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The theory of sonics is a branch of continuum mechanics which describes the transmission of mechanical energy through vibrations.The birth of the theory of sonics [1] is the publication of the book A treatise on transmission of power by vibrations in 1918 by the Romanian scientist Gogu Constantinescu.
Experimentally measured vibration response spectrum as a function of the shaft's rotation speed (waterfall plot), the peak locations for each slice usually corresponding to the eigenfrequencies. In acoustical engineering
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.
Regarding the arbitrarily varying excitation p(t) as a superposition of a series of impulses: < ()then it is known from the linearity of system that the overall response can also be broken down into the superposition of a series of impulse-responses:
The whirling frequency of a symmetric cross section of a given length between two points is given by: = where: E = Young's modulus, I = second moment of area, m = mass of the shaft, L = length of the shaft between points.
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).
Abraham, R.; Marsden, J. E. (2008). Foundations of Mechanics: A Mathematical Exposition of Classical Mechanics with an Introduction to the Qualitative Theory of Dynamical Systems (2nd ed.).