Sound & Vibration Magazine 30 th Anniversary Issue March, 1997 Page - 1 Is It a Mode Shape, or an Operating Deflection Shape? Mark H. Richardson, Vibrant Technology, Inc., Jamestown, California Abstract Mode shapes and operating "deflection" shapes are re- lated to one another. In fact, one is always measured in order to obtain the other. Yet, they are quite different from one another in a number of ways. This article dis- cusses the relationships between modal testing, modal analysis and operating deflection shape measurements. Introduction The question, "Is it a mode shape, or an operating deflec- tion shape?" is probably asked more often than any other when testing structures, especially when attempting to identify their resonant or modal properties. Another way that it is asked is, "When the excitation changes, the mode shape changes. What's going on here?" The subject of mode shapes versus operating deflection shapes has certainly been written about before. In fact, a previous Sound and Vibration magazine article [1] covered them quite extensively. I recommend that you read that article, because it provides valuable insight and contains a number of examples. To shed more light on this subject, I will point out other similarities and differences between the two types of shapes, and discuss the measurements required to obtain each of them. Over the past 20 years, the number of ways in which modal testing has been done has proliferated greatly. Tradition- ally, most modal testing was done using sine wave based methods and analog instrumentation. During the late 1960s however, the discovery of the Fast Fourier Transform (FFT) algorithm and the use of digital computers in labo- ratory testing systems allowed experimentalists to begin exploring the use of new excitation and signal processing techniques for modal testing. Because the FFT provides the frequency spectrum of a sig- nal in fractions of a second, various kinds of broad band random, swept sine, and transient signals, which excite many frequencies at once, could be used to excite structures and measure their responses. Impact testing has become the most popular modal testing method today. It can be done rather quickly and inexpensively using an instru- mented hammer, an accelerometer, a 2 channel FFT ana- lyzer, and post processing software. Also, the availability of lower cost transducers, PC based data acquisition sys- tems, portable data collectors, desktop and notebook com- puters, and more powerful software have all helped to put modal testing into the hands of more practitioners. Nevertheless, modal analysis has often been shrouded in a veil of mystery, while the concept of an operating deflection shape has remained relatively straightforward. Ole Dossing began his article with the statements, "Operational deflection shapes (ODSs) can be measured directly by relatively simple means. They provide very useful information for understanding and evaluating the absolute dynamic behavior of a machine, component or an entire structure.'' This suggests that maybe mode shapes are not so easy to measure. If not, then why not. What Are Modes? Modes are associated with structural resonances. The ma- jority of structures can be made to resonate. That is, under the proper conditions, a structure can be made to vibrate with excessive, sustained motion. Striking a bell with a hammer causes it to resonate. Striking a sandbag, however, will not cause it to resonate. Resonant vibration is caused by an interaction between the inertial and elastic properties of the materials within a structure. Furthermore, resonant vibration is the cause of, or at least a contributing factor to, many of the vibration related problems that occur in structures and operating ma- chinery. These problems include failure to maintain toler- ances, noisy operation, uncontrollability, material failure, premature fatigue, and shortened product life. To better understand a structural vibration problem, we need to characterize the resonances of a structure. A com- mon and useful way of doing this is to define its modes of vibration. Each mode is defined by a modal frequency, modal damping, and a mode shape. Can we define modes experimentally by measuring operat- ing deflection shapes, which are easy to measure? To an- swer this question requires a better understanding of mode shapes and operating deflection shapes. What Are Operating Deflection Shapes? Traditionally, an ODS has been defined as the deflection of a structure at a particular frequency. However, an ODS can be defined more generally as any forced motion of two or more points on a structure. Specifying the motion of two or