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  • 2000-2004  (2)
  • 1975-1979  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    On the thickness expansion of the electric potential in the determination of two-dimensional equations for the vibration of electroded piezoelectric plates (2002)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 91 (2002), S. 2277-2283 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In the derivation of two-dimensional equations for the vibration of piezoelectric plates from variational equations, expansions of the mechanical and electrical variables in the thickness coordinate are employed. If the major surfaces of the plate are electroded and the electric potential is expanded in functions of the thickness coordinate which do not vanish at the electrodes, the variations of the different orders of the expansion potentials are not independent because the electric potential must satisfy constraint conditions at the electrodes where it is independent of position. In this work, the electric potential is expanded in functions of the thickness coordinate which do not vanish at the surface electrodes and the constraint conditions are included by means of the method of Lagrange multipliers. The resulting piezoelectric plate equations are obtained along with an integral condition on the Lagrange multipliers over the electrodes, which results in the equation for the current through the electrodes. It is shown that the elimination of the Lagrange multipliers results in a reduced system of electrostatic plate equations and associated edge conditions, which is easier to use. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1426242
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  • 2
    Electronic Resource
    Electronic Resource
    Forced vibrations of the fundamental family of modes in AT-cut quartz strip resonators (2001)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 89 (2001), S. 575-585 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Mindlin's equations for the vibrations of elastic crystal plates are employed in the description of AT-cut quartz strip resonators. The electrically driven three-dimensional piezoelectric pure thickness solution is incorporated in the treatment. The driving voltage appearing in this thickness solution is included in the variational principle from which the plate equations are obtained. In this way the resulting Mindlin equations contain the driving voltage and hold for plates with small piezoelectric coupling. The equations are applied in the analysis of strip resonators. The eigensolutions are obtained by solving a sequence of one-dimensional problems that are defined by utilizing the results from the previous problem variationally. The driven solution is obtained by means of an expansion in the eigensolutions and a lumped parameter representation of the admittance, which is valid in the vicinity of a resonance, is obtained. Calculated results are presented for a range of geometries and the influence of the couplings is exhibited. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1323749
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  • 3
    Electronic Resource
    Electronic Resource
    On integral forms of the balance laws for deformable semiconductors (1978)
    Springer
    Archive for rational mechanics and analysis 68 (1978), S. 27-36 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The general nonlinear differential equations describing the interaction of finitely deformable, polarizable, heat conducting intrinsic n-type semiconductors with the quasi-static electric field are transformed from the unknown present coordinate description to the known reference coordinate description, which is the form needed in the treatment of problems. For the differential form of each balance equation in the reference coordinate description, the associated integral form is obtained. The resulting integral forms turn out as expected with the exception of the one due to the balance of linear momentum for the semiconducting fluid, in which an important change in and simplification from the form used heretofore is introduced. More importantly, the previous existing integral form of the equation of the balance of energy in the present coordinate description is transformed to a different form, which is equivalent to the original form only when the field variables are differentiable. The revised integral form in the present coordinate description is then transformed to the reference coordinate description, from which an energetic jump condition across a moving non-material surface of discontinuity is obtained which is consistent with all the other jump conditions obtained from the other integral forms. In addition, the expression for the quasi-static electric Poynting vector in the reference coordinate description is determined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276177
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  • 4
    Electronic Resource
    Electronic Resource
    A theory of composites modeled as interpenetrating solid continua (1977)
    Springer
    Archive for rational mechanics and analysis 65 (1977), S. 153-192 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The differential equations and boundary conditions describing the behavior of a finitely deformable, heat-conducting composite material are derived by means of a systematic application of the laws of continuum mechanics to a well-defined macroscopic model consisting of interpenetrating solid continua. Each continuum represents one identifiable constituent of the N-constituent composite. The influence of viscous dissipation is included in the general treatment. Although the motion of the combined composite continuum may be arbitrarily large, the relative displacement of the individual constituents is required to be infinitesimal in order that the composite not rupture. The linear version of the equations in the absence of heat conduction and viscosity is exhibited in detail for the case of the two-constituent composite. The linear equations are written for both the isotropic and transversely isotropic material symmetries. Plane wave solutions in the isotropic case reveal the existence of high-frequency (optical type) branches as well as the ordinary low-frequency (acoustic type) branches, and all waves are dispersive. For the linear isotropic equations both static and dynamic potential representations are obtained, each of which is shown to be complete. The solutions for both the concentrated ordinary body force and relative body force are obtained from the static potential representation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276554
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    Paper (German National Licenses)
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