Jan Tich#: ~genmpuuecran areuea~e~tm~tan cxe,ua samyxamudux rone6auuft uzeu6a. . .

npoBepi<a Ao c~x IIOp BLIBe~eHH~X ~?opMya. O~HoBpeMemto 5yAeT nonesHo HCCJIe~OBaTb TeOpeTHqeCKH BJII~HHIIe BHemHeFO TpeHI~g Ha BenIItl]AHI,I aael~Tpl~- qecHo~ OHB/aBaneHTHO~I CXeMl, I.

Ton~oK I~ pa6OTaM, IIOCBameHHI~IM onei~wp~qeci(ofi OKB~BaneHTHO~ cxeMe i~oneSarmfi nt, eBo~nei~Tpla,~ecrmx mnn(~OB, ~aJI npo~p. B. HeTpmnnI~a. H eMy oqen~, 5naroaapen 3a IIOCTOHHHOe BHHMalti~e II 3a MHOFHe EieHHI, Ie CO- BeTU. BLIpax~alo iici~penmolo 6naro~ap~ocT~, 3a ~ei~oTop~ie sa~te,mm~a H. X a a o y n ~ e ~ aCCHCTeHTy (I:). C o n / R e .

HoCTylIHaO 15. 10. 1955.

THE ELECTRICAL-EQUIVALENT CIRCUIT OF DAMPED FLEXUI%AL VIBRATIONS OF PIEZOELECTRIC BARS

(Abstract of preceding paper)

JAN TICH~ Chair o/Mathematics and Physics, Faculty o] Engineering, Ziberec

The paper first gives the equation of motion for damped flexural vibrations of an infinitely thin bar (8) derived with regard to the damping caused by internal friction. If we consider the arrangement of electrodes shown in Fig. 3 for the piezoelectric ex- citation of flexural vibrations we can write the exciting moment of the piezoelectric strain in the form (11). ~(x) denotes the function of x which, with the given arrangement of electrodes, takes on the values (12). The equation of motion for forced flexural vibrations of a piezoelectric bar (13) is solved by means of the series expansion (16). The vibrations in the stat ionary state have the same frequency .as the exciting force bu t are displaced in phase. The mechanical deformations (30) are calculated and from them, by the usual method, the desired values of the electrical equivalent circuit (40)--(43) are obtained. The effect of gaps between the electrodes and the piezoelectric bar is also considered.

:Received 15. 10. 1955.

J l u m e p a m y p a - Re/erences

[1] C a d y W. G.: Piezoelectricity, ~r Graw-Hill, New York-London 1946. [2] C h a l o u p k a P.: qexoc~. ~?ns. mypH. 4 (1954), 453. [3] C h a l o u p k a P., T i c h ~ J.: Slaboproud2 obzor 16 (1955), 33. (In Czech). [4] K e l l e r J.: Wir. Eng. 28 (1951), 179. [5] M a s o n W. P.: Piezoelectric Crystals and their Application to Ultrasonics, D. yon

Nostrand, New York 1950. [6] Pe t r$11ka V.: Piezoelekt~ina, P~irodov~deckd vydavatelstvl, Praha 1951. (In Czech). [7] P e t r ~ i l k a V., K o t l e r Al.: V~stnik Krs 5esk4 spoleSnosti hank, ti'ida matema-

ticko-pHrodov~deckA (1947). (In Czech). [8] V o i g t W.: Lehrbuch der Kristallphysik, Teubner 1910. [9] W i e n W., H a r m s F.: Handbuch tier Experimentalphysik, Akademische Verlags-

gesellschaft, Leipzig 1910, sv. 17, dil 1, str. 310.

452 qexoc:i. Caa. myp-. 6 (1956) 5