Power spectrum and amplification function


ApplicationPLAXIS 2D
Issue status✔ Solved
First Affected VersionPLAXIS 2D 2010.01
Found in VersionPLAXIS 2D 2010.01
Fixed and Released in VersionPLAXIS 2D 2012.00
Issue #16639
Date created11 April 2013
Date modified24 October 2016

Problem description

In Plaxis Output it is possible to see the results of a dynamics analysis both in time domain (time series) and in frequency domain (spectrum). Additionally, Plaxis Output offers the possibility to make an amplification function in frequency domain defined as the ratio between the spectra of two points. These two points are referred to as “Top” and “Bottom” as these are typically chosen on ground surface (Top) and at bedrock level (Bottom). This means that the amplification function shows for every frequency the amplification of response between Top and Bottom.

Power spectra: PLAXIS Output 2010

However, in Plaxis Output 2010 the spectra shown are normalized to the peak value calculated. This results in a spectrum with dimensionless values along the vertical axis and a peak value of 1. Unfortunately this normalization prevents the user from seeing the real peak value of the spectrum and therefore starting from Plaxis Output 2011 the spectra are no longer normalized so that the real peak value can be obtained and the vertical axis has the dimension of the quantity for which a spectrum was made. For instance, if a spectrum is made from an acceleration-time history, the spectrum will be in acceleration-frequency for Plaxis Output 2011 and later.

Amplification function: PLAXIS Output 2010/2011

In both Plaxis Output 2010 and Plaxis Output 2011 the amplification function presented is unfortunately not the intended amplification function defined as mentioned above, but just the power spectrum of the Top point.

Solution

Starting from PLAXIS 2D 2011’s Output the spectra are no longer normalized so that the real peak value can be obtained and the vertical axis has the dimension of the quantity for which a spectrum was made.

The amplification function is fixed since PLAXIS 2D 2012’s Output where the amplification function really is the ratio between the spectra of the (user-defined) points Top and Bottom.