General Mechanical

General Mechanical

Should I do a Response Spectrum Analysis? A Tech. Support point of view.

    • Dave Looman
      Ansys Employee
      If you do tech. support long enough you will discover there are only 10 Questions. Oh, of course there are a myriad of small difficulties, irritations, limitations and complaints that customers call in about, but I'm not talking about those. I’m referring to questions which are almost philosophical in nature.  In my area of linear dynamics, one of the ten is Should I do a Response Spectrum Analysis? nOne might be tempted to answer that if you were supposed to do a response spectrum analysis you would know. Certainly in the Nuclear Industry that is the case. The NRC or the engineer that wrote the spec. you must satisfy would make that very clear. But it’s not a customer from the Nuclear Industry that asks this question. It’s an engineer analyzing a rear view mirror that has been given a mil spec or some shaker table results or wants to do an impact test.  A "spectrum" plot of ground displacement/velocity/acceleration vs frequency looks exactly like a response spectrum. The difference is that a response spectrum is the solution to a certain ground motion (e.g., a strong earthquake), not the excitation itself. If you have a graph of ground acceleration vs. frequency you should do a harmonic sweep instead. If you have a graph of motion vs. time you should do a transient. In general, if you aren’t given a response spectrum, that is, an envelope of peak response vs. modal frequency you should be using another method. However, it is possible to create your own response spectrum from ground motion vs. time. I’ll talk about that option in Part II.nA response spectrum is created by performing a transient analysis of a certain ground motion time-history on a set of 1 degree of freedom oscillators of varying frequency. The peak response of each oscillator over the duration of the transient becomes a point on the response spectrum graph vs. the frequency or period of the oscillator that produced it. Usually the peak responses are enveloped by a set of straight lines.  The peak responses can be in the form of displacement, velocity or acceleration.   Sometime all three are plotted simultaneously on a single tripartite graph vs. period instead of frequency and using log-log scales with the apparent purpose of discouraging the uninitiated from attempting to use the method.nThe graph has the same information in the three different forms since for a given frequency, displacement, velocity and acceleration differ by the ratio omega and omega^2.nIt’s not always explicitly indicated on the response spectrum graph that it was obtained assuming a certain amount of damping.  As a result, it is not uncommon for users to specify damping in conjunction with a spectrum analysis and expect that it will diminish the response to the response spectrum. It doesn’t, damping is already "in there."  Damping input is used, however, to interpolate between multiple spectrums of different damping values [SV,damping ratio].  When damping has been specified as a material property the interpolation is done on mode by mode based on the amount of strain energy per material a mode has. Damping is also used by some of the combination methods to combine closely spaced modes.   nWhat makes a response spectrum so useful is that the peak response of a single mode of a multi-dof model to a transient excitation can be computed from the peak response of a single dof oscillator of the same frequency. I’ve never lost a sense of wonder at this beautiful property of structural modes and it still interests me to think about questions like - At what location in my mode shape will I find this peak response? Because of this property of modes, every supplier of equipment or structure on a job site can perform a dynamic evaluation by a simple mode combination all using the same response spectrum, whether they are analyzing a fire hydrant or a "sky scraper." nTo summarize, you should do a response spectrum if you or someone else has created one for you. If you have a specification for the ground motion itself, do a harmonic, random vibration or transient analysis. If your spectrum has units of g2/hz do a Random Vibration analysis, which although referred to as a spectrum method is more like a harmonic sweep than a response spectrum An excellent reference on this topic is the book, "Response spectrum method in seismic analysis and design of structures" by Ajay Gupta.n
    • Keyur Kanade
      Ansys Employee
      Thanks!n
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