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00:00:00 – 00:11:13
The video delves into the concept and application of random vibration analysis, a critical aspect of structural engineering used to understand how structures respond to unpredictable vibration loads. Key examples include vibrations experienced by vehicles, aircraft, and offshore structures. The theoretical foundation relies on power spectrum density (PSD) and the mode superposition method to statistically analyze the responses in terms of displacement and stress.
A practical example using ANSYS Mechanical is provided, focusing on a printed circuit board (PCB) subjected to truck-induced vibrations. The procedure involves linking modal solutions to random vibration setups and using mesh controls, fixed supports, and frequency range settings to run modal analysis on the PCB, with results indicating natural frequencies between 90 to 2200 hertz for the first 20 modes. The analysis scopes Z-direction deformation using one sigma and three sigma scale factors to compare deformation probabilities, with significant probability metrics established for deformation thresholds.
Concluding insights highlight that response vibration analysis is linear, grounded in the mode superposition method, and yields statistically significant output responses. The importance of understanding how average power distributes by frequency at resonant points is emphasized, with practical use cases urging further engagement with the platform for more in-depth learning.
00:00:00
In this part of the video, the presenter introduces random vibration analysis, important for understanding how structures respond to vibration loads that are random in nature. Examples include loads on an aircraft during flight, trucks on rough roads, and wave impacts on offshore structures. The video explains that vibrations in vehicles, which combine various frequencies, are not deterministic and require a statistical approach to evaluate the response. The analysis involves capturing the frequency content and statistical aspects of vibrations, termed power spectrum density (PSD). Using a mode superposition method, which involves input from linear natural frequency analysis and PSD curves, the analysis calculates the root mean square responses of displacements and stresses due to constant random vibrations over time.
00:03:00
In this part of the video, the focus is on performing a random vibration analysis using ANSYS Mechanical. The example centers on a printed circuit board (PCB) subjected to random vibrations due to transportation in a truck, with the objective of calculating the probability that the PCB’s out-of-plane deformation does not exceed 3 millimeters. The analysis considers input power spectrum density (PSD) from road conditions to understand the output responses such as displacement and stress. The workflow involves setting up a mode superposition analysis, including both modal and random vibration systems. The initial steps include opening the workbench project file, linking modal solutions to random vibration setups, and noting material assignments within the mechanical setup.
00:06:00
In this part of the video, the mesh controls are set to ‘linear’, with body sizing and sweep method strategically scoped to the main board for efficiency. Fixed supports are added to the two holes at opposite ends of the board before running the modal analysis, where 20 modes of vibration are requested with default frequency range settings. The results show natural frequencies of the PCB ranging from 90 to 2200 hertz for the first 20 modes.
A PSDG (Power Spectral Density Graph) acceleration is then inserted, scoped to all supports, and set to the z-axis to analyze the probability of a component deforming in that direction and potentially hitting a neighboring PCB. The g acceleration data is defined at different values for varying hertz levels.
The random vibration analysis is prepared and solved, and the Z-direction deformation is scoped to the tallest component on the PCB. Results are set with scale factors of one sigma and three sigma for comparison. A response PSD tool is then inserted, scoped to a vertex on the PCB board, to extract the Z component of displacement.
00:09:00
In this part of the video, the speaker evaluates the results by examining the one sigma and three sigma directional deformation results for a PCB component. There is a 68.3% probability that the deformation will be below 0.98 millimeters for one sigma, and a 99.7% probability that it will be below 2.96 millimeters for three sigma. The response PSD provides information on where the average power is distributed by frequency, with peak g acceleration response at resonant frequencies. The segment concludes the demo by summarizing that response vibration is a linear analysis based on the mode superposition method, requiring a modal analysis to extract natural frequencies and mode shapes. The excitation is in the form of power spectral density (PSD), and the output responses are statistical in nature. The video ends with a call to action to share, comment, subscribe, and visit a website for more courses.