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Shock Response

August 9, 2016 By: James Kosloski

No, I am not talking about standing around with your mouth open.  In this post, I am going to talk about how you can use a Response Spectrum Analysis to analyze transient shock loads.  Transient shock loads can come in any form. However, three common shock forms that often need to be analyzed are: half sine pulse, saw-tooth pulse and trapezoid pulse, see Figure 1.

To analyze the response of a structure to shock loads, one can always run a transient analysis. However, transient analyses can often be costly and time consuming. An alternative approach is to use a response spectrum analysis. In part 1 of his 3-part blog on response spectrum analysis, Nick Veikos describes how a spectrum in the frequency domain can be obtained from a transient time history and then be used to get a quick estimate of the peak response. In many cases the spectrum may be supplied by some specification or authority. In other cases, however, you may be supplied an acceleration vs. time curve, as in Figure 1 (shown above), and need to generate your own spectrum input. The response spectrum transforms the transient load from the time domain to the frequency domain. Only the peak amplitude at each frequency is retained (phase information is lost). Once obtained, the response spectrum for a given transient load and a given damping ratio can be used for any model.

This method of manually generating a spectrum from a transient load can be tedious.  It requires the solution of the transient response for multiple single degree of freedom systems with different natural frequencies, capturing the peak response for each. Fortunately, some finite element codes, like ANSYS, have a built in method of performing these calculations and, given a transient displacement, can generate a response spectrum automatically.

In ANSYS, this is done using the RESP command. The RESP command needs the transient displacements, a list of frequencies and the damping, and it will generate a response spectrum as shown in Figure 2. Usually, transient impulse loads are given in the form of acceleration vs. time. To obtain the required transient displacements, we can simply apply the acceleration curve to a unit point mass.


Figure 2 - Response Spectrum from Saw Tooth Pulse


The response spectrum can be simplified by enveloping the actual curves (this is a conservative approach) as shown in Figure 3.
 

 

Figure 3 - Envelope Spectrum


While this tool is very convenient, it requires a few steps to set up, so CAE Associates has created a series of input files that will generate the response spectrum for the three common types of shock impulses shown in Figure 1:

Calcresp_halfsin.inp – Half-sine
Calcresp_saw.inp - Sawtooth
Calcresp_trap.inp - Trapezoidal

These input files are available to download from our Resource Library.  Make sure to edit the file to set up the inputs, which describe the impulse load you have and the damping level you require. Then, run the file in ANSYS and it will generate a CSV file output of the response spectrum (Frequency vs. Acceleration).  The user should use their judgement to create an envelope from this data before using it in their response spectrum analysis.

I hope your found this post helpful, and not too “shocking”.  I welcome your comments!