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The example shows how the Rayleigh's quotient is capable of getting an accurate estimation of the lowest natural frequency. The practice of using the static displacement vector as a trial vector is valid as the static displacement vector tends to resemble the lowest vibration mode.
where m is the (equivalent) mass, x stands for the amplitude of vibration, t for time, c for the viscous damping coefficient, and k for the stiffness of the system or structure.
Vibration (from Latin vibrāre 'to shake') is a mechanical phenomenon whereby oscillations occur about an equilibrium point.Vibration may be deterministic if the oscillations can be characterised precisely (e.g. the periodic motion of a pendulum), or random if the oscillations can only be analysed statistically (e.g. the movement of a tire on a gravel road).
The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration.It is common to use the finite element method (FEM) to perform this analysis because, like other calculations using the FEM, the object being analyzed can have arbitrary shape and the results of the calculations are acceptable.
In structural engineering, modal analysis uses the overall mass and stiffness of a structure to find the various periods at which it will naturally resonate.These periods of vibration are very important to note in earthquake engineering, as it is imperative that a building's natural frequency does not match the frequency of expected earthquakes in the region in which the building is to be ...
Use of the vibration-fatigue methods is well-suited, as structural analysis is studied in the frequency-domain. Common practice in the automotive industry is the use of accelerated vibration tests. During the test, a part or a product is exposed to vibration, that are in correlation with those expected during the service-life of the product. To ...
Vibration mode of a clamped square plate. The vibration of plates is a special case of the more general problem of mechanical vibrations.The equations governing the motion of plates are simpler than those for general three-dimensional objects because one of the dimensions of a plate is much smaller than the other two.
Pogo oscillation is a self-excited vibration in liquid-propellant rocket engines caused by combustion instability. [1] The unstable combustion results in variations of engine thrust, causing variations of acceleration on the vehicle's flexible structure, which in turn cause variations in propellant pressure and flow rate, closing the self-excitation cycle.