural factors normally dominate the highly-undulating areas(e.g., moderate relief areas). As for the intermediately undulating areas(i.e.,medium relief amplitudes), a combined influence of natural and human factors result in the highest varieties of landscape types. The results also show that in micro-relief areas and small relief areas where natural factors and human factors are more or less equally active,landscape types are affected by a combination of natural and human factors.The combination leads to a high fragmentation and a high diversity of landscape patterns. It seems that appropriate human interferences in these areas can be conducive to enhancing landscape diversity and that inappropriate human interferences can aggravate the problems of landscape fragmentation.
文摘The equations representing the free vibration of any thin shells of revolution, except the shells with constant curvature (cylindrical and spherical shell), have a simple turning point, when the frequency parameter Ω lies at a certain interval and the waves in the circumferential direction are not too many. All of their asymptotic solutions are developed, which are valid for the whole range of the shell surface and satisfy the required accuraracy of the theory of thin shells. Three categories of the generalized function Z_h (h=1, 2, 3, 4), R and J are defined, of which a singular membrane solution and four bending solutions can be expressed. Particularly, the second category of the generalized function R is first obtained which is a generalization of a new solution to the related equation. This new solution is found by modifying the Laplace transform method. The frequency equation of the truncated shells of revolution clamped at their two boundaries is finally given.
