메뉴 건너뛰기




Volumn 77, Issue 6, 1997, Pages 429-445

Numerical algorithms for dynamics of thermopiezoceramic bars

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0343947844     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.19970770608     Document Type: Article
Times cited : (6)

References (104)
  • 3
  • 5
    • 0004086853 scopus 로고
    • TZOU, H. S.; ANDERSON, G. I. (eds.): Kluwer Academic Publishers, Boston
    • TZOU, H. S.; ANDERSON, G. I. (eds.): Intelligent structural systems. Kluwer Academic Publishers, Boston 1992.
    • (1992) Intelligent Structural Systems
  • 6
    • 0028485223 scopus 로고
    • Intelligent structures for aerospace: A technology overview and assessment
    • CRAWLEY, E. F.: Intelligent structures for aerospace: a technology overview and assessment. AIAA Journal 32 (1994) 8, 1689-1099.
    • (1994) AIAA Journal , vol.32 , Issue.8 , pp. 1689-11099
    • Crawley, E.F.1
  • 7
    • 0028422104 scopus 로고
    • Piezoelectricity and its use in disturbance sensing and control of flexible structures: A survey
    • RAO, S. S.; SUNAR, M.: Piezoelectricity and its use in disturbance sensing and control of flexible structures: a survey. Appl. Mech. Rev. 47 (1994) 4, 113-123.
    • (1994) Appl. Mech. Rev. , vol.47 , Issue.4 , pp. 113-123
    • Rao, S.S.1    Sunar, M.2
  • 8
    • 84935357059 scopus 로고
    • IRE Standards on piezoelectric crystals: Measurements of piezoelectric ceramics
    • IEEE Standard 179
    • IRE Standards on piezoelectric crystals: measurements of piezoelectric ceramics. Proc. IRE 49 (1961), 1161-1169. IEEE Standard 179.
    • (1961) Proc. IRE , vol.49 , pp. 1161-1169
  • 10
    • 33748510518 scopus 로고
    • GOST (All-Union state standard) 12370-72: Piezoceramic materials
    • Izd. Standartov, Moscow
    • GOST (All-Union state standard) 12370-72: Piezoceramic materials. Testing methods (in Russian). Izd. Standartov, Moscow 1973.
    • (1973) Testing Methods (in Russian)
  • 11
    • 0019702159 scopus 로고
    • Piezoelectric ceramics: Characteristics and applications
    • BERLINCOURT, D.: Piezoelectric ceramics: characteristics and applications. J. Acoust. Soc. Am. 70 (1981) 6, 1586-1595.
    • (1981) J. Acoust. Soc. Am. , vol.70 , Issue.6 , pp. 1586-1595
    • Berlincourt, D.1
  • 13
    • 45949127490 scopus 로고
    • Recent advances: Vibrations of piezoelectric crystals
    • DÖKMECI, M. C.: Recent advances: vibrations of piezoelectric crystals. Int. J. Engng. Sci. 18 (1980) 3, 431-448.
    • (1980) Int. J. Engng. Sci. , vol.18 , Issue.3 , pp. 431-448
    • Dökmeci, M.C.1
  • 14
    • 0040086047 scopus 로고
    • Dynamic applications of piezoelectric crystals; Pt. I: Fundamentals; Pt. II: Theoretical studies; and Pt. III: Experimental studies
    • DÖKMECI, M. C.: Dynamic applications of piezoelectric crystals; Pt. I: Fundamentals; Pt. II: Theoretical studies; and Pt. III: Experimental studies. Shock Vib. Digest 15 (1983) 3, 9-20,
    • (1983) Shock Vib. Digest , vol.15 , Issue.3 , pp. 9-20
    • Dökmeci, M.C.1
  • 17
    • 0002394486 scopus 로고
    • Recent progress in the dynamic applications of piezoelectric crystals
    • DÖKMECI, M. C.: Recent progress in the dynamic applications of piezoelectric crystals. Shock Vib. Digest 20 (1988) 2, 3-20.
    • (1988) Shock Vib. Digest , vol.20 , Issue.2 , pp. 3-20
    • Dökmeci, M.C.1
  • 23
    • 33748517762 scopus 로고
    • Determination of the third-order piezoelectric constants of quartz using the extensional mode of rods
    • HRUSKA, C. K.: Determination of the third-order piezoelectric constants of quartz using the extensional mode of rods. J. Appl. Phys. 66 (1989) 3, 1071-1074.
    • (1989) J. Appl. Phys. , vol.66 , Issue.3 , pp. 1071-1074
    • Hruska, C.K.1
  • 25
    • 0021640406 scopus 로고
    • Electrode stress effects for length-cxtensional and flexural resonant vibrations of quartz bar
    • IEEE, New York
    • EERNlSSE, E. P.: Electrode stress effects for length-cxtensional and flexural resonant vibrations of quartz bar. Proc. 38th Annu. Symp. Freq. Contr., IEEE, New York 1984, pp. 126-131.
    • (1984) Proc. 38th Annu. Symp. Freq. Contr. , pp. 126-131
    • Eernlsse, E.P.1
  • 26
    • 0019899883 scopus 로고
    • Depolarizing-field effect in piezoelectric resonators
    • IKEDA, T.: Depolarizing-field effect in piezoelectric resonators. Ferroelectrics 43 (1982), 3-15.
    • (1982) Ferroelectrics , vol.43 , pp. 3-15
    • Ikeda, T.1
  • 27
    • 0024079588 scopus 로고
    • Thermoelectromechanical behavior of composite piezoelectric ceramic rods subjected to bending vibrations
    • KIRICHOK, I. F.: Thermoelectromechanical behavior of composite piezoelectric ceramic rods subjected to bending vibrations. Sov. Appl. Mech. 24 (1989) 3, 281-288;
    • (1989) Sov. Appl. Mech. , vol.24 , Issue.3 , pp. 281-288
    • Kirichok, I.F.1
  • 28
    • 33748492238 scopus 로고    scopus 로고
    • Prikl. Mekh. 24, 3, 83-88.
    • Prikl. Mekh. , vol.24 , Issue.3 , pp. 83-88
  • 29
    • 0025734137 scopus 로고
    • Dynamic behavior of a piezoelectric beam
    • SÖDERKVIST, J.: Dynamic behavior of a piezoelectric beam. J. Acoust. Soc. Am. 90 (1991) 2, 686-692.
    • (1991) J. Acoust. Soc. Am. , vol.90 , Issue.2 , pp. 686-692
    • Söderkvist, J.1
  • 30
    • 0027993992 scopus 로고
    • The three-dimensional equivalent circuit and the natural frequencies of rectangular piezoelectric ceramic resonators
    • SHUYU, L.: The three-dimensional equivalent circuit and the natural frequencies of rectangular piezoelectric ceramic resonators. J. Acoust. Soc. Am. 90 (1994) 6, 1620-1626.
    • (1994) J. Acoust. Soc. Am. , vol.90 , Issue.6 , pp. 1620-1626
    • Shuyu, L.1
  • 31
    • 33748505146 scopus 로고
    • Torsional vibration of a circular cylinder of piezoelectric β-quartz
    • PAUL, H. S.: Torsional vibration of a circular cylinder of piezoelectric β-quartz. Archiwum Mechaniki Stosowanej 14 (1962) 5, 127-134.
    • (1962) Archiwum Mechaniki Stosowanej , vol.14 , Issue.5 , pp. 127-134
    • Paul, H.S.1
  • 32
    • 0023849250 scopus 로고
    • The torsional vibration of a piezoelectric solid cylinder of arbitrary cross-section of (622) class
    • PAUL, H. S.; VENKATESAN, M.: The torsional vibration of a piezoelectric solid cylinder of arbitrary cross-section of (622) class. Int. J. Engng. Sci. 26 (1988) 5, 437-443.
    • (1988) Int. J. Engng. Sci. , vol.26 , Issue.5 , pp. 437-443
    • Paul, H.S.1    Venkatesan, M.2
  • 33
    • 0024742423 scopus 로고
    • Propagation of acoustoelectric torsional waves in a circumferentially poled piezoceramic cylinder
    • SHUL'GA, N. A.: Propagation of acoustoelectric torsional waves in a circumferentially poled piezoceramic cylinder. Sov. Appl. Mech. 25 (1989) 4, 319-324;
    • (1989) Sov. Appl. Mech. , vol.25 , Issue.4 , pp. 319-324
    • Shul'ga, N.A.1
  • 34
    • 33748487743 scopus 로고    scopus 로고
    • Prikl. Mekh. 25, 4, 3-9.
    • Prikl. Mekh. , vol.25 , Issue.4 , pp. 3-9
  • 35
    • 0024879011 scopus 로고
    • Wave propagation in a piezoelectric solid cylinder of arbitrary cross-section of class 6 (bone)
    • PAUL, H. S.; VENKATESAN, M.: Wave propagation in a piezoelectric solid cylinder of arbitrary cross-section of class 6 (bone). Int. J. Engng. Sci. 27 (1989) 7, 848-853.
    • (1989) Int. J. Engng. Sci. , vol.27 , Issue.7 , pp. 848-853
    • Paul, H.S.1    Venkatesan, M.2
  • 36
    • 0026406721 scopus 로고
    • Wave propagation in a piezoelectric bone with a cylindrical cavity of arbitrary shape
    • PAUL, H. S.; VENKATESAN, M.: Wave propagation in a piezoelectric bone with a cylindrical cavity of arbitrary shape. Int. J. Engng. Sci. 29 (1991) 12, 1601-1607.
    • (1991) Int. J. Engng. Sci. , vol.29 , Issue.12 , pp. 1601-1607
    • Paul, H.S.1    Venkatesan, M.2
  • 37
    • 0016471012 scopus 로고
    • Radial vibrations of axially polarized piezoelectric ceramic cylinders
    • ADELMAN, N. T.; STAVSKY, Y.; SEGAL, E.: Radial vibrations of axially polarized piezoelectric ceramic cylinders. J. Acoust. Soc. Am. 57 (1975) 2, 356-360.
    • (1975) J. Acoust. Soc. Am. , vol.57 , Issue.2 , pp. 356-360
    • Adelman, N.T.1    Stavsky, Y.2    Segal, E.3
  • 38
    • 0026155837 scopus 로고
    • Vibration of infinite piezoelectric cylinders with anisotropic properties using cylindrical finite elements
    • BUCHANAN, G. R.; PEDDIESON, JR., J.: Vibration of infinite piezoelectric cylinders with anisotropic properties using cylindrical finite elements. IEEE Trans. Ultrason. Ferroelec. Freq. Contr. UFFC 38 (1991) 3, 291-296.
    • (1991) IEEE Trans. Ultrason. Ferroelec. Freq. Contr. UFFC , vol.38 , Issue.3 , pp. 291-296
    • Buchanan, G.R.1    Peddieson Jr., J.2
  • 39
    • 0029031865 scopus 로고
    • Coupled vibration in hollow cylinders of longitudinally polarized piezoelectric ceramics
    • SHUYU, L.: Coupled vibration in hollow cylinders of longitudinally polarized piezoelectric ceramics. J. Acoust. Soc. Am. 97 (1995) 6, 3599-3604.
    • (1995) J. Acoust. Soc. Am. , vol.97 , Issue.6 , pp. 3599-3604
    • Shuyu, L.1
  • 40
    • 0025420536 scopus 로고
    • Vibrations of an axially polarized piezoceramic cylinder during electrical loading
    • SHUL'GA, N. A.; BORISENKO, L. V.: Vibrations of an axially polarized piezoceramic cylinder during electrical loading. Sov. Appl. Mech. 25 (1990) 11, 1070-1074.
    • (1990) Sov. Appl. Mech. , vol.25 , Issue.11 , pp. 1070-1074
    • Shul'ga, N.A.1    Borisenko, L.V.2
  • 41
    • 33748514914 scopus 로고
    • Prikl. Mekh. 25 (1989) 11, 15-19.
    • (1989) Prikl. Mekh. , vol.25 , Issue.11 , pp. 15-19
  • 42
    • 0003083710 scopus 로고
    • Measurement and calculation of electromechanical parameters of piezoceramic thin cylindrical tube transducers
    • HONGZHANG, W.; DECHU, Q.; YING, D.: Measurement and calculation of electromechanical parameters of piezoceramic thin cylindrical tube transducers. Chinese J. Acoust. 5 (1986) 3, 214-226.
    • (1986) Chinese J. Acoust. , vol.5 , Issue.3 , pp. 214-226
    • Hongzhang, W.1    Dechu, Q.2    Ying, D.3
  • 45
    • 0020763630 scopus 로고
    • Nonlinear extensional vibrations of quartz rods
    • TIERSTEN, H. F.; BALLATO, A.: Nonlinear extensional vibrations of quartz rods. J. Acoust. Soc. Am. 73 (1983) 6, 2022-2033.
    • (1983) J. Acoust. Soc. Am. , vol.73 , Issue.6 , pp. 2022-2033
    • Tiersten, H.F.1    Ballato, A.2
  • 46
    • 0002941880 scopus 로고
    • Electromagnetic effects in the theory of rods
    • GREEN, A. E.; NAGHDI, P. M.: Electromagnetic effects in the theory of rods. Phil. Trans. R. Soc. Lond. A314 (1985), 311-352.
    • (1985) Phil. Trans. R. Soc. Lond. , vol.A314 , pp. 311-352
    • Green, A.E.1    Naghdi, P.M.2
  • 49
    • 0016050690 scopus 로고
    • A theory of high-frequency vibrations of piezoelectric crystal bars
    • DÖKMECI, M. C.: A theory of high-frequency vibrations of piezoelectric crystal bars. Int. J. Solids Structures 10 (1974) 4, 401-409.
    • (1974) Int. J. Solids Structures , vol.10 , Issue.4 , pp. 401-409
    • Dökmeci, M.C.1
  • 51
    • 0022900157 scopus 로고
    • Nonlinear electroelastic equations of wave propagation and vibrations in quartz bar
    • New York
    • DÖKMECI, M. C.: Nonlinear electroelastic equations of wave propagation and vibrations in quartz bar. Proc. 40th Annu. Freq. Contr. Symp., IEEE, New York 1986; pp. 168-178;
    • (1986) Proc. 40th Annu. Freq. Contr. Symp., IEEE , pp. 168-178
    • Dökmeci, M.C.1
  • 54
    • 0023857017 scopus 로고
    • Fields of displacement and electric potential produced by moving dislocations in anisotropic piezoelectric crystals
    • SHINTANI, K.; MINAGAWA, S.: Fields of displacement and electric potential produced by moving dislocations in anisotropic piezoelectric crystals. Int. J. Engng. Sci. 26 (1988) 8, 893-901.
    • (1988) Int. J. Engng. Sci. , vol.26 , Issue.8 , pp. 893-901
    • Shintani, K.1    Minagawa, S.2
  • 55
    • 0024096473 scopus 로고
    • Spurious bulk waves in SAW filters with apodized transducers
    • IEEE, New York
    • WAGNER, K. C.: Spurious bulk waves in SAW filters with apodized transducers. Proc. Ultrasonics Symposium; Vol. 1. IEEE, New York 1988, pp. 35-38.
    • (1988) Proc. Ultrasonics Symposium , vol.1 , pp. 35-38
    • Wagner, K.C.1
  • 56
    • 0342552962 scopus 로고
    • Axisymmetric vibration of a piezoelectric solid cylinder guided by a thin film
    • PAUL, H. S.; VENKATESAN, M.: Axisymmetric vibration of a piezoelectric solid cylinder guided by a thin film. J. Acoust. Soc. Am. 80 (1986) 4, 1091-1096.
    • (1986) J. Acoust. Soc. Am. , vol.80 , Issue.4 , pp. 1091-1096
    • Paul, H.S.1    Venkatesan, M.2
  • 57
    • 33748515599 scopus 로고
    • Analyse piezoelektrischer Breitbandschwinger unter Anlehnung an die Differenzengleichung
    • SALAMAN, R.; CHINCHURRETA, F.: Analyse piezoelektrischer Breitbandschwinger unter Anlehnung an die Differenzengleichung. Acustica 67 (1988), 19-29.
    • (1988) Acustica , vol.67 , pp. 19-29
    • Salaman, R.1    Chinchurreta, F.2
  • 58
    • 0024096225 scopus 로고
    • Accurate determination of material constants of piezoelectric crystal from SAW velocity measurements
    • IEEE, New York
    • KOVACS, G.; TRATTNIG, G.; LANGER, E.: Accurate determination of material constants of piezoelectric crystal from SAW velocity measurements. Proc. Ultrasonics Symposium. IEEE, New York 1988, pp. 269-272.
    • (1988) Proc. Ultrasonics Symposium , pp. 269-272
    • Kovacs, G.1    Trattnig, G.2    Langer, E.3
  • 59
    • 0020835119 scopus 로고
    • Complete solutions of the transient behavior of a transmitting thickness-mode piezoelectric transducer and their physical interpretations
    • ZHANG, H. L.; LI, M. X.; YING, C. F.: Complete solutions of the transient behavior of a transmitting thickness-mode piezoelectric transducer and their physical interpretations. J. Acoust. Soc. Am. 74 (1983) 4, 1105-1114.
    • (1983) J. Acoust. Soc. Am. , vol.74 , Issue.4 , pp. 1105-1114
    • Zhang, H.L.1    Li, M.X.2    Ying, C.F.3
  • 60
    • 0008750011 scopus 로고
    • Scattering of plane wave by piezoelectric cylinder-transfer function, transient response and phase reconstruction of transducer
    • SHUCHU, R.: Scattering of plane wave by piezoelectric cylinder-transfer function, transient response and phase reconstruction of transducer. Chinese J. Acoustics 5 (1986), 237-248;
    • (1986) Chinese J. Acoustics , vol.5 , pp. 237-248
    • Shuchu, R.1
  • 61
    • 33748510931 scopus 로고
    • Acta Acustica 9 (1986), 345-348.
    • (1986) Acta Acustica , vol.9 , pp. 345-348
  • 62
    • 0020942301 scopus 로고
    • Rapid solutions to the transient response of piezoelectric elements by z-transform techniques
    • CHALLIS, R. E.; HARRISON, J. A.: Rapid solutions to the transient response of piezoelectric elements by z-transform techniques. J. Acoust. Soc. Am. 74 (1983) 6, 1673-1680.
    • (1983) J. Acoust. Soc. Am. , vol.74 , Issue.6 , pp. 1673-1680
    • Challis, R.E.1    Harrison, J.A.2
  • 63
    • 0014767052 scopus 로고
    • Finite element method for piezoelectric vibration
    • ALLIK, H.; HUGHES, J. R.: Finite element method for piezoelectric vibration. Int. J. num. Meth. Engng. 2 (1970) 1, 151-157.
    • (1970) Int. J. Num. Meth. Engng. , vol.2 , Issue.1 , pp. 151-157
    • Allik, H.1    Hughes, J.R.2
  • 64
    • 0015052063 scopus 로고
    • Finite element formulation of general electrothermoelasticity problems
    • ODEN, J. T.; KELLEY, B. E.: Finite element formulation of general electrothermoelasticity problems. Int. J. num. Meth. Engng. 3 (1971) 1, 161-179.
    • (1971) Int. J. Num. Meth. Engng. , vol.3 , Issue.1 , pp. 161-179
    • Oden, J.T.1    Kelley, B.E.2
  • 65
    • 33748518540 scopus 로고
    • A boundary element formulation in linear piezoelectric problems
    • TANAKA, K.; TANAKA, M.: A boundary element formulation in linear piezoelectric problems. J. Appl. Math. Mechs. (ZAMP) 31 (1980) 5, 568-580.
    • (1980) J. Appl. Math. Mechs. (ZAMP) , vol.31 , Issue.5 , pp. 568-580
    • Tanaka, K.1    Tanaka, M.2
  • 66
    • 84939019837 scopus 로고
    • The method of moments for vibrations of piezoelectric laminae
    • IEEE, New York
    • DÖKMECI, M. C.: The method of moments for vibrations of piezoelectric laminae. Proc. Ultrasonics Symposium, IEEE, New York 1992, pp. 1025-1028.
    • (1992) Proc. Ultrasonics Symposium , pp. 1025-1028
    • Dökmeci, M.C.1
  • 73
    • 33748495487 scopus 로고
    • Numerical algorithm for dynamics of piezoelectric laminae
    • Paper presented at the Univ. Virginia, Charlottesville, VA. June 6-9
    • AŞKAR ALTAY, G.; DÖKMECI, M. C.: Numerical algorithm for dynamics of piezoelectric laminae. Paper presented at the First AMD-ASME, EM-ASCE and SES Meeting, Univ. Virginia, Charlottesville, VA. June 6-9. 1993.
    • (1993) First AMD-ASME, EM-ASCE and SES Meeting
    • Aşkar Altay, G.1    Dökmeci, M.C.2
  • 76
    • 0001960766 scopus 로고
    • On the equations of motion of piezoelectric crystals
    • RADOK, J. R. M. (ed.): SIAM, Philadelphia
    • MINDLIN, R. D.: On the equations of motion of piezoelectric crystals. In: RADOK, J. R. M. (ed.): Problems of continuum mechanics. SIAM, Philadelphia 1961, pp. 282-290.
    • (1961) Problems of Continuum Mechanics , pp. 282-290
    • Mindlin, R.D.1
  • 80
    • 0016073063 scopus 로고
    • Equations of high frequency vibrations of thermopiezoelectric crystal plates
    • MINDLIN, R. D.: Equations of high frequency vibrations of thermopiezoelectric crystal plates. Int. J. Solids Structures 10 (1974), 625-637.
    • (1974) Int. J. Solids Structures , vol.10 , pp. 625-637
    • Mindlin, R.D.1
  • 81
    • 0000316890 scopus 로고    scopus 로고
    • Fundamental variational equations of discontinuous thermopiezoelectric fields
    • AŞKAR ALTAY, G.; DÖKMECI, M. C.: Fundamental variational equations of discontinuous thermopiezoelectric fields. Int. J. Engng. Sci. 34 (1996) 7, 769-782.
    • (1996) Int. J. Engng. Sci. , vol.34 , Issue.7 , pp. 769-782
    • Aşkar Altay, G.1    Dökmeci, M.C.2
  • 82
    • 0001725293 scopus 로고
    • Natural boundary and initial conditions from a modification of Hamilton's principle
    • TIERSTEN, H. F.: Natural boundary and initial conditions from a modification of Hamilton's principle. J. Math. Phys. 9 (1968) 9, 1445-1451.
    • (1968) J. Math. Phys. , vol.9 , Issue.9 , pp. 1445-1451
    • Tiersten, H.F.1
  • 83
    • 0000895524 scopus 로고
    • Forced vibrations of piezoelectric crystal plates
    • TIERSTEN, H. F.; MINDLIN, R. D.: Forced vibrations of piezoelectric crystal plates. Q. Appl. Math. 20 (1962) 2, 107-119.
    • (1962) Q. Appl. Math. , vol.20 , Issue.2 , pp. 107-119
    • Tiersten, H.F.1    Mindlin, R.D.2
  • 84
    • 33748492473 scopus 로고
    • Techniques in reducing equations of mathematical physics
    • DÖKMECI, M. C.: Techniques in reducing equations of mathematical physics. Abstr. Int. Congr. Math. Helsinki 1978, pp. 183.
    • (1978) Abstr. Int. Congr. Math. Helsinki , pp. 183
    • Dökmeci, M.C.1
  • 87
    • 0001654235 scopus 로고
    • The elastic dielectric
    • TOUPIN, R. A.: The elastic dielectric. J. Rational Mech. Anal. 5 (1956) 6, 849-915.
    • (1956) J. Rational Mech. Anal. , vol.5 , Issue.6 , pp. 849-915
    • Toupin, R.A.1
  • 88
    • 0024646407 scopus 로고
    • On a principle of virtual work for thermo-elastic bodies
    • BATRA, G.: On a principle of virtual work for thermo-elastic bodies. J. Elasticity 21 (1989), 131-146.
    • (1989) J. Elasticity , vol.21 , pp. 131-146
    • Batra, G.1
  • 89
    • 0004178638 scopus 로고
    • Benjamin/Cummings Publ. Company, Menlo Park, Ca.
    • KOONIN, S. E.: Computational physics. Benjamin/Cummings Publ. Company, Menlo Park, Ca. 1985.
    • (1985) Computational Physics
    • Koonin, S.E.1
  • 92
    • 0040844623 scopus 로고
    • Vibrations of AT-cut quartz strips of narrow width and finite length
    • LEE, P. C. Y.; WANG, J.: Vibrations of AT-cut quartz strips of narrow width and finite length. J. Appl. Phys. 75 (1994), 7081-7695.
    • (1994) J. Appl. Phys. , vol.75 , pp. 7081-7695
    • Lee, P.C.Y.1    Wang, J.2
  • 94
    • 0015604262 scopus 로고
    • Approximate solutions by utilizing hill functions
    • KAO, R.: Approximate solutions by utilizing hill functions. Compt. Structs. 3 (1973), 387-412.
    • (1973) Compt. Structs. , vol.3 , pp. 387-412
    • Kao, R.1
  • 95
    • 0005071673 scopus 로고
    • Higher order effects in thick rectangular beams
    • SOLER, A.: Higher order effects in thick rectangular beams. Int. J. Solids Struct. 4 (1968), 723-739.
    • (1968) Int. J. Solids Struct. , vol.4 , pp. 723-739
    • Soler, A.1
  • 96
    • 84996315974 scopus 로고
    • Axially symmetric waves in elastic rods
    • MINDLIN, R. D.; MCNIVEN, H. D.: Axially symmetric waves in elastic rods. J. Appl. Mech. 27 (1960), 145-151.
    • (1960) J. Appl. Mech. , vol.27 , pp. 145-151
    • Mindlin, R.D.1    Mcniven, H.D.2
  • 97
    • 0001290370 scopus 로고
    • Acoustic fields and velocities for surface acoustic wave propagation in multilayered structures: An extension of the Laguerre polynomial approach
    • KIM, Y.; HUNT, W. D.: Acoustic fields and velocities for surface acoustic wave propagation in multilayered structures: An extension of the Laguerre polynomial approach. J. Appl. Phys. 68 (1990), 4993-4997.
    • (1990) J. Appl. Phys. , vol.68 , pp. 4993-4997
    • Kim, Y.1    Hunt, W.D.2
  • 98
    • 0026122054 scopus 로고
    • Refined engineering beam theory based on the asymptotic expansion approach
    • FAN, H.; WIDERA, G. E. O.: Refined engineering beam theory based on the asymptotic expansion approach. AIAA Journal 29 (1991), 444-449.
    • (1991) AIAA Journal , vol.29 , pp. 444-449
    • Fan, H.1    Widera, G.E.O.2
  • 101
    • 0026743617 scopus 로고
    • Piezothermoelastic behavior of a laminated plate
    • TAUCHERT, T. R.: Piezothermoelastic behavior of a laminated plate. J. Thermal Stresses 15 (1992), 25-37.
    • (1992) J. Thermal Stresses , vol.15 , pp. 25-37
    • Tauchert, T.R.1
  • 102
    • 0029345324 scopus 로고
    • Analysis of methods for determining electromechanical coupling coefficients of piezoelectric elements
    • CHANG, S. H.; ROGACHEVA, N. N.; CHOU, C. C.: Analysis of methods for determining electromechanical coupling coefficients of piezoelectric elements. IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 42 (1995) 4, 630-640.
    • (1995) IEEE Trans. Ultrason. Ferroelec. Freq. Contr. , vol.42 , Issue.4 , pp. 630-640
    • Chang, S.H.1    Rogacheva, N.N.2    Chou, C.C.3
  • 104
    • 0029000276 scopus 로고
    • Modeling of piezoelectric ceramic vibrators including thermal effects. Part I: Thermodynamic property considerations, and Part II. Derivation of partial differential equations
    • MOON, W.; BUSCH-VISCHNIAC, I. J.: Modeling of piezoelectric ceramic vibrators including thermal effects. Part I: Thermodynamic property considerations, and Part II. Derivation of partial differential equations. J. Acoust. Soc. Am. 98 (1995), 403-412 and 413-421.
    • (1995) J. Acoust. Soc. Am. , vol.98 , pp. 403-412
    • Moon, W.1    Busch-Vischniac, I.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.