Vibration Detection by a Quartz Oscillator

Yousef, Y L; Sultan, Farooq

doi:10.1063/1.1741598

Cited by 7 publications

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“…Because the capacity is inversely proportional to the interelectrode separation, linear detection is obtained only when the dynamic displacements are small compared to the gap setting. A second detection method has been described byYousef and Sultan (1949) and subsequently used byKamel (1953) for specimens vibrating either in torsion or flexure at~100 Hz. This method employs a slightly detuned single stage 6-MHz quartz crystal oscillator.…”

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Anelastic Relaxation in Crystalline Solids

1972

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We are espe cially grateful for the support of much of the research leading to this book, as well as partial support of the writing itself, by the U. S. Atom ic Energy Commission. We thank Miss Maureen Weaver for her skill ful typing of a substantial fraction of the manuscript. Finally, we wish to express our deepest gratitude to our wives for their encouragement and understanding over the several years during which this book was being written.XV Dielectric relaxation has been the subject of a recent book by Daniel (1967). * It should be remembered in what follows that the terminology "force," "mass," and "displacement" is symbolic and would actually become "torque," "moment of inertia," and "angle of twist" in the case of the torsion pendulum. * Actually, an exponential decay with time is a direct consequence of linearity. De parture from exponential decay indicates that the material is not behaving anelastically, in that the internal friction is a function of strain amplitude. t These quantities are now total energies rather than energies per unit volume. 40 2 THE BOLTZMANN SUPERPOSITION PRINCIPLE aid of the Boltzmann principle. Although this is a major step forward, it does not meet all the requirements of a complete formal theory. Since a response function only describes the behavior of a material under given experimental conditions, the use of such a function to define the anelasticproperties of a solid is not a completely satisfactory one. We may suspect that there is a more basic description of anelastic behavior in terms of which all of the response functions can be expressed. It will become apparent in the next two chapters that such a description is possible, and involves the concept of a relaxation spectrum. PROBLEMS 2-1. Verify the equivalence of Eqs. (2.2-1) and (2.2-2). 2-2. Show that for A <^1 , the following relation exists between the normalized creep function ip(t) and the normalized stress relaxation function ( 0Combine this result with Problem 1-2, to show that l/A/(0=/(*) +°(zl2) where 0(zl2) means terms of order A"1.General References . "Mathematical Structure of the Theories of Viscoelasticity." Her mann, Paris.

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