3 Chapter 3Figure 3.1-1 Geometry of stresses in tensor form.Figure 3.1-2 Geometry of stresses in matrix notation.Figure 3.1-3 A long thin bar with waves traveling within the bar.Figure 3.1-4 Eigenmodes for longitudinal waves in a bar with clamped boundar...Figure 3.1-5 Eigenmodes for longitudinal waves in a bar with free boundary c...Figure 3.1-6 Equivalent circuit representation for longitudinal vibrations i...Figure 3.1-7 Two‐port network for longitudinal vibrations in a bar.Figure 3.1-8 Conditions at end of the bar.Figure 3.1-9 Mass‐loaded bar with one end free.Figure 3.1-10 Equivalent circuit for a mass‐loaded bar with one end free.Figure 3.1-11 Velocity profile in a mass‐loaded bar with one free end and M ...Figure 3.1-12 Velocity profile in a mass‐loaded bar with one free end and M ...Figure 3.1-13 Mass‐loaded bar with one end clamped.Figure 3.1-14 Equivalent circuit for a mass‐loaded bar with one end clamped....Figure 3.1-15 Velocity profile in a mass‐loaded bar with one clamped end and...Figure 3.1-16 Velocity profile in a mass‐loaded bar with one clamped end and...Figure 3.1-17 Distributed equivalent circuit for wave propagation in a bar....Figure 3.1-18 Lumped equivalent circuit for wave propagation in a bar.Figure 3.1-19 Spring/mass model equivalent to the lumped parameter equivalen...Figure 3.1-20 Spring/mass model of a mass‐loaded longitudinal vibrator.Figure 3.1-21 Mass ratio for spring with different load impedances.Figure 3.1-22 The geometry of a hollow cylinder.Figure 3.1-23 Distributed equivalent circuit representation for longitudinal...Figure 3.1-24 Two‐port representation for longitudinal vibrations in a cylin...Figure 3.1-25 Geometry of a conical section.Figure 3.1-26 Geometry of an exponential section.Figure 3.2-1 Illustration of piezo‐electric effect.Figure 3.2-2 Geometry of Hooke’s law and piezo‐electric effect.Figure 3.2-3 Geometry of a 33 mode piezo‐ceramic bar.Figure 3.2-4 Geometry of a 31 mode piezo‐ceramic bar.Figure 3.2-5 Piezo‐electric ceramic material properties matrix shows relevan...Figure 3.3-1 Geometry of a rod and disk piezo‐electric ceramic element.Figure 3.3-2 Geometry of a piezo‐ceramic disk element.Figure 3.3-3 Geometry of a piezo‐ceramic disk element operating in a thickne...Figure 3.3-4 An equivalent circuit for a piezo‐electric ceramic disk transdu...Figure 3.3-5 Geometry of a piezo‐ceramic rod element.Figure 3.3-6 An equivalent circuit for a piezo‐electric ceramic bar transduc...Figure 3.3-7 Frequency constants for coupled fundamental modes in a piezo‐ce...Figure 3.3-8 Geometry for piezo‐ceramic parallelepipeds.Figure 3.3-9 Geometry for piezo‐ceramic 31 mode parallelepiped with one larg...Figure 3.3-10 Equivalent circuit for a 31 mode length expander bar with elec...Figure 3.3-11 Geometry for piezo‐ceramic 33 mode parallelepiped with one lar...Figure 3.3-12 Equivalent circuit for a 33 mode length expander bar with elec...Figure 3.3-13 Geometry for piezo‐ceramic “33” mode parallelepiped with large...Figure 3.3-14 Equivalent circuit for thickness mode vibrations in thin plate...Figure 3.3-15 Geometry for piezo‐ceramic parallelepiped with one large dimen...Figure 3.3-16 Resonances for parallelepiped of PZT‐4 with one large dimensio...Figure 3.3-17 Geometry for piezo‐ceramic parallelepiped with one small dimen...Figure 3.3-18 Resonances for parallelepiped of PZT‐4 with one small dimensio...Figure 3.3-19 Geometry for piezo‐ceramic parallelepiped with one small dimen...Figure 3.3-20 Resonances for parallelepiped of PZT‐4 with one small dimensio...Figure 3.3-21 Geometry for general piezo‐ceramic parallelepiped.Figure 3.3-22 Resonances for parallelepiped of PZT‐4 with applied field para...Figure 3.3-23 A tonpilz transducer using piezo‐electric ceramic cylinders as...Figure 3.3-24 Geometry of an axially polarized piezo‐electric ceramic cylind...Figure 3.3-25 An equivalent circuit for length longitudinal mode vibrations ...Figure 3.3-26 Frequency constants for coupled modes in a piezo‐electric, thi...Figure 3.3-27 Geometry of a radially polarized piezo‐electric ceramic cylind...Figure 3.3-28 An equivalent circuit for length longitudinal mode vibrations ...Figure 3.3-29 Frequency constants for longitudinal modes in a piezo‐electric...Figure 3.3-30 Geometry of a radially polarized piezo‐electric ceramic cylind...Figure 3.3-31 An equivalent circuit for radial vibrations in a piezo‐electri...Figure 3.3-32 Geometry of a radially polarized segmented piezo‐electric cera...Figure 3.3-33 An equivalent circuit for length longitudinal mode of a piezo‐...Figure 3.3-34 Frequency constants for longitudinal modes in a piezo‐electric...Figure 3.3-35 An equivalent circuit for radial vibrations in a piezo‐electri...Figure 3.3-36 Geometry for the spherical radiator.Figure 3.3-37 Equivalent circuit for the piezo‐ceramic sphere.
4 Chapter 4Figure 4.1‐1 The tonpilz projector transducer represents one of the more com...Figure 4.1‐2 A two‐port network for non‐piezoelectric elements.Figure 4.1‐3 A series combination of two‐port networks for non‐piezoelectric...Figure 4.1‐4 A parallel combination of two‐port networks for non‐piezoelectr...Figure 4.1‐5 A series combination of two‐port networks for piezoelectric ele...Figure 4.1‐6 Typical transducer ladder network.Figure 4.1‐7 Ladder network series termination.Figure 4.1‐8 Ladder network parallel termination.Figure 4.1‐9 Ladder network termination.Figure 4.1‐10 Ladder network termination.Figure 4.2‐1 Projector technology for different frequency ranges.Figure 4.2‐2 Geometry for the spherical radiator.Figure 4.2‐3 An equivalent circuit for the spherical projector (top) showing...Figure 4.2‐4 The ratio of in‐water to in‐air resonant frequency for a spheri...Figure 4.2‐5 Q m vs. mean diameter‐to‐wall thickness ratio.Figure 4.2‐6 Transmitting Voltage Response (TVR) for a lossless, air‐backed ...Figure 4.2‐7 An equivalent circuit for the spherical projector showing mecha...Figure 4.2‐8 The fluid‐filled spherical projector.Figure 4.2‐9 An equivalent circuit for the spherical projector showing compl...Figure 4.2‐10 The impact of a castor oil fill fluid on the resonance frequen...Figure 4.2‐11 The radially polarized cylindrical projector.Figure 4.2‐12 Equivalent circuit model for a radially polarized cylindrical ...Figure 4.2‐13 The ratio of in‐water to in‐air resonant frequency for a cylin...Figure 4.2‐14 Q m vs. mean diameter‐to‐wall thickness ratio.Figure 4.2‐15 Source level for an air‐backed cylinder projector vs. piezo‐ce...Figure 4.2‐16 Geometry of fiber‐wrapped cylinder.Figure 4.2‐17 Beam pattern for a cylinder with kL = 6π.Figure 4.2‐18 TVR for an air‐backed cylindrical projector example.Figure 4.2‐19 The radially polarized cylindrical projector with interior flu...Figure 4.2‐20 Equivalent circuit model for a radially polarized cylindrical ...Figure 4.2‐21 Fluid‐filled/air‐backed resonance frequency.Figure 4.2‐22 A squirter cylindrical radiator in a baffle.Figure 4.2‐23 Beam patterns for the radially polarized, squirter cylindrical...Figure 4.2‐24 A squirter cylindrical radiator equivalent circuit.Figure 4.2‐25 The TVR of a squirter cylindrical radiator. The in‐water reson...Figure 4.2‐26 The free‐flooded, radially polarized, cylindrical projector.Figure 4.2‐27 Radiation from the free‐flooded, radially polarized, cylindric...Figure 4.2‐28 Beam patterns for the free‐flooded, radially polarized, cylind...Figure 4.2‐29 The TVR of a radially polarized, free‐flooded cylindrical radi...Figure 4.2‐30 The free‐flooded, radially polarized, cylindrical projector wi...Figure 4.2‐31 Beam patterns for the free‐flooded, radially polarized, cylind...Figure 4.2‐32 The TVR of a radially polarized, free‐flooded cylindrical radi...Figure 4.2‐33 The barrel stave projector.Figure 4.2‐34 The barrel stave projector equivalent circuit.Figure 4.2‐35 The TVR of a circumferentially polarized, air‐backed cylindric...Figure 4.2‐36 Beam patterns for the free‐flooded, circumferentially polarize...Figure 4.2‐37 The TVR of a circumferentially polarized, free‐flooded cylindr...Figure 4.2‐38 A circumferentially polarized “striped” cylinder.Figure 4.2‐39 (Top) The electric field lines for a circumferentially polariz...Figure 4.2‐40 Geometry of electric field lines in a striped cylinder.Figure 4.2‐41 Effect of stripe spacing‐to‐cylinder thickness ratio on effect...Figure 4.2‐42 Effect of stripe width‐to‐stripe spacing ratio on effective