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Natural frequency, measured in terms of eigenfrequency, is the rate at which an oscillatory system tends to oscillate in the absence of disturbance. A foundational example pertains to simple harmonic oscillators, such as an idealized spring with no energy loss wherein the system exhibits constant-amplitude oscillations with a constant frequency.
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.
The previous equation can be written also as the following: = where =, in which represents the natural frequency, M and K are the real positive symmetric mass and stiffness matrices respectively.
In the most popular version of the Kuramoto model, each of the oscillators is considered to have its own intrinsic natural frequency, and each is coupled equally to all other oscillators. Surprisingly, this fully nonlinear model can be solved exactly in the limit of infinite oscillators, N → ∞; [ 5 ] alternatively, using self-consistency ...
These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions.
If a structure's natural frequency matches an earthquake's frequency [citation needed], the structure may continue to resonate and experience structural damage. Modal analysis is also important in structures such as bridges where the engineer should attempt to keep the natural frequencies away from the frequencies of people walking on the bridge.
The Minnaert resonance [1] [2] [3] is a phenomenon associated with a gas bubble pulsating at its natural frequency in a liquid, neglecting the effects of surface tension and viscous attenuation. It is the frequency of the sound made by a drop of water from a tap falling in water underneath, trapping a bubble of air as it falls.
The natural frequency of the very simple mechanical system consisting of a weight suspended by a spring is: = where m is the mass and k is the spring constant.For a given mass, stiffening the system (increasing ) increases its natural frequency, which is a general characteristic of vibrating mechanical systems.