Dynamics can be thought of as the kinetic behavior of an object. That is, if an object is moving, it is involved in a dynamic activity.
However, from an analytical point of view, moving objects can usually be divided into two classes:
Further, the relative magnitude of the motion or deformation needs to be considered as well. If the object is moving very slowly, it could still be considered a static problem for any arbitrarily short period of time.
A further refinement to the definition of dynamics would relate to the loading and motion. If the rate of loading is such that it is roughly equal to the object’s natural frequency, then the response will be dynamic. That is, the loading will interact with the system’s natural frequencies. At slow loading rates, the natural frequencies are not excited and the model can be considered static. In the dynamic range, the loading will excite certain natural frequencies which will change the response from a strictly static sense. At higher frequencies, the system will not have time to respond to the excitation, and the excitation will have little effect on the system.
The dynamic response of a structure is impacted by:
There are several types of problems that are analyzed with finite elements that are dynamic in nature.
Most common are a system’s natural frequencies. Any non-rigid system will have one or more natural vibration frequencies. A modal or natural frequency analysis (also known as normal modes or eigenvalue analysis) will find these frequencies and the corresponding mode shapes (eigenvectors).
Examples of such systems include structures (buildings, bridges, towers), bodies (support brackets, housings), and shafts.
The benefits of this type of analysis are:
The modal analysis will output:
If a system is known to be dynamic, a frequency (harmonic) response analysis will calculate the response of the system to a series of enforced sinusoidal loads or acceleration. If the load is assumed to continue indefinitely, the solution to these problems can be found in closed form, resulting in a series of static-like results at a series of excitation frequencies.
Examples of enforced sinusoidal loads (oscillatory excitation) include rotating machinery, unbalanced tires, and helicopter blades.
The benefits of this type of analysis are:
The frequency response analysis will output:
If the loading in not periodic, it may be necessary to load the model in the time domain. In this case, the model is solved at a series of time steps that trace the response of the system over time. A transient analysis does this, using the solution at each time step as the initial condition for the next time step.
Examples of structures subjected to transient events would be buildings, bridges, towers, and bodies like housings and support brackets.
The benefits of a transient response analysis are:
The transient response analysis will output:
If the actual excitation of a structure is unknown, but the loading can be roughly quantified as a power spectrum, a random (vibration) analysis can be done. A random analysis is run after a frequency response analysis, and the responses at the different frequencies are combined into a single result based on the relative magnitude of the spectrum at different frequencies. The result is a single set of results, incorporating the contributions of all the different excitation values.
Examples of random vibration include earthquake ground motion, ocean wave heights and frequencies, wind pressure fluctuations on aircraft and tall buildings, and acoustic excitation due to rocket and jet engine noise.
A response spectrum analysis is similar to a random analysis in that the actual loads are unknown. In a spectral response solution, the peak accelerations at different frequencies are specified instead of a power density. But like the random analysis, the results at different natural frequencies are combined to produce a single result.
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