By A.J Pretlove (Auth.)
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Extra info for Basic Mechanical Vibrations
It will also be seen that for small damping the polar response diagram closely approximates a circle. Indeed, the theory for hysteretic damping shows that the diagram is a circle passing through the origin with a diameter coincident with the negative y-axis. 1 for the machine system which has been used to illustrate all the examples in this chapter. 6. This starts at time t = 0 and builds up to a peak of 1000 N at t = 1 after which the force is zero. The displacement response is required for three seconds from t = 0.
For real roots no vibration quantities have any meaning and so after printing the roots the program stops. , etc. The information gained is then plotted on polar graph paper to form a Polar or Vector Response Diagram. 4) provided that the damping ratio is small. 18) for a range of frequencies. It also converts these values to rectangular coordinates x and y so that the polar diagram can be plotted on ordinary graph paper. If the reader is prepared to venture into computer graphics the program may easily be extended to display the polar diagram.
The continuous forcing function may also contain a random element such as in the excitation of tall buildings by wind. The calculation of the response in such cases is also based on Fourier analysis but is beyond the scope of this book. However, see Further reading, ref. 3, for details of the appropriate theory. 6 Transient forcing The previous section has dealt with steady state vibration forcing. Engineers are also concerned occasionally with forcing in which the transient response is important, such as shock loading and abrupt changes in continuous loadings.