Simulating Shock and Vibrations in Ansys - Response Spectrum
Introduction to Response Spectrum Analysis
In this session, we will discuss the concept of response spectrum analysis. This method is used to perform a fast analysis to determine the maximum results due to dynamic loads such as shocks or earthquakes. The results obtained can include deflections, velocities, accelerations, forces, stresses, and strains. Response spectrum analysis is faster than traditional structural analysis.
What is a Response Spectrum?
A response spectrum is essentially a collection of maximum results produced by a transient structural analysis of an array of single degree of freedom oscillators. These results are applied to natural frequencies to scale them. Response spectrums are readily available or can be created manually.
As an input, the response spectrum can quickly predict the response of a system under dynamic loading conditions. It is important to note that the damping is built into the response spectrum.
Developing a Response Spectrum
To develop a response spectrum, consider a system of single degree of freedom oscillators with varying masses and natural frequencies. Define a load, perform a transient analysis, and obtain the response for each oscillator. The largest magnitude of response from each oscillator is plotted against its natural frequency to produce the response spectrum.
Response spectrums can be converted between forms using simple equations, considering pseudo displacement, pseudo velocity, and pseudo acceleration.
Demonstration and Examples
Example 1: Transient Structural Analysis
In this example, we have a transient structural analysis setup with springs and varying masses to produce different natural frequencies. An acceleration impulse is defined, and the analysis is run to derive the response spectrum.
By applying the response spectrum in terms of accelerations, we can compare deflection results with those from a transient solution, noting that the response spectrum method is more efficient.
Example 2: Simple Bar Model
A simple bar model is constrained at one end, and a modal analysis is performed. The frequencies are closely spaced in groups of two, with orthogonal mode shapes. This symmetry results in closely spaced frequencies, which is crucial for response spectrum analysis.
Performing a Response Spectrum Analysis
- Access the analysis pulldown menu and choose response spectrum.
- Indicate the modal analysis to be used.
- Visit the analysis settings and use all modes by default.
- Select the spectrum type (single or multiple points) and mode combination type (SRSS, complete quadratic combination, or Rosenbluth method).
- Calculate velocity and acceleration for comprehensive results.
- Define the response spectrum and its direction of application.
- Run the analysis for quick results.
Results and Observations
The results include deflections, velocities, accelerations, forces, stresses, and strains. The mode combination methods affect how damping is considered in the analysis:
- SRSS Method: Does not incorporate additional damping.
- Complete Quadratic Combination: Requires additional damping definition.
- Rosenbluth Method: Handles closely spaced frequencies effectively.
Conclusion
Response spectrum analysis is a powerful tool for predicting system responses to dynamic loads. It is efficient and provides valuable insights into maximum response characteristics. We look forward to further discussions on related topics, such as random vibration, with Cameron.
I am going to talk about the response spectrum. So, let's take a look at it. Why would I perform a response spectrum analysis? I want to perform a fast analysis, and I want to learn what the maximum results would be as a result of some sort of shock, earthquake, or other dynamic load.
The kinds of results I can obtain are deflections, velocities, accelerations, forces, stresses, and strains. It's faster than structural analysis, but the question becomes how. What is a response spectrum? Well, it really is a response.
It's really a result that we're applying to our natural frequencies to scale them. There are response spectra readily available, and we can also create these ourselves.
As an output, a response spectrum is a collection of maximum results produced by a transient structural analysis of an array of single degree of freedom oscillators. It can be used as an input to quickly predict the response of a system to a dynamic load.
When we develop a response spectrum, the damping is built into it. By simulating a single degree of freedom system, we can directly predict its response.
If we have a collection of single degree of freedom oscillators and a load that we want to learn what the response spectrum would look like, we would define our load, perform a transient analysis, and get our response at each one of these different single degree of freedom systems.
We pick out the largest magnitude of our response from each one of these oscillators and plot that versus the frequency, the natural frequency of that oscillator. And what we produce is a response spectrum. We can convert a response spectrum from one form to another by using simple equations.
Whenever we are making a response spectrum, we're thinking in terms of pseudo displacement, pseudo velocity, and pseudo acceleration. Let's take a look at a couple of demonstrations. I'm going to discuss the number of modes, spectrum type, modal combination type, output controls, and results.
I'm going to use this example of a transient structural analysis with different natural frequencies. We define a load, such as an acceleration impulse, and run the analysis. Each oscillator has its own type of plotted data, and we can derive the response spectrum from that.
If we perform a response spectrum analysis on the same geometry and apply our response spectrum to it in terms of accelerations, we can see what our deflection results would be. Let's look at a different example. This is a simple bar with closely spaced frequencies.
When we have symmetric geometry like this, we will get closely spaced frequencies. This becomes important whenever we want to perform a response spectrum analysis. To perform a response spectrum analysis, we go to the analysis pulldown menu and choose response spectrum.
We indicate what modal analysis we're using, visit the analysis settings, and choose the spectrum type and mode combination type. We calculate velocity and acceleration, and define the response spectrum.
We run the analysis, and can get results such as deflections, velocities, accelerations, forces, stresses, and strains.
We need to have modal analysis results as input, and the response spectrum is applied through the supports, defined either as displacement versus frequency, velocity versus frequency, or acceleration versus frequency.
If we want to consider added damping in our response spectrum analysis, we can use the complete quadratic combination method, which requires that we define additional damping. The Rosenbluth method is another method that can consider damping.
The results we obtain are deflections, velocities, accelerations, forces, stresses, and strains, reflecting back what our response spectrum input was on our new geometry. I'm looking forward to hearing more about random vibration.
