TORSIONAL VIBRATION OF DISSIMILAR MATERIALS CONTAINING A CYLINDRICAL CRACK.
Item
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Title
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TORSIONAL VIBRATION OF DISSIMILAR MATERIALS CONTAINING A CYLINDRICAL CRACK.
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Identifier
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AAI8205752
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identifier
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8205752
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Creator
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BANDYOPADHYAY, KAMAL KANTI.
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Contributor
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Jacques E. Benveniste | David H. Cheng
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Date
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1982
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Language
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English
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Publisher
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City University of New York.
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Subject
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Engineering, Civil
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Abstract
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This dissertation studies the torsional vibration of two cylinders of different elastic materials. The two cylindrical media are assumed to be perfectly bonded along their entire contact surface except for a cylindrical crack of finite length near the boundary surface. The time-dependent torsional load is applied on the free surface of the inner cylinder. Both the steady-state and transient vibrations are considered, and the corresponding axisymmetric wave equations are solved separately. The determination of the stress and displacement fields is reduced to the solution of Fredholm integral equations of the second kind in the physical complex plane for the steady-state vibration, and in the Laplace domain for the transient case. The local dynamic stress fields in the vicinity of the crack tip are determined in elementary closed form, and are observed to have square-root singularity like other crack problems in linear elastic fracture mechanics. To this end, the singularity parameter, k(,3), defined as the dynamic stress-intensity factor for the torsional mode (tearing) and known to control the fracture behavior of structural components undergoing torsional oscillations, is calculated for both cases of vibration by solving the Fredholm equations numerically. The numerical solution involves computer programming with complex arithmetic for the steady-state vibration, and numerical inversion of Laplace transform for the transient condition. The results indicate a dynamic amplification of the stress-intensity factor for both cases. For a harmonic input, k(,3) increases with the frequency, reaches a peak comparable to resonance, and then rapidly diminishes. The transient response to a sudden application of torsional loading is characterized by producing a similar sharp peak in k(,3) at a time comparable to that required for the shear wave to travel the crack depth, and then its value oscillates about and slowly approaches the static value.;Studied also in some detail is the influence of varying the ratio of moduli of rigidity of the cylinders and the length of the crack on the dynamic factor k(,3). Such results are useful in the theory of brittle fracture where crack-like flaws are developed in structures subjected to mechanical vibrations and in load transfer problems involving compound cylinders.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
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Program
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Engineering
