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Reliable analysis of foundation vibrations is available for practicing engineers. Present techniques follow those based on an elastic half-space model. The frequency of maximum response and geometric damping is obtained from machine and foundation geometry and the soil shear modulus. Knowing the unbalanced machine forces and moments, amplitudes can also be obtained. Five case histories illustrate the accuracy of these techniques. Case one is for two V-12, 4000-hp engines; it compares a predicted rocking frequency of 342 rpm with measured frequencies of 339 and 341 rpm. Case two illustrates the validity of predicting rocking amplitudes for a four-cylinder horizontal compressor; the predicted rocking motion of 0.0042 in. compares well to the 0.003 in. actually measured. Case three describes the AMRAD radar tower; the predicted average rocking frequency of 7.5 Hz compares well with 6.3 Hz measured after construction. Agreement in the torsional mode is not as good. Case four illustrates the analysis of a large car shredder subjected to transient moments; using a phase-plane analysis the predicted rocking frequency is 7 Hz compared to a measured frequency of 7.6 Hz. Case five demonstrates the accuracy of a simple transient excitation test for obtaining the frequency and damping of a passive foundation slab.

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