Modal Metrics How Are Eigenvalues, Eigenvectors, and Eigenmodes Related?Īny object can be considered a connection of complicated springs, and then the system response “x” for any applied input “y” could be given using a scaling factor as In other words, the result of modal analysis are these frequencies at which the amplitude increases to infinity. As the frequency increases towards the “resonant frequency,” the amplitude of response asymptotically increases to infinity. It is also the frequency where the object will allow a transfer of energy from one form to another with minimal loss-here it is from vibrational to kinetic. 01, every object has an internal frequency (or resonant frequency) at which the object can naturally vibrate. the frequency of the applied input (x-axis) ( Source)Īs shown in Fig. 01: Amplitude of system response (y-axis) w.r.t. For example, for a particular input (like an applied load of certain amplitude and frequency), what are the limits of the system’s response (for example, when and what is the maximum displacement). In contrast to quasi-static and dynamic, modal analysis provides an overview of the limits of the response of a system. Both types provide a one-to-one relationship between a particular input (for example, a force applied on a system) to its system response (for example, a displacement of the system due to its load). Dynamic analysis is where the effects of acceleration cannot be ignored. The most common type of analysis is quasi-static analysis, where the load is applied at a very slow rate so that the acceleration is negligible (or almost zero). Let’s briefly explain the difference between quasi-static, dynamic, and modal analysis. More often these terms develop out of necessity, but many times it’s to express things with mathematical accuracy. People always prefer to make things sound more complicated than they need to be. We often hear the terms “modal analysis,” “eigenvalues,” “eigenmodes” or “eigenfrequencies”, and by the time one comprehends a single terminology, a new terminology emerges.