kaist.lecture.01.2003 University of Colorado （kaist.lecture.01.2003科罗拉多大学）.pdfVIP

. 17 Methods for Vibration Analysis 17–1 Chapter 17: METHODS FOR VIBRATION ANALYSIS 17–2 §17.1 PROBLEM CLASSIFICATION According to S. H. Krandall (1956), engineering problems can be classified into three categories: • equilibrium problems • eigenvalue problems • propagation problems Equilibrium problems are characterized by the structural or mechanical deforma- tions due to quasi-static or repetitive loadings. In other words, in structural and mechanical systems the solution of equilibrium problems is a stress or deforma- tion state under a given load. The modeling and analysis tasks are thus to obtain the system stiffness or flexibility so that the stresses or displacements computed accurately match the observed ones. Eigenvalue problems can be considered as extentions of equilibrium problems in that their solutions are dictated by the same equilibrium states. There is an additional distinct feature in eigenvalue problems: their solutions are characterized by a unique set of system configurations such as resonance and buckling. Propagation problems are to predict the subsequent stresses or deformation states of a system under the time-varying loading and deformation states. It is called initial- value problems in mathematics or disturbance transmissions in wave propagation. Modal testing is perhaps the most widely accepted words for activities involving the characterization of mechanical and structural vibrations through testing and measurements. It is primarily concerned with the determination of mode shapes (eigenvevtors) and modes (eigenvalues), and to the extent possible the damping ratios of a vibrating system. Therefore, modal testing can be viewed as experimental solutions of eigenv