Читать книгу Vibrations of Linear Piezostructures - Andrew J. Kurdila - Страница 4

1 Chapter 1Figure 1.1 Barium titanate and lead zirconate titanate. (Left) Barium titana...Figure 1.2 Polarization versus applied electrical field for ferroelectric ab...Figure 1.3 and domains in , [31].Figure 1.4 Polarization versus electrical field hysteresis below the Curie t...Figure 1.5 The direct piezoelectric effect.Figure 1.6 The converse piezoelectric effect.Figure 1.7 Piezoelectrically based microphones from PCB®,Figure 1.8 Piezoelectric stack actuators available from PI ceramic®, Source:...Figure 1.9 Piezoelectric bender actuators available from PI ceramic®, Source...

2 Chapter 2Figure 2.1 Frames generated by basis vectors and , , and their cyclic pe...Figure 2.2 Unit cell and lattice parameters.Figure 2.3 The unit cell of the triclinic unit cell.Figure 2.4 Crystallographic coordinates, directions, and planes.Figure 2.5 The fourteen Bravais lattices, seven crystal systems, and associa...Figure 2.6 Rotoinversion of the point . The rotation of is followed by ...Figure 2.7 Examples of objects with two, three, and fourfold symmetry about ...Figure 2.8 Unit cell of monoclinic crystal system.Figure 2.9 Invariance of the monoclinic lattice with respect to reflection a...Figure 2.10 Invariance of the monoclinic lattice with respect to rotation th...

3 Chapter 3Figure 3.1 (Left) Continuum body having surface and the stress vector ...Figure 3.2 Tetrahedron with surface normal used to derive Cauchy's formula...Figure 3.3 (Left) Differential cube with surface stresses, (Right) All stres...Figure 3.4 Undeformed configuration , deformed configuration , and the def...Figure 3.5 Axial rod geometry, coordinate alignment, and displacementFigure 3.6 Beam geometry, coordinate alignment, and displacementFigure 3.7 Geometry of the thin, rectangular, Kirchoff plateFigure 3.8 Linearly elastic body , applied external stress field , boundar...

4 Chapter 4Figure 4.1 Point charges located at points , respectively, position vecto...Figure 4.2 Wire loops carrying the currents and , vectors and , and di...Figure 4.3 A typical crystal lattice, an asymmetric unit cell, the centers o...Figure 4.4 A dielectric parallel plate capacitor.Figure 4.5 A volume that straddles the top electrodes surface of the volum...Figure 4.6 A planar loop of wire carrying current , having area , and norm...Figure 4.7 A lattice with point charges at each corner.Figure 4.8 A finite wire with uniform linear charge density.Figure 4.9 An infinite duct.Figure 4.10 A nonplanar current carrying wire.

5 Chapter 5Figure 5.1 (Left) Uniaxial test to measure electric displacement, (Right) El...Figure 5.2 (Left) Uniaxial test to measure stress, (Right) Stress versus ele...Figure 5.3 Decomposition of surface into complementary surfaces and

6 Chapter 6Figure 6.1 Displacement assumed mode .Figure 6.2 Potential assumed mode .Figure 6.3 Piezoelectric uniaxial rod with the top and bottom surfaces elect...Figure 6.4 Piezoelectrically actuated composite beam.Figure 6.5 Shear and bending moment acting on a typical beam section.Figure 6.6 Piezoelectrically actuated composite plate driven by two voltage ...Figure 6.7 Composite piezoelectric beam actuated by two patches.Figure 6.8 Axial piezoelectric specimen with tip mass.Figure 6.9 Axial piezoelectric specimen with prescribed base motion .Figure 6.10 Piezoelectric composite beam specimen with rigidly attached tip ...Figure 6.11 Piezoelectric composite beam specimen prescribed base motion ....

7 Chapter 7Figure 7.1 Piezoelectric composite beam connected to a passive resistive shu...Figure 7.2 Schematic diagram of piezoelectric element with shunt resistorFigure 7.3 Piezoelectric composite beam connected to a passive capacitive sh...Figure 7.4 Piezoelectric element with capacitive shuntFigure 7.5 Stack actuator, orientation of layers, and electroding patternFigure 7.6 Coordinate systems for odd and even layers

8 Chapter 8Figure 8.1 Piecewise linear finite elementsFigure 8.2 Comparison of analytical natural frequencies and numerical estima...Figure 8.3 Transient response of axial piezoelectric specimenFigure 8.4 Comparison of Bode plots for models where the number of degrees o...Figure 8.5 Conventional beam finite element functions over element with ...Figure 8.6 Nodes, elements, and beam finite element basis defined over a bea...Figure 8.7 Comparison of numerically computed frequencies and analytic fre...Figure 8.8 Transient response of composite piezoelectric beam specimenFigure 8.9 Comparison of Bode plot for and degrees of freedom in the Gal...Figure 8.10 Experimental Setup, [27] Source: Vijaya Venkata Malladi / https:...Figure 8.11 Clamped‐clamped traveling waves, (a) analytical, (b) experimenta...Figure 8.12 Clamped‐free traveling waves, (a) analytical, (b) experimental [...Figure 8.13 Free‐free traveling waves, (a) analytical, (b) experimental [27]...Figure 8.14 Analytical estimates of traveling waves, (a) clamped‐clamped, (b...Figure 8.15 Envelopes of traveling waves, (a) clamped free, 285 Hz, (b) free...

9 Supplementary MaterialFigure 8.16 First four fixed‐fixed modes for the axial elementFigure 8.17 First four fixed‐free modes for the axial elementFigure 8.18 First four cantilever modes of the Bernoulli–Euler beam