By Robert Milne
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Additional resources for A theory of programming language semantics, part A
Note that the generic displacement Uj (j = 1,2,3) includes both in-plane deformations (a membrane component) and out-of-plane rotations (a bending component). These two components will be further separated in later derivations. The electric fields Ei's in all three directions are considered in this case. [ 24 ] • Piezoelectric Shells. 2) and collect coefficients of similar terms. Because of tedious and complicated procedures, only crucial steps in the derivations are outlined. The variation of kinetic energy is presented first and followed by energies associated with electric enthalpy J'I, traction forces tj' and electric charge Q.
10 ] • Piezoelectric Shells. , 1987, "Wave Propagation in a Piezoelectric Solid Cylinder of Arbitrary Cross Section," J. Acoust. Soc. Am. 2013-2020. 133-139. 371-388. 677-684. 213-216. 220-226. l06-111. A. , 1980, "Equations on the Theory of Piezoceramic Shells," In: Mechanics of a solid deformable body and related analytical problems. Moscow, Izd. mosk. Inst. Chim. R. , 1981, "Piezoelectricity in Polyvinylidene Fluoride," J. Acoust. Soc. 1596-1608. , 1987, "Vibration Isolation for Spacecraft Using the Piezoelectric Polymer PVF 2," Proc.
17-34. 500-505, September 1991. 207-211, 1990 ASME Winter Annual Meetings, Dallas, Texas, Nov. 25-30, 1990; "Electromechanics and Vibrations of Piezoelectric Shell Distributed Systems," ASME Journal of Dynamic Systems, Measurements, and Control, 1993. , 1991, "Sensor Mechanics of Distributed Shell Convolving Sensors Applied to Flexible rungs," Structural Vibration and Acoustics, Edrs. 67-74, Symposium on Intelligent Structural Systems, 1991 AS ME 13th Biennial Conference on Mechanical Vibration and Noise, Miami, Florida, September 22-25, 1991.
A theory of programming language semantics, part A by Robert Milne