Apparently I still need to learn how these blog posts work, I think they’re not supposed to have abstracts…
This post is a medium length (14 pages) exploration of the differences in results that occur when a lifting lug finite element model is analyzed using linear and nonlinear techniques. From the results presented it is shown:
- The ASME BPVC is unclear on which stress limits should be applied to a non-pressure retaining component using linear analysis techniques, and
- For the geometry considered, the rated load for the lug is significantly increased when nonlinear techniques are applied.
The post is written at a mild technical level. There are no equations, but an understanding of stress analysis is helpful. Detailed modeling procedures, such as the selection of mesh density, are outside of the scope of a “short” post on nonlinear analysis and are not provided. Sufficient graphical information and discussion is provided to allow interpretation of the results. The post ends with a discussion of the pros and cons of linear and nonlinear analysis techniques, framed in terms of the lug analysis and PMI’s past experience.
By Sean McGuffie
In engineering, the damping ratio (ζ) is a dimensionless measure describing how oscillations in a system decay after a disturbance. One way to evaluate the damping ratio is to excite the system and then use what is called the log decrement method to evaluate the damping. Figure 1 illustrates the log decrement method.
Unfortunately, real systems don’t always behave in a way that allows clear use of the log decrement. Figure 2 illustrates the motion of a tall (~80 m) exhaust stack that is excited and then allowed to vibrate freely.
The vibration signal has been filtered to remove all but the natural frequency (~0.54 Hz) of the stack. If the stack was viscously damped, we would expect to see an exponential decay in the motion and the log decrement method could be used to evaluate the damping ratio. If coulomb (friction) damping controlled, we would expect to see a linear decay in the motion with time. Looking at Figure 2, neither type of decay is evident.
In order to get a clearer measure of the damping, it is often useful to use a technique that is often used in the acoustical world. If the vibration amplitude is plotted on a logarithmic scale, it can be shown that:
ζ = 0.183/n Equation 1
Where: n = number of cycles required for the amplitude to drop by 10 dB (a factor of approximately 3.16).
The motion data in Figure 2 has been potted with a logarithmic scale in Figure 3.
There are two distinct regions of decay in this portion of the signal. A straight line passing through the first decay segment indicates that the signal would take approximately 12 cycles to decay by 10 dB. A line passing through the second decay segment indicates that the signal would take approximately 20 cycles to decay 10 dB. Using the Equation 1, the respective damping values would be 0.015 and 0.009. The decreasing damping ratio as a function of amplitude is a strong indication that the damping in the stack is coulomb or frictional rather than viscous.
By: Mike Porter