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notes_10 - ME 563 Mechanical Vibrations ME 563 MECHANICAL...

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ME 563 Mechanical Vibrations Fall 2010 1-1 ME 563 MECHANICAL VIBRATIONS Fall 2010 Potter MWF 4:30 p.m.-5:20 p.m. Instructor: Prof. D. E. Adams Room: ME 361 Email: deadams@purdue.edu Phone: 496-6033
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ME 563 Mechanical Vibrations Fall 2010 1-2 1 Introduction to Mechanical Vibrations 1.1 Bad vibrations, good vibrations, and the role of analysis Vibrations are oscillations in mechanical dynamic systems. Although any system can oscillate when it is forced to do so externally, the term “vibration” in mechanical engineering is often reserved for systems that can oscillate freely without applied forces. Sometimes these vibrations cause minor or serious performance or safety problems in engineered systems. For instance, when an aircraft wing vibrates excessively, passengers in the aircraft become uncomfortable especially when the frequencies of vibration correspond to natural frequencies of the human body and organs. In fact, it is well known that the resonant frequency of the human intestinal tract (approx. 4-8 Hz) should be avoided at all costs when designing high performance aircraft and reusable launch vehicles because sustained exposure can cause serious internal trauma (Leatherwood and Dempsey, 1976 NASA TN D-8188). If an aircraft wing vibrates at large amplitudes for an extended period of time, the wing will eventually experience a fatigue failure of some kind, which would potentially cause the aircraft to crash resulting in injuries and/or fatalities. Wing vibrations of this type are usually associated with the wide variety of flutter phenomena brought on by fluid-structure interactions. The most famous engineering disaster of all time was the Tacoma Narrows Bridge disaster in 1940 (see Figure 1.1 below). It failed due to the same type of self-excited vibration behavior that occurs in aircraft wings. Figure 1.1: (left) View of Tacoma Narrows Bridge along deck; (right) view of torsional vibration In reading books and technical papers on vibration including the previous paragraph, engineering students are usually left with the impression that all vibrations are detrimental because most publicized work discusses vibration reduction in one form or another. But
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ME 563 Mechanical Vibrations Fall 2010 1-3 vibrations can also be beneficial. For instance, many different types of mining operations rely on sifting vibrations through which different sized particles are sorted using vibrations. In nature, vibrations are also used by all kinds of different species in their daily lives. Orb web spiders, for example, use vibrations in their webs to detect the presence of flies and other insects as they struggle after being captured in the web for food. The reason that mechanical systems vibrate freely is because energy is exchanged between the system’s inertial (masses) elements and elastic (springs) elements. Free vibrations usually cease after a certain length of time because damping elements in systems dissipate energy as it is converted back-and-forth between kinetic energy and
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notes_10 - ME 563 Mechanical Vibrations ME 563 MECHANICAL...

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