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Vibrations are a common occurrence in oil and gas activities that can affect operations, planning, facility design, and interpretation of results. Vibration is common in drillstrings, on platforms, wherever large engines are operating, in seismic operations, and many other aspects of oil and gas. Understanding vibration theory and the mathematics of vibrations are important to successful operations. A refresher ondifferential calculus can come in handy as well. The fundamental theories of vibration are not new. Indeed, Saint-Venant[1] published his theory on the vibrations of rods in 1867, and Love[2] published an entire treatise on vibration theory in 1926. The mathematics of vibration theory involves infinite series, complex functions, and Fourier integral transforms, and its physics involves Newtonian mechanics and stress analyses. Until recently, except under relatively simple conditions, the complexity of such mathematics had restrained the application of vibration theory to solving simple common problems. Now, however, state-of-the-art computers can perform these complex calculations in a reasonable time frame, making possible a wave of new studies.
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