Unitarity of Displacement Mode, Strain Mode and Curvature Mode and Their Modal Parameter Identification Methods

摘要

Traditionally vibration equations are established in accordance with the d'Alembert's principle. The differential element of the dynamic structure is assumed to be in equilibrium state in the existence of the external applied force, the forces of structural resistance and the damping resistance. In this force system, the coordinates of equations are coupled. Whereas, modal coordinates, as a vector, related to the bases that are the eigen-vectors. Eigen-vectors are orthogonal and each of them represents a peculiar state of vibrational deformation of the structure corresponding to eigen frequency. Modal coordinates are independent of each other. Response is the superposition of the contributions of modal deformations, and the modal coordinates can be regarded as the energy portions on which modal deformations rely for existence respectively. The displacement modal shape, the strain modal shape and the curvature modal shape are merely the different representations of the same eigen deformation. And therefore the responses of displacement, strain and curvature must have the same coordinate corresponding to the same modal frequency. It is in this sense, these three kinds of modes are unifiable. The modal parameter identification methods of these three kinds deformation modes are derived and explained as well.