Читать книгу Introduction to Mechanical Vibrations - Ronald J. Anderson - Страница 4

1 Chapter 1Figure 1.1 A bead on a wire.Figure 1.2 Free Body Diagram of a bead on a wire.Figure 1.3 A 2D representation of the bead on a wire.Figure 1.4 A linear viscous damper.Figure 1.5 A simple pendulum.Figure 1.6 Nonlinear structural element – Linearization and effective stiffn...Figure E1.1 Figure E1.2 Figure E1.5 Figure E1.6

2 Chapter 2Figure 2.1 A mass on a spring.Figure 2.2 Independent front suspension.Figure 2.3 Assembly of the mass/spring system.Figure 2.4 FBD of the mass/spring system.Figure 2.5 A spring element.Figure 2.6 The linear spring constitutive relationship.Figure 2.7 A mass on a spring.Figure 2.8 A mass on a spring – FBD.Figure 2.9 A simple pendulum.Figure 2.10 Spring deflection due to a large angle of rotation.Figure 2.11 A body with a rotational DOF: How to deal with a spring, a dampe...Figure 2.12 Gravitational effects.Figure E2.2 Figure E2.3 Figure E2.4 Figure E2.5 Figure E2.6

3 Chapter 3Figure 3.1 Simple harmonic motion.Figure 3.2 Simple harmonic motion with a phase shift.Figure 3.3 Mass/spring/damper system.Figure 3.4 Mass/spring/damper FBD.Figure 3.5 The underdamped response.Figure 3.6 The critically damped response.Figure 3.7 The overdamped response.Figure 3.8 The root locus.Figure E3.1 Figure E3.2 Figure E3.3 Figure E3.4 Figure E3.5 Figure E3.6 Figure E3.7

4 Chapter 4Figure 4.1 SDOF system with a harmonically applied force.Figure 4.2 SDOF system with a harmonically applied force – FBD.Figure 4.3 Widely separated frequencies.Figure 4.4 The Beating phenomenon.Figure 4.5 Resonance.Figure E4.2

5 Chapter 5Figure 5.1 SDOF system with a harmonically applied force.Figure 5.2 Frequency response – SDOF undamped system.Figure 5.3 Magnification Factor ‐ SDOF undamped system.Figure 5.4 Damped SDOF system with a harmonically applied force.Figure 5.5 Magnification Factor – SDOF damped system.Figure 5.6 Damped SDOF system with harmonic base motion.Figure 5.7 Free body diagram – damped SDOF system with harmonic base motion.Figure 5.8 Magnification Factor – Harmonic base motion.Figure 5.9 Force transmissibility – Harmonic base motion.Figure 5.10 Damped SDOF system with a rotating unbalance.Figure 5.11 Free body diagram – Damped SDOF system with a rotating unbalance...Figure 5.12 Amplitude Ratio – SDOF rotating unbalance.Figure 5.13 Schematic layout of a typical piezoelectric accelerometer.Figure 5.14 Model of a typical piezoelectric accelerometer.Figure 5.15 Free body diagram of the accelerometer model.Figure 5.16 Piezoelectric accelerometer – % error.Figure E5.1 Figure E5.3 Figure E5.8 Figure E5.9

6 Chapter 6Figure 6.1 A linear viscous damper.Figure 6.2 Test setup for energy removed by a linear viscous damper.Figure 6.3 Hysteresis loop for a linear viscous damper.Figure 6.4 Experimental hysteresis loops for two shock absorbers.Figure 6.5 Friction force magnitude and direction.Figure 6.6 A system with Coulomb friction.Figure 6.7 Response with Coulomb friction.Figure 6.8 The underdamped response.Figure E6.1 Figure E6.3

7 Chapter 7Figure 7.1 A 2DOF undamped system.Figure 7.2 Free body diagram for the 2DOF undamped system.Figure 7.3 First mode shape for the 2DOF undamped system.Figure 7.4 Second mode shape for the 2DOF undamped system.Figure 7.5 Another sample system.Figure 7.6 A 2DOF undamped, forced, system.Figure 7.7 A model of a machine experiencing large amplitudes.Figure 7.8 The machine with the vibration absorber mounted.Figure 7.9 The cart and pendulum system.Figure 7.10 The cart and pendulum system – FBD.Figure E7.1Figure E7.2Figure E7.3Figure E7.5Figure E7.6Figure E7.7

8 Chapter 8Figure 8.1 A taut string.Figure 8.2 The first five string modes.Figure 8.3 Deflections of a uniform beam.Figure 8.4 A beam element.Figure 8.5 A cantilever beam.Figure 8.6 The first three cantilever beam modes.

9 Chapter 9Figure 9.1 A beam element.Figure 9.2 A non‐uniform beam.Figure 9.3 An elastic rod.Figure 9.4 An elastic rod element.Figure 9.5 An element of the element.Figure 9.6 versus for the element.Figure 9.7 The rod element with nodal forces applied.Figure 9.8 A statically loaded rod modeled with one element.Figure 9.9 The velocity of the element of the element.Figure 9.10 Two rod elements in an assembly.Figure 9.11 Free body diagrams of the two rod elements.Figure 9.12 The global mass matrix.Figure 9.13 The global stiffness matrix.Figure 9.14 The two‐noded beam element.Figure 9.15 versus for the element.Figure 9.16 Node and element numbering.Figure 9.17 Node and element numbering.Figure 9.18 Externally applied forces and moments.Figure 9.19 The harmonically varying applied load.Figure E9.3 Figure E9.4

10 Chapter 10Figure 10.1 An inerter implementation.Figure 10.2 A screw.Figure 10.3 The inerter symbol. Figure 10.4 Single degree of freedom system with an inerter.Figure 10.5 Free Body Diagram for the single degree of freedom system with a...Figure 10.6 Two degree of freedom system with inerters.Figure 10.7 Simplified two degree of freedom system with an inerter.Figure 10.8 A single degree of freedom system with harmonic ground motion.Figure 10.9 Free body diagram for the single degree of freedom system with h...Figure 10.10 A single degree of freedom system with an inerter and harmonic ...Figure 10.11 Free body diagram for the single degree of freedom system with ...

11 Chapter 11Figure 11.1 A measured variable plotted versus time.Figure 11.2 The square of plotted versus time.Figure 11.3 The example function, , plotted versus time.Figure 11.4 The DFT amplitudes of the example function, , plotted versus fr...Figure 11.5 Aliasing.Figure 11.6 The folding frequency.Figure 11.7 Aliased DFT results.Figure 11.8 The DFT for the first example.Figure 11.9 The DFT for the second example.Figure 11.10 CFT approximation to the square wave.Figure 11.11 The Hanning window.Figure 11.12 The data from Equation 11.83.Figure 11.13 The windowed data.Figure 11.14 The DFT for the second example with windowing.Figure 11.15 The DFT before downsampling.Figure 11.16 The DFT after downsampling.Figure 11.17 The time series before and after digital filtering.Figure 11.18 The DFT after decimating.Figure 11.19 A low‐pass filter circuit.Figure 11.20 Low‐pass filter frequency response in dB on a logarithmic scale...Figure 11.21 Low‐pass filter frequency response on a linear scale.Figure 11.22 Exponential moving average smoothed data.Figure 11.23 Exponential moving average DFT.Figure 11.24 Low‐pass digital filter frequency response.Figure 11.25 Low‐pass filter frequency response near the cut‐off frequency.Figure 11.26 Noisy time signal.Figure 11.27 Noisy time signal zoomed.Figure 11.28 DFT – 1 average.Figure 11.29 DFT – 10 averages.Figure 11.30 DFT – 20 averages.Figure E11.5

12 Chapter 12Figure 12.1 A mass on a spring.Figure 12.2 A spring connecting two masses.Figure 12.3 Lift and drag in a wind tunnel.Figure 12.4 Typical lift and drag forces versus angle of attack.Figure 12.5 A suspended airfoil in steady flow.Figure 12.6 Free body diagram of the airfoil.Figure 12.7 Representation of a von Karman vortex street in a wake.Figure 12.8 Helical strakes on tall chimneys.Figure 12.9 A railway truck supported by its two wheelsets.Figure 12.10 Parameters for a railway wheelset.Figure 12.11 Back‐to‐back cones forming a railway wheelset.Figure 12.12 Wheelset degrees of freedom.Figure 12.13 Creep forces.Figure 12.14 Wheelset free body diagram.Figure 12.15 Wheelset instability.Figure 12.16 System with a rigid body mode.Figure 12.17 The three modes.Figure 12.18 A spring/mass system.Figure 12.19 The model of a double wishbone suspension.Figure E12.1 Figure E12.3

13 Appendix AFigure A.1 Three data points and two Least Squares curve fits.

14 Appendix BFigure B.1 Parallel Axis Theorem.