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Extra resources for Applied structural and mechanical vibrations : theory and methods

Sample text

By contrast, it is also a fact that acceleration-sensitive transducers (accelerometers) are often preferred in applications because of their versatility – where by this term we mean a number of desirable properties such as small physical dimensions, wide frequency and dynamic ranges, easy commercial availability, and so on. However, in spite of the fact that all these considerations must be taken into account when making a choice, the primary factors to be considered are, not surprisingly, the nature of the problem at hand and the final scope of the investigation.

3). Physically, the two original waves remain nearly in phase for a certain time and reinforce each other; after a while, however, the crests of the first wave correspond to the troughs of the other and they practically cancel out. 6). 0). 3. Maximum amplitude occurs when ω t = nπ (n = 0, 1, 2, …), that is, every π ω seconds. Therefore, the frequency of the beats is ω π = ν 2 − ν1, equal to the frequency difference between the two original signals. When the signals have unequal amplitudes (say, A and B), the total amplitude does not become zero but varies between A + B and |A − B|.

7 – sometimes called the phasor representation of x(t) – is the temporary replacement of a real physical quantity by a complex number for purposes of calculation, with the understanding that only the real part of the phasor has physical significance. 9 is assigned a physical meaning. In using phasors, however, some care must be exercised when dealing 6 Applied structural and mechanical vibrations: Theory and methods with the energy associated with the oscillatory motion. ), in fact, depend on the square of vibration amplitudes, and since Re(x 2) ≠ [Re(x)]2 we need to take the real part first and then square to find the energy.

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