Response spectrum

A response spectrum is a plot of the peak or steady-state response (displacement, velocity or acceleration) of a series of <a href="/facts/Oscillators/6vSrm84a">oscillators</a> of varying <a href="/facts/Natural_frequency/pqTgYguB">natural frequency</a>, that are forced into motion by the same base <a href="/facts/Vibration/sGgDqG71">vibration</a> or <a href="/facts/Shock_(mechanics)/AjThlASN">shock</a>. The resulting plot can then be used to pick off the response of any <a href="/facts/Linear/fChtg3KC">linear</a> system, given its natural frequency of oscillation. One such use is in assessing the peak response of buildings to <a href="/facts/Earthquake/NGjIzagw">earthquakes</a>. The science of <a href="/facts/Strong_ground_motion/emmJ0FC9">strong ground motion</a> may use some values from the ground response spectrum (calculated from recordings of surface ground motion from <a href="/facts/Seismograph/CCc9vwqf">seismographs</a>) for correlation with seismic damage.
If the input used in calculating a response spectrum is steady-state periodic, then the steady-state result is recorded. Damping must be present, or else the response will be infinite. For transient input (such as seismic ground motion), the peak response is reported. Some level of damping is generally assumed, but a value will be obtained even with no damping.
Response spectra can also be used in assessing the response of linear systems with multiple modes of <a href="/facts/Oscillation/6vSrm84a">oscillation</a> (multi-degree of freedom systems), although they are only accurate for low levels of damping. <a href="/facts/Modal_analysis/BLxYhRcE">Modal analysis</a> is performed to identify the modes, and the response in that mode can be picked from the response spectrum. These peak responses are then combined to estimate a total response. A typical combination method is the square root of the sum of the squares (SRSS) if the modal frequencies are not close. The result is typically different from that which would be calculated directly from an input, since phase information is lost in the process of generating the response spectrum.
The main limitation of response spectra is that they are only universally applicable for <a href="/facts/Linear/fChtg3KC">linear</a> systems. Response spectra can be generated for <a href="/facts/Non-linear/4aYItALC">non-linear</a> systems, but are only applicable to systems with the same non-linearity, although attempts have been made to develop non-linear seismic design spectra with wider structural application. The results of this cannot be directly combined for multi-mode response.

Response spectrum open-in-new

Response spectrum