In the second case the lowest natural frequency is

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Unformatted text preview: m hb = 5.275 x 10-3 m r = 27.5 x 10-3 m Loading V = 1 volt Constitutive Matrices NEPEC 6 “Stiffness” Matrix [c] x 10-10 N/m2 ANSYS Verification Manual . ANSYS Release 9.0 . 002114 . © SAS IP, Inc. 1–395 VM176 12. 8 6. 8 6. 6 0 0 12.8 6. 6 11.0 0 0 0 0 2 .1 0 2 .1 Symmetric 0 0 0 0 2. 1 0 NEPEC 6 Piezoelectric Matrix [e] C/m2 0 0 −6.1 0 0 −6.1 0 0 15.7 0 0 0 0 0 0 0 0 0 NEPEC 6 Dielectric Matrix [εr] 0 0 993.55 993.55 0 0 0 0 993.55 Analysis Assumptions and Modeling Notes The transducer has circumferential symmetry and is symmetric about the midplane, so the model is reduced to a single wedge of elements with an additional symmetry plane at z = 0. No internal losses (damping) are assumed. The top surface of the piezoceramic is electroded, resulting in an equipotential surface. The nodes modeling the surface have their voltage DOF coupled so that the applied potential load can be conveniently placed on a single node. The 1 volt potential load translates into a 0.5 volt potential gradie...
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