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Titlebook: Linear Piezoelectric Plate Vibrations; Elements of the Line H. F. Tiersten Book 1969 Springer Science+Business Media New York 1969 electric

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Hoare logic, imperative and functional programs.Work with pre- and post-conditions.Use data types, pattern matching, and classes.Dive into verification examples for potential re-use for your own projects.Who Th978-1-4842-7977-9978-1-4842-7978-6
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Elements of Vector and Tensor NotationConsider the orthogonal coordinate system with axes .., .., and .. shown in Fig. 1. The base vectors are .. (. = 1, 2, 3), where |e.|= 1. Clearly, the vector . may be written . and since the coordinate system is orthogonal, . where δ. is the Kronecker delta defined by . and we have introduced the summation convention (.) for repeated indices.
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Infinitesimal Deformation TheoryConsider a line element .. which moves in such a manner that it rotates and extends (or contracts) to .. as shown in Fig. 4. From Fig. 4 it is clear that .. and from (3.1) and (3.2) we have
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https://doi.org/10.1007/978-1-4899-6453-3electricity; elements; Vibration
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978-1-4899-6221-8Springer Science+Business Media New York 1969
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The Linear Theory of Piezoelectricityate of increase of energy (kinetic plus internal) is equal to the rate at which work is done by the surface tractions acting across . less the flux of electric energy outward across .. Thus we have . as the equation of the conservation of energy. Basically, this equation postulates the existence of the internal energy function ..
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