An Analysis of Intermodulation in Thickness-Shear and Trapped Energy Resonators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Analysis of Intermodulation in Thickness-Shear and Trapped Energy Resonators write by H. F. Tiersten. This book was released on 1974. An Analysis of Intermodulation in Thickness-Shear and Trapped Energy Resonators available in PDF, EPUB and Kindle. Electroelastic equations containing terms up to cubic in the small mechanical displacement field, but no higher than linear in the electric variables, are applied in the analysis of intermodulation in rotated Y-cut quartz oscillators. Both pure thickness-shear vibrators and essentially thickness-shear trapped energy resonators are treated. Lumped parameter representations of the solutions, which are valid in the vicinity of a resonance, are presented for the linear and nonlinear portions of both the pure thickness-shear and trapped energy thickness-shear problems. The influence of the driving and detecting circuitry is included and, in particular, in each case the relation between the intermodulation and driving voltage is obtained. Application of this relation to a number of AT-cut quartz fundamental and third overtone trapped energy resonators yields good agreement with experiment and an estimate of the fourth order elastic constant for the AT-cut. (Modified author abstract).
An Analysis of Nonlinear Resonance in Thickness Shear and Trapped Energy Resonators
An Analysis of Nonlinear Resonance in Thickness Shear and Trapped Energy Resonators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Analysis of Nonlinear Resonance in Thickness Shear and Trapped Energy Resonators write by Harry F. Tiersten. This book was released on 1975. An Analysis of Nonlinear Resonance in Thickness Shear and Trapped Energy Resonators available in PDF, EPUB and Kindle. Electroelastic equations containing terms up to cubic in the small mechanical displacement field, but no higher than linear in the electric variables, are applied in the analysis of nonlinear resonance in rotated Y-cut quartz oscillators. Both pure thickness-shear vibrators and essentially thickness-shear trapped energy resonators are treated. Lumped parameter representations of the solutions, which are valid in the vicinity of a resonance and relate the amplitude of the dominant mode nonlinearly to the voltage across the crystal, are presented for both the pure thickness-shear and trapped energy thickness-shear problems. In each instance the expression for the current through the crystal is determined, the influence of the external circuitry is included in the analysis and, ultimately, an expression cubic in the mode amplitude and linear in the driving voltage is obtained. The analyses hold for the fundamental and odd overtone thickness-shear modes. Nonlinear resonance curves are presented for AT-cut quartz.
Proceedings of the Annual Symposium on Frequency Control
Proceedings of the Annual Symposium on Frequency Control - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proceedings of the Annual Symposium on Frequency Control write by . This book was released on 1975. Proceedings of the Annual Symposium on Frequency Control available in PDF, EPUB and Kindle.
An Analysis of Trapped Energy Resonators Operating in Overtones of Coupled Thickness-Shear and Thickness-Twist
An Analysis of Trapped Energy Resonators Operating in Overtones of Coupled Thickness-Shear and Thickness-Twist - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Analysis of Trapped Energy Resonators Operating in Overtones of Coupled Thickness-Shear and Thickness-Twist write by H. F. Tiersten. This book was released on 1975. An Analysis of Trapped Energy Resonators Operating in Overtones of Coupled Thickness-Shear and Thickness-Twist available in PDF, EPUB and Kindle. The equations of three-dimensional linear piezoelectricity are applied in the analysis of trapped energy resonators with rectangular electrodes vibrating in coupled thickness-shear and thickness-twist in the vicinity of the fundamental and odd overtone thickness-shear frequencies. Closed form asymptotic expressions for the frequency wavenumber dispersion relations for the fundamental and odd overtone coupled thickness-shear and thickness-twist waves near cutoff are obtained for both the electroded and unelectroded regions of the trapped energy resonator. The influence of piezoelectric stiffening, electrode mass loading and electrical shorting is included in the analysis. Simple approximate boundary conditions at a junction between an electroded and unelectroded region of the plate are obtained in a manner exhibiting the natural limitations inherent in the approximation.
Continuum Mechanics of Electromagnetic Solids
Continuum Mechanics of Electromagnetic Solids - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Continuum Mechanics of Electromagnetic Solids write by G.A. Maugin. This book was released on 2013-10-22. Continuum Mechanics of Electromagnetic Solids available in PDF, EPUB and Kindle. This volume is a rigorous cross-disciplinary theoretical treatment of electromechanical and magnetomechanical interactions in elastic solids. Using the modern style of continuum thermomechanics (but without excessive formalism) it starts from basic principles of mechanics and electromagnetism, and goes on to unify these two fields in a common framework. It treats linear and nonlinear static and dynamic problems in a variety of elastic solids such as piezoelectrics, electricity conductors, ferromagnets, ferroelectrics, ionic crystals and ceramics. Chapters 1-3 are introductory, describing the essential properties of electromagnetic solids, the essentials of the thermomechanics of continua, and the general equations that govern the electrodynamics of nonlinear continua in the nonrelativistic framework (e.g. Maxwell's equations, the fundamental balance laws of continuum mechanics, basic thermodynamical inequalities for electromagnetic continua, jump relations for studying the propagation of shock waves, nonlinear constitutive equations for large classes of materials).The remainder of the text presents in detail special cases, applications, solved problems, and more complex schemes of electromagnetic matter. Chapters 4 and 5 examine material schemes whose description relies on the above-mentioned equations. Chapters 6 and 7 are more advanced, reporting on recent progress in the field.Suitable for graduate teaching, the volume will also be useful to research workers and engineers in the field of electromagnetomechanical interactions, and to those interested in the basic principles, mathematical developments and applications of electroelasticity and magnetoelasticity in a variety of solid materials, such as crystals, polycrystals, compounds and alloys.
