SignalProcessing/ResponseSpectrum - Maple Help

SignalProcessing

 ResponseSpectrum
 plot the response spectrum of a signal

 Calling Sequence ResponseSpectrum(data, timeStep, dT, maxT) ResponseSpectrum(dataT, dataA, timeStep, dT, maxT)

Parameters

 data - rtable(numeric) : 2-D rtable where column 1 is time and column 2 is acceleration for the time-acceleration history dataT, dataA - rtable(numeric) : 1-D rtables containing, respectively, the time and acceleration for the time-acceleration history timeStep - numeric : positive time step of input time-acceleration data and output velocity/displacement-time history dT - numeric : positive time step of period in output spectrum maxT - numeric : positive maximum period in output spectrum

Options

 • 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.

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$
 > $\mathrm{datafile}≔\mathrm{FileTools}:-\mathrm{JoinPath}\left(\left[\mathrm{kernelopts}\left('\mathrm{datadir}'\right),"datasets","el-centro_NS.txt"\right]\right):$
 > $\mathrm{data}≔\mathrm{ImportMatrix}\left(\mathrm{datafile},'\mathrm{delimiter}'=""\right):$
 > $\mathrm{results}≔\mathrm{ResponseSpectrum}\left(\mathrm{data},0.02,0.01,5,'\mathrm{\zeta }'=0.02,'\mathrm{\beta }'=0.25,'\mathrm{\gamma }'=0.5\right):$

The primary content of the record returned by ResponseSpectrum are a number of charts:

 > $\mathrm{results}:-\mathrm{absoluteaccelerationplot}$
 > $\mathrm{results}:-\mathrm{relativevelocityplot}$
 > $\mathrm{results}:-\mathrm{relativedisplacementplot}$
 > $\mathrm{results}:-\mathrm{pseudovelocityplot}$
 > $\mathrm{results}:-\mathrm{pseudoaccelerationplot}$
 > $\mathrm{results}:-\mathrm{displacementplot}$
 > $\mathrm{results}:-\mathrm{velocityplot}$
 > $\mathrm{results}:-\mathrm{accelerationplot}$

Additional raw data used to generate these plots are available in other slots of the record.

 > $\mathrm{results}:-\mathrm{perioddata}$
 > $\mathrm{results}:-\mathrm{absoluteaccelerationdata}$
 > $\mathrm{results}:-\mathrm{relativevelocitydata}$
 > $\mathrm{results}:-\mathrm{relativedisplacementdata}$
 > $\mathrm{results}:-\mathrm{pseudovelocitydata}$
 > $\mathrm{results}:-\mathrm{pseudoaccelerationdata}$
 > $\mathrm{results}:-\mathrm{velocitydata}$
 > $\mathrm{results}:-\mathrm{displacementdata}$

References

 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

Compatibility

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