Simulating Shock and Vibrations in Ansys - Harmonic Analysis
Harmonic response analysis is a crucial tool available in Workbench, alongside all major analysis types. This method involves evaluating a structure's response to sinusoidal input, akin to shaking a structure and observing its behavior.
Applications of Harmonic Response Analysis
- Ocean Waves: Offshore structures, such as wind turbines, must account for ocean wave impacts during design.
- Wind Loads: Critical for aircraft design, particularly for wings, to understand behavior under sinusoidal conditions.
- Civil Structures: Large structures, such as bridges, benefit from this analysis to prevent failures like the Tacoma Narrows Bridge collapse.
Key Considerations
When starting a new analysis, understanding the underlying assumptions is vital:
- No nonlinearities, limiting material selection (e.g., no plasticity or hyper-elastic models).
- Exclusion of frictional contacts.
- Initial transient effects are ignored, focusing on steady-state sinusoidal responses.
Theoretical Background
ANSYS solves Newton's law using matrix manipulations, resulting in an equation where the force vector equals the stiffness matrix times the displacement vector. This equation is similar to that in static structural analysis, but with frequency-dependent terms.
Methods of Harmonic Response Analysis
- Full Method: Requires a fine mesh with many nodes, potentially time-consuming.
- Modal Superposition Method: Depends on the number of modes retained, allowing for faster simulations with fewer modes.
Example Model
A beam fixed at both ends demonstrates different modes:
- First mode: Half sine wave
- Second mode: Full sine wave
- Third mode: Three halves sine wave
This frequency domain-based analysis uses Fourier analysis to decompose signals into sine and cosine components.
Frequency Response Function
By inserting the frequency response function into the Workbench model, you can analyze the response to an input signal. For instance, with a 1 meter per second loading on a beam structure, resonance occurs at:
- 51.6 Hertz
- 266 Hertz
The transmissibility factor, defined as output divided by input, indicates a transmission of 17 times the input signal at 51.6 Hertz and 4 times at 266 Hertz.
Conclusion
By examining the string of frequencies associated with resonances, you can input frequency and phase to obtain detailed graphs. Thank you, Pat, for your patience. I'll now turn it back over to you to discuss the response spectrum.
Harmonic response analysis is available in Workbench, one of the major analysis types. To use it, simply drag and drop harmonic response into the project schematic. This analysis method is akin to shaking a structure and evaluating its response, with a sinusoidal input shaking.
It can be used in nature, such as ocean waves incident on an offshore structure like a wind turbine, or in designing aircraft, particularly the wings, to understand how they behave under sinusoidal conditions.
It's also applicable to large civil structures, such as the Tacoma Narrows Bridge, which collapsed due to wind loading. When starting a new analysis, it's important to understand the underlying assumptions.
In harmonic response, there are no nonlinearities, so plasticity models or hyper-elastic models cannot be used, and frictional contacts must be excluded. Additionally, initial transient effects are ignored, with results based on the amplitude of the steady state.
ANSYS solves Newton's law in the form of a force vector being a stiffness matrix times a displacement vector, with the terms being functions of frequency. There are two methods for harmonic response: the full method and the modal superposition method.
The full method has as many terms as there are degrees of freedom in the matrix, requiring a fine mesh and taking a long time to solve. The modal superposition method depends on the number of modes kept, with only a few modes sometimes providing 90% of the result, making for faster simulations.
In this example, a beam fixed at both ends was used to demonstrate the modes associated with the structure. The frequency response function, obtained from a one-meter-per-second loading on the beam structure, shows resonance at 51.6 Hertz, 200 Hertz, and 66 Hertz.
The transmission of the input signal at these frequencies is 17 times and four times, respectively. Thank you for your patience. I will now turn it back over to you to talk about response spectrum.
