A connection between linear normal modes and lines of curvature on the potential surface

作者：Zhang Xinhua^*

来源：Mechanics Research Communications, 2007, 34(3): 235-240.

DOI：10.1016/j.mechrescom.2006.12.001

• linear normal mode
• natural frequency
• line of curvature
• principal curvature
• potential surface

For the N-degree-of-freedom of linear conservative vibratory systems, the corresponding potential functions can be viewed as N-hypersurfaces in (N + 1)-dimensional space. In this paper, a connection between the geometrical properties (principal curvatures, curvature lines) of potential surfaces and the vibratory characteristics (natural frequencies, linear modes) of the system is built. It is proved that the linear normal modes are exactly the projections of the lines of curvature on the potential surface onto the configuration space with metric my (the mass-matrix); and that the squared natural frequencies are exactly the principal curvatures, at the origin of the configuration space, of the potential surface.

• 出版日期2007-4
• 单位西安交通大学