The equation of motion for the mass can, if there are no external forces, be written asĭividing by the mass, and using customary notation, Analysis of an SDOF SystemĬonsider a mass-spring-damper system attached to a moving base. Thus, it is not a direct representation of the frequency content of the excitation (as in a Fourier transform), but rather of the effect that the signal has on a postulated system with a single degree of freedom (SDOF). The response spectrum is a function of the natural frequency of the oscillator and of its damping. Definition of a Response SpectrumĪ response spectrum is a function of frequency or period, showing the peak response of a simple harmonic oscillator that is subjected to a transient event. In most cases, the engineer performing a response spectrum analysis is presented with a given design response spectrum, in which case the two first parts can be considered as background material. The use of a given response spectrum in a structural analysis.Generation of a response spectrum from a given time history.The text below is separated into three parts: The idea is to provide an input that gives a limit to how much an eigenmode having a certain natural frequency and damping can be excited by an event of this type. The response spectrum method is based on a special type of mode superposition. Due to the short length of the event, it cannot be considered as an ergodic ("stationary") process, so a random response approach is not applicable either. Since the exact time history of the load is not known, it is difficult to perform a time-dependent analysis. Examples of such events are earthquakes and shocks. Response spectrum analysis is a method to estimate the structural response to short, nondeterministic, transient dynamic events. Structural Mechanics Response Spectrum Analysis What Is Response Spectrum Analysis?
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