zeta : numeric : Non-negative damping ratio, with default 0.05.

beta : numeric : First non-negative constant which determines the discretization scheme for the equation of motion, with default 0.25.

gamma : numeric : Second non-negative constant which determines the discretization scheme for the equation of motion, with default 0.5.

periodfrequency : identical(period, frequency) : One of the names period (default) or frequency.

xscale : identical(log, linear) : One of the names log or linear (default).

yscale : identical(log, linear) : One of the names log or linear (default).

output : The type of output. The supported options are:

absoluteaccelerationdata: Vector, of datatype float[8], containing the absolute acceleration data.

absoluteaccelerationplot: Plot of the absolute acceleration versus period.

accelerationdata: Vector, of datatype float[8], containing the acceleration data.

accelerationplot: Plot of the acceleration versus time.

displacementdata: Vector, of datatype float[8], containing the displacement data.

displacementplot: Plot of the displacement versus time.

perioddata: Vector, of datatype float[8], containing the period data.

pseudoaccelerationdata: Vector, of datatype float[8], containing the pseudospectral acceleration data.

pseudoaccelerationplot: Plot of the pseudospectral acceleration versus period.

pseudovelocitydata: Vector, of datatype float[8], containing the pseudospectral velocity data.

pseudovelocityplot: Plot of the pseudospectral velocity versus period.

relativedisplacementdata: Vector, of datatype float[8], containing the relative displacement response spectrum data.

relativedisplacementplot: Plot of the relative displacement response spectrum versus period.

relativevelocitydata: Vector, of datatype float[8], containing the relative velocity response spectrum data.

relativevelocityplot: Plot of the relative velocity response spectrum versus period.

timedata: float[8] Vector of the time data.

velocitydata: Vector, of datatype float[8], containing the velocity data.

velocityplot: Plot of the velocity versus time.

record: Returns a record with the previous options. This is the default.

list of any of the above options: Returns an expression sequence with the corresponding outputs, in the same order.

A response spectrum is a plot of how a structure or system responds to varying frequencies of ground motion or input excitation. It is commonly used in structural engineering and earthquake engineering to assess the potential response of a structure to seismic events.

A response spectrum is generated by calculating the maximum response of a structure to different frequencies of ground motion. An acceleration time history is used to perturb a single degree of freedom harmonic oscillator. Typically period is plotted on the $x$-axis against acceleration, velocity or position on the $y$-axis.

This procedure computes the response spectrum of an input accelerogram (time-acceleration history). It numerically solves the differential equation for a harmonic oscillator with one degree of freedom.

The parameters $\mathrm{\beta }$, $\mathrm{\gamma }$, and $\mathrm{\zeta }$ are the same as those described in the Newmark-beta Method.

$\mathrm{with}\left(\mathrm{SignalProcessing}\right)\:$

$\mathrm{datafile}≔\mathrm{FileTools}:-\mathrm{JoinPath}\left(\left[\mathrm{kernelopts}\left('\mathrm{datadir}'\right)\,''datasets''\,''el-centro\_NS.txt''\right]\right)\:$

$\mathrm{data}≔\mathrm{ImportMatrix}\left(\mathrm{datafile}\,'\mathrm{delimiter}'=''''\right)\:$

$\mathrm{results}≔\mathrm{ResponseSpectrum}\left(\mathrm{data}\,0.02\,0.01\,5\,'\mathrm{\zeta }'=0.02\,'\mathrm{\beta }'=0.25\,'\mathrm{\gamma }'=0.5\right)\:$

$\mathrm{results}:-\mathrm{absoluteaccelerationplot}$

$\mathrm{results}:-\mathrm{relativevelocityplot}$

$\mathrm{results}:-\mathrm{relativedisplacementplot}$

$\mathrm{results}:-\mathrm{pseudovelocityplot}$

$\mathrm{results}:-\mathrm{pseudoaccelerationplot}$

$\mathrm{results}:-\mathrm{displacementplot}$

$\mathrm{results}:-\mathrm{velocityplot}$

$\mathrm{results}:-\mathrm{accelerationplot}$

$\mathrm{results}:-\mathrm{perioddata}$

$\mathrm{results}:-\mathrm{absoluteaccelerationdata}$

$\mathrm{results}:-\mathrm{relativevelocitydata}$

$\mathrm{results}:-\mathrm{relativedisplacementdata}$

$\mathrm{results}:-\mathrm{pseudovelocitydata}$

$\mathrm{results}:-\mathrm{pseudoaccelerationdata}$

$\mathrm{results}:-\mathrm{velocitydata}$

$\mathrm{results}:-\mathrm{displacementdata}$

Aeran, Ashish and Hirpa G. Lemu. "Time Integration Schemes in Dynamic Problems: Effect of Damping on Numerical Stability and Accuracy". International Workshop of Advanced Manufacturing and Automation (IWAMA), pp. 213-220. Atlantis Press, 2016.

"Newmark-beta Method", Wikipedia. https://en.wikipedia.org/wiki/Newmark-beta_method

"Response Spectrum", Wikipedia. https://en.wikipedia.org/wiki/Response_spectrum

The SignalProcessing[ResponseSpectrum] command was introduced in Maple 2024.

For more information on Maple 2024 changes, see Updates in Maple 2024.