## Definition of Constants for Piezoceramic MaterialsThis monograph consists of investigation results obtained on the new theoretically well-grounded method for the total set of the compatible material constants for different piezoceramics. With this aim, there were carried out theoretical and experimental analysis, and various oscillation modes of electroelastic bars and plates were identified. Moreover, the physical and geometrical restrictions on the sample form were stated by using modified method of definition of the piezomodule d33 in quasistatic regime. These limitations allowed the authors to calculate the valid values of d33 for various piezoceramic families. By this, the boundaries of application of the above methods are discussed in this book. The results of identification of the various oscillation modes for bars and plates, and also the method and algorithm of the definition of total set of compatible material constants may significantly help in the development of the computation methods for characteristics of piezocomposite materials for force piezoactuators. One of the approaches in order to achieve this aim consists of practice forms of maximum displacements that could be created by using the stiffness matrices of composite based on the calculation algorithm of total set of the compatible piezoceramic material constants. Moreover, above modified algorithm may be used for research and development of new composites, in particular polymer-composite materials. This book is addressed to students, post-graduate students and specialists, taking part in the development, preparation and researching new materials and devices on their base. |

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### Contents

Methods for Deﬁnition of Piezoelectric Material | 49 |

Deﬁnition of Piezomodule d3 | 105 |

Deﬁnition of Elastic Constants for Piezoceramics | 119 |

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### Common terms and phrases

ACELAN acoustic AFC spectra Akopyan Amplitude-frequency characteristic analysis antiresonance axis beam bending oscillations boundary conditions calculated capacitance ceramics components constitutive equations corresponding cross-section Curie point decrease deﬁne deﬁnition device dielectric permeability displacement dynamic elastic module elastic constants elastic modules electric charge electric ﬁeld intensity electric potential electro-elasticity electrodes electromechanical couple error ferroelectric Figure ﬁnite-element ﬁrst frequencies of resonance frequency f fulﬁlled geometric identiﬁcation inﬂuence investigated Kramarov longitudinal mode material constants mean-on-sampling values measurement mechanical stresses method Mode PMP Nasedkin non-polarized piezoceramics obtained oscillation mode BL overtones parameters piezoceramic constants piezoceramic material piezoceramics PZTB-3 Piezoelectric Materials piezoelements polarization plane polarization vector polarized piezoceramics present prismatic samples problem properties PZTNB-1 quasistatic regime rectangular relationship resonance frequencies Rostov State University Rostov-on-Don sample length shear oscillation signiﬁcant signiﬁcantly sufﬁciently Table taking into account temperature dependencies tensor total set Transducers transverse voltage width