Piezoelectric ceramic materials are widely used in solid state actuators
and sensors. For piezoceramic elements, the use of the d15-effect
is of particular interest since the shear piezoelectric coefficient
is much higher than the other piezoelectric coefficients d31 or d33. Although this fact is widely known, the application
of shear actuators is somewhat rare. Shear induced vibrations are
more complex to describe mathematically and there is not an adequate
understanding of nonlinear shear induced vibration behavior. At weak
electric fields, piezoceramics are described by linearized constitutive
relations around an operating point. However, in near resonance frequency
excitation of the flexural vibration of piezoceramic beam using d15-effect,
even at weak electric field, typical nonlinear vibration behavior
is observed. This vibration behavior can not be adequately defined
by the linear theories.
In this paper, authors have attempted to model this nonlinear
behavior using higher order cubic conservative and nonconservative
terms in the constitutive equations. The linear eigenfunctions are
used to discretize the nonlinear equation of motion obtained by
Hamilton's principle. Perturbation methods are used to solve
approximately the nonlinear equation of motion. Using this
solution, nonlinear parameters are identified by comparing the
theoretical and experimental results. The nonlinear effects and
the modeling described herein may have strong influence on the
design of existing applications and on the development of new
applications based on the d15-effect.
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