Volume 6, Number 1

January 1991

January issue. -- The International Journal of Analytical and Experimental Modal Analysis 6(1) 1991 Jan. ELIMINATION OF RIGID BODY MODES FROM ASYMMETRIC DYNAMICAL SYSTEMS by S. Natsiavas and H. D. Nelson, Arizona State University This investigation presents a methodology for analyzing the dynamic response of semi-definite mechanical systems with linear but asymmetric equations of motion. This is done by deriving a modified set of equations, characterized by a nonsingular stiffness matrix, after proper elimination of the rigid body modes from the original equations of motion. Standard modal analysis procedures are employed and both undamped and damped systems are analyzed. The applicability and accuracy of the method is illustrated by a number of numerical examples. COMPLEX MODAL ANALYSIS OF NON-PROPORTIONALLY DAMPED CONTINUOUS RODS by G. Prater, Jr., University of Louisville and R. Singh, The Ohio State University This paper presents techniques that can be used to formulate, solve and interpret the complex eigenproblems associated with nonproportionally damped, longitudinally vibrating continuous rods. The formulation procedures yield none of the errors associated with discretized system approaches, and the algorithm used to solve the nonlinear eigenvalue equation is efficient and accurate. Interpretation of the system normal modes is facilitated by special complex domain normalization techniques that allow immediate assessment of the degree of nonproportionality. The concepts involved have been implemented in a computer program, and this is used to analyze example cases involving lumped and distributed viscous damping elements and various classical boundary conditions. The modal data are compared with values from a closed-form analytical solution and a lumped parameter model. Graphical results show how the eigenfunctions and eigenvalues change with increasing degrees of nonproportional damping and which parts of the system are most affected when the damper location and magnitude are changed. PROBABILISTIC DISTRIBUTION OF MULTIPLE CRACKS IN STRUCTURES DUE TO RANDOM MODAL OSCILLATIONS Y.-M. Lu, the Aerospace Corporation and F.D. Ju, University of New Mexico This paper considers the development of the probabilistic methodology for the prediction of multiple-crack distribution in a structure of beam elements associated with individual modal oscillations. The probabilistic measure of crack distribution can then be used for the probabilistic diagnosis of crack damage (depth) and its location (spacing) under random loading and to resolve some of the intrinsic uncertainties in the modal theories of fracture diagnosis. The structural system considers some randomness of material strength. The arresting fracture toughness is characterized as a random variable with the appropriate probability distribution. The application of LEFM (Linear Elastic Fracture Mechanics) in connection with the stress relief effect due to the presence of a crack suggests a means of predicting depth and spacing of tension cracks at a given random modal oscillation. The resulting redistributed random bending stresses (moments) will be a measure to compute the subsequent crack state. With postulation that secondary cracking is dominantly affected by its immediately preceding crack, the process of the successive cracking can be treated as a Markov process. The analyses are performed, under these probabilistic assumptions, for the first few representative normal modes of interest. The probability distribution of the overall structural system, therefore, is obtained dependent on a weighted distribution of modes for a particular excitation spectrum. EMPLOYING PATTERN RECOGNITION FOR DETECTING CRACKS IN A BRIDGE MODEL M. M. Samman, M. Biswas and A. K. Pandey, Duke University A scaled model of a typical highway bridge is used to investigate the change in the frequency-response-function signals due to development of cracks in its girders. The Freeman's code for boundary recognition, a method used in the fields of pattern recognition and image processing, is modified and employed to accentuate the differences in the frequency- response function between the intact-bridge signal and the cracked-bridge signal. The method is a good candidate for detecting cracks in full scale bridges and other structures because it is found to be capable of detecting relatively minor cracks. The method is also helpful in estimating the location of the crack. Since this method requires only one signal per girder, the time and effort required for inspection are kept at a minimum. CALCULATED AND MEASURED DYNAMICS OF ELASTOMER SUPPORT MOUNTS L. Gaul, University of the Federal Armed Forces Hamburg Optimization of active and passive isolation of machine foundations requires knowledge about the propagation of structureborne sound in its substructures. The substructure behavior of elastomer isolators for resiliently mounted engines defines mixed boundary value problems for the field equations. It is shown that the CAD compatible boundary element method (BEM) provides a powerful tool to predict the substructure dynamics in the design state by taking complicated three-dimensional (3-D) geometry, viscoelastic material properties and temperature influence into account. DETERMINATION OF MODAL PARAMETERS OF TALL BUILDINGS WITH AMBIENT VIBRATION MEASUREMENTS Z. W. Bao, Tsinghua University and J. M. Ko, Hong Kong Polytechnic Dynamic characteristics of tall buildings are essential for the assessment of earthquake loads and the corresponding dynamic responses. In addition, they are useful for safety evaluation of existing structures. This paper gives the natural frequencies, the mode shapes and the damping ratios of five buildings in Hong Kong. These characteristics were determined by spectral analysis of the ambient vibration signal. The data analysis is discussed including the method of determining mode shapes, how to improve the accuracy of damping ratios, and the identification and decomposition of torsional vibration.