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IssuesArchive of Issues2014-4pp.435-444

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D.A. Shlyakhin, "Forced Axisymmetric Vibrations of a Thick Circular Rigidly Fixed Piezoceramic Plate," Mech. Solids. 49 (4), 435-444 (2014)
Year 2014 Volume 49 Number 4 Pages 435-444
DOI 10.3103/S0025654414040086
Title Forced Axisymmetric Vibrations of a Thick Circular Rigidly Fixed Piezoceramic Plate
Author(s) D.A. Shlyakhin (Samara State Architecture and Civil Engineering University, ul. Molodogvardeyskaya 194, Samara, 443001 Russia, d-612-mit2009@yandex.ru)
Abstract A new closed-form solution of the axisymmetric nonstationary problem of elasticity is constructed for a circular thick piezoceramic plate whose outer cylindrical surface is rigidly fixed. The use of mixed boundary conditions for a curvilinear plane allows one to obtain sufficiently simple computational relations. The closed-form solution is constructed by the method of expansion in the vector eigenfunctions in the form of a structure algorithm of finite transformations. The obtained solutions are used to determine the natural vibration frequency, the stress-strain state of the considered element, and all characteristics of the induced electric field.
Keywords forced axisymmetric vibrations, thick piezoceramic plate, problem of electroelasticity
References
1.  V. T. Grinchenko, A. F. Ulitko, and N. A. Shul'ga, Mechanics of Coupled Fields in Structural Elements. Vol. 5. Electroelasticity (Naukova Dumka, Kiev, 1989) [in Russian].
2.  N. A. Shul'ga and A. M. Bolkiev, Oscillations of Piezoelectric Bodies (Naukova Dumka, Kiev, 1990) [in Russian].
3.  M. Hussein and P. R. Heyliger, "Discrete Layer Analysis of Axisymmetric Vibrations of Laminated Piezoelectric Cylinders," J. Sound Vibr. 192 (5), 995-1013 (1996).
4.  A. Ya. Grigorenko, T. A. Efimova, and I. A. Loza, "On an Approach to the Study of Vibrations of Hollow Piezoceramic Cylinders of Finite Length," Dokl. NAN Ukr., No. 6, 61-67 (2009).
5.  Yu. E. Senitskii, "The Dynamic Problem of Electroelasticity for a Non-Homogeneous Cylinder," Prikl. Mat. Mekh. 57 (1), 116-122 (1993) [J. Appl. Math. Mech. (Engl. Transl.) 57 (1), 133-139 (1993)].
6.  D. A. Shlyakhin, "Nonstationary Axisymmetric Problem of Electroelasticity for a Piezoceramic Cylinder with Circular Polarization," Zh. Prikl. Mekh. Tekhn. Fiz. 50 (1), 12-21 (2009) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 50 (1), 9-17 (2009)].
7.  V. Z. Parton and B. A. Kudryavtsev, Electromagnetoelasticity of Piezoelectrics and Electrically Conductive Solid (Nauka, Moscow, 1988; Gordon & Breach Science Publishers, New York-London-Paris-Montreux-Tokyo-Melbourne, 1988).
8.  A. N. Guz' (Editor), Spatial Problems of Elasticity and Plasticity, (Naukova Dumka, Kiev, 1985) [in Russian].
Received 18 October 2011
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