{{One source, date=April 2023 The Extreme Response Spectrum (ERS) (or Maximum Response Spectrum (MRS)) is defined as a curve giving the value of the highest peak of the response of a linear Single Degree of Freedom System (SDOF system) to vibration, according to its

natural frequency Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving force. The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all pa ...

, for a given

damping ratio Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples inc ...

. The response is described here by the

relative movement Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a fiel ...

of the mass of this system in relation to its support. The

x-axis A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...

refers to the natural frequency and the

y-axis A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured i ...

to the highest peak multiplied by the square of the quantity (2 π x natural frequency), by analogy with the relative displacement

shock response spectrum A Shock Response Spectrum (SRS)Acronym
Acronym is a graphical representation of a

Power Spectral Density The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, ...

(PSD) of the vibratory signal) the highest instantaneous relative displacement experienced by the mass element of this SDOFs at any time during exposure to the vibration in question. Plot this value multiplied by the square of (2 π x natural frequency) against the natural frequency of the hypothetical system;
4. Repeat steps 2 and 3 for other values of the natural frequency. The resulting plot is called an ''Extreme

response spectrum A response spectrum is a plot of the peak or steady-state response (displacement, velocity or acceleration) of a series of oscillators of varying natural frequency, that are forced into motion by the same base vibration or shock. The resulting plo ...

''.

Note

Vibrations can damage a mechanical system as a result of several processes, among which are: * the exceeding of characteristic instantaneous stress limits (

yield stress In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and wi ...

, ultimate stress etc.) * the damage by fatigue following the application of a large number of cycles. ERS is used according to the first criterion. The second is considered with the '' fatigue damage spectrum'' (FDS).

References

* Lalanne, C., ''Mechanical Vibration and Shock Analysis. Volume 5: Specification Development'', Second Edition, ISTE - Wiley, 2009. * AFNOR, NF X50-144: Demonstration of resistance to environmental conditions, 2019 Mechanical vibrations