Volume 6, Number 2

April 1991

================================================================== Maia, N. M. M., Technical University of Lisbon 6 (2): 69-80; Apr. 1991 REFLECTIONS OF SOME SINGLE-DEGREE-OF-FREEDOM (SDOF) MODAL ANALYSIS METHODS ABSTRACT - In the present paper, some of the most important single-degree-of-freedom (SDOF) methods of modal analysis are described and compared, based on experience gained while applying them to both theoretical and experimental cases. The work is descriptive, as the main objective is to stress and explore the concepts involved and the existing similarities. It is believed that a contribution is made in the sense of providing a deeper understanding of Dobsons method relating it to the inverse method. Mioduchowski, A., University of Alberta and W. Nadolski, Polish Academy of Sciences 6(2): 81-88; Apr. 1991 ON TORSIONAL RESONANT DEFORMATIONS OF SIMPLIFIED NONHOMOGENEOUS DRIVE SYSTEMS ABSTRACT - In this paper the one-dimensional discrete - continuous model of a simple nonhomogeneous drive system is considered. The system consists of three rigid disks and two torsionally deformable shafts of different materials, but such that torsional wave speeds in both shafts are equal. Damping is taken into account by means of an equivalent external damping of the viscous type and an equivalent damping of the Voigt type. Numerical results for the amplitude - frequency curves for selected cross- sections are presented in graphical form. Wright, J. R., University of Manchester and M. A. Al-Hadid, Scientific Studies and Research Centre 6(2): 89-103; Apr. 1991 SENSITIVITY OF THE FORCE-STATE MAPPING APPROACH TO MEASUREMENT ERRORS ABSTRACT - In this paper the application of the force-state mapping approach to the identification of nonlinear systems is considered. In particular, the sensitivity of the basic method to systematic amplitude and phase errors, and to random errors, in the measurements is investigated analytically using a linear single degree of freedom system subject to steady state excitation. It is shown that the identified damping estimates are very sensitive to small systematic errors in the phase of the measured or integrated signals when the system itself is lightly damped, and that significantly biased results can be obtained. Other forms of error are far less important. The study highlights the need for extremely accurate instrumentation if this identification approach is to be used successfully in practice. Jara-Almonte, J., Clemson University and L. D. Mitchell, Virginia Polytechnic Institute and State University 6(2): 105-115; Apr. 1991 A HYBRID EIGENPROBLEM FORMULATION USING THE FINITE ELEMENT METHOD; PART I: THEORY ABSTRACT - A hybrid technique to reduce the size of finite- element-method based eigen problems is presented in this paper. Numerical examples using this method are presented in Part II. In this hybrid method, a continuum transfer matrix beam element is used as an exact dynamical element. The exact element is incorporated into a finite element model, and is used as a substructure, resulting in smaller matrices. The terms in the exact dynamical representation are functions of frequency. Thus the ensuing eigenproblem is a transcendental eigenproblem. A frequency-scan extraction algorithm is employed to find the eigenvalues. The eigenvectors can be reconstructed for both finite and exact elements; however, the exact formulation yields eigenvectors with virtually any desired spatial precision. One result of this hybrid, finite element and transfer matrix, method is smaller matrices, albeit with a transcendental eigenvalue problem. Another result is that the hybrid method has the ability to extract higher eigenfrequencies as easily and as accurately as lower eigenfrequencies. Moreover, the formulation allows the extraction of an average of six eigenfrequencies/vectors for every degree of freedom in the model. In contrast, the finite element method models usually require four or more degrees of freedom per accurate eigenfrequency (within 5% of the true eigenvalue). Jara-Almonte, J., Clemson University and L. D. Mitchell, Virginia Polytechnic Institute and State University. 6(2): 117-130; Apr. 1991 A HYBRID EIGENPROBLEM FORMULATION USING THE FINITE ELEMENT METHOD; PART II: EXAMPLES ABSTRACT - This paper contains numerical examples of the method presented in Part I , which dealt with the theory. The proposed method incorporates continuum transfer matrices into a finite element discretization for substructuring purposes. The two examples presented in this paper, a portal arch and Vierendeel truss, show that the proposed method reduced the number of degrees of freedom of the finite element models and at the same time improved the accuracy of the predicted higher eigenvalues. These improvements came at the expense of having to solve a transcendental eigenproblem. The implementation and solution of the hybrid model is also presented. McConnell, K. G., Iowa State University and Rogers, J. D., Sandia National Laboratories 6(2): 131-145; Apr. 1991 TUTORIAL: TRANSDUCER REQUIREMENTS FOR USE IN MODAL ANALYSIS ABSTRACT - The art of Experimental Modal Analysis starts with the transducers and system components used in making the required measurements. Many different instrument systems can be used. The objective of the first set of four papers in this tutorial series is to understand instrumentation requirements and measurement system characteristics as applied to experimental modal analysis. A second set of tutorial papers will explore the requirements for understanding and using frequency analysis. A third set of papers will explore the art of pulling it all together in order to obtain the natural frequencies, mode shapes, structural damping, etc. These tutorial papers are based on a series of yearly seminars given at the spring meetings of the Society of Experimental Mechanics as well as current research and experience of the authors. The first paper is limited to the general measurement requirements and beginning definitions used in instrumentation systems. It addresses several topics necessary for the understanding of modal analysis measurements. The first section gives a very brief overview of the concepts of modal analysis. The next two sections deal with transducer characteristics. The last five sections discuss background material on measurements systems, operational amplifiers, and convenient methods for dealing with complex values. Each section was written independently from the others to provide for convenient review as reference material. Thus, some readers may find it more beneficial to read the background material first, while others may choose to skip that material entirely.