Cover -- Title Page -- Copyright -- Contents -- Foreword to Series -- Introduction -- List of Symbols -- Chapter 1. The Need -- 1.1. The need to carry out studies into vibrations and mechanical shocks -- 1.2. Some real environments -- 1.2.1. Sea transport -- 1.2.2. Earthquakes -- 1.2.3. Road vibratory environment -- 1.2.4. Rail vibratory environment -- 1.2.5. Propeller airplanes -- 1.2.6. Vibrations caused by jet propulsion airplanes -- 1.2.7. Vibrations caused by turbofan aircraft -- 1.2.8. Helicopters -- 1.3. Measuring vibrations and shocks -- 1.4. Filtering -- 1.4.1. Definitions -- 1.4.2. Digital filters -- 1.5. Digitizing the signal -- 1.5.1. Signal sampling frequency -- 1.5.2. Quantization error -- 1.6. Reconstructing the sampled signal -- 1.7. Characterization in the frequency domain -- 1.8. Elaboration of the specifications -- 1.9. Vibration test facilities -- 1.9.1. Electro-dynamic exciters -- 1.9.2. Hydraulic actuators -- 1.9.3. Test Fixtures -- Chapter 2. Basic Mechanics -- 2.1. Basic principles of mechanics -- 2.1.1. Principle of causality -- 2.1.2. Concept of force -- 2.1.3. Newton's first law (inertia principle) -- 2.1.4. Moment of a force around a point -- 2.1.5. Fundamental principle of dynamics (Newton's second law) -- 2.1.6. Equality of action and reaction (Newton's third law) -- 2.2. Static effects/dynamic effects -- 2.3. Behavior under dynamic load (impact) -- 2.4. Elements of a mechanical system -- 2.4.1. Mass -- 2.4.2. Stiffness -- 2.4.3. Damping -- 2.4.4. Static modulus of elasticity -- 2.4.5. Dynamic modulus of elasticity -- 2.5. Mathematical models -- 2.5.1. Mechanical systems -- 2.5.2. Lumped parameter systems -- 2.5.3. Degrees of freedom -- 2.5.4. Mode -- 2.5.5. Linear systems -- 2.5.6. Linear one-degree-of-freedom mechanical systems -- 2.6. Setting an equation for n degrees-of-freedom lumped parameter mechanical system.

2.6.1. Lagrange equations -- 2.6.2. D'Alembert's principle -- 2.6.3. Free-body diagram -- Chapter 3. Response of a Linear One-Degree-of-Freedom Mechanical System to an Arbitrary Excitation -- 3.1. Definitions and notation -- 3.2. Excitation defined by force versus time -- 3.3. Excitation defined by acceleration -- 3.4. Reduced form -- 3.4.1. Excitation defined by a force on a mass or by an acceleration of support -- 3.4.2. Excitation defined by velocity or displacement imposed on support -- 3.5. Solution of the differential equation of movement -- 3.5.1. Methods -- 3.5.2. Relative response -- 3.5.3. Absolute response -- 3.5.4. Summary of main results -- 3.6. Natural oscillations of a linear one-degree-of-freedom system -- 3.6.1. Damped aperiodic mode -- 3.6.2. Critical aperiodic mode -- 3.6.3. Damped oscillatory mode -- Chapter 4. Impulse and Step Responses -- 4.1. Response of a mass-spring system to a unit step function (step or indicial response) -- 4.1.1. Response defined by relative displacement -- 4.1.2. Response defined by absolute displacement, velocity or acceleration -- 4.2. Response of a mass-spring system to a unit impulse excitation -- 4.2.1. Response defined by relative displacement -- 4.2.2. Response defined by absolute parameter -- 4.3. Use of step and impulse responses -- 4.4. Transfer function of a linear one-degree-of-freedom system -- 4.4.1. Definition -- 4.4.2. Calculation of H(h) for relative response -- 4.4.3. Calculation of H(h) for absolute response -- 4.4.4. Other definitions of the transfer function -- 4.5. Measurement of transfer function -- Chapter 5. Sinusoidal Vibration -- 5.1. Definitions -- 5.1.1. Sinusoidal vibration -- 5.1.2. Mean value -- 5.1.3. Mean square value - rms value -- 5.1.4. Periodic vibrations -- 5.1.5. Quasi-periodic signals -- 5.2. Periodic and sinusoidal vibrations in the real environment.

5.3. Sinusoidal vibration tests -- Chapter 6. Response of a Linear One-Degree-of-Freedom Mechanical System to a Sinusoidal Excitation -- 6.1. General equations of motion -- 6.1.1. Relative response -- 6.1.2. Absolute response -- 6.1.3. Summary -- 6.1.4. Discussion -- 6.1.5. Response to periodic excitation -- 6.1.6. Application to calculation for vehicle suspension response -- 6.2. Transient response -- 6.2.1. Relative response -- 6.2.2. Absolute response -- 6.3. Steady state response -- 6.3.1. Relative response -- 6.3.2. Absolute response -- 6.4. Responses lω0ż/ẍml, lω0z/ẋml and √kmż/fm -- 6.4.1. Amplitude and phase -- 6.4.2. Variations of velocity amplitude -- 6.4.3. Variations in velocity phase -- 6.5. Responses kz/Fm and ω20 z/ẍm -- 6.5.1. Expression for response -- 6.5.2. Variation in response amplitude -- 6.5.3. Variations in phase -- 6.6. Responses y/xm, ẏ/ẋm, ÿ/ẍm and Ft/Fm -- 6.6.1. Movement transmissibility -- 6.6.2. Variations in amplitude -- 6.6.3. Variations in phase -- 6.7. Graphical representation of transfer functions -- 6.8. Definitions -- 6.8.1. Compliance - stiffness -- 6.8.2. Mobility - impedance -- 6.8.3. Inertance - mass -- Chapter 7 Non-viscous Damping -- 7.1. Damping observed in real structures -- 7.2. Linearization of non-linear hysteresis loops - equivalent viscous damping -- 7.3. Main types of damping -- 7.3.1. Damping force proportional to the power b of the relative velocity -- 7.3.2. Constant damping force -- 7.3.3. Damping force proportional to the square of velocity -- 7.3.4. Damping force proportional to the square of displacement -- 7.3.5. Structural or hysteretic damping -- 7.3.6. Combination of several types of damping -- 7.3.7. Validity of simplification by equivalent viscous damping -- 7.4. Measurement of damping of a system -- 7.4.1. Measurement of amplification factor at resonance.

7.4.2. Bandwidth or √2 method -- 7.4.3. Decreased rate method (logarithmic decrement) -- 7.4.4. Evaluation of energy dissipation under permanent sinusoidal vibration -- 7.4.5. Other methods -- 7.5. Non-linear stiffness -- Chapter 8. Swept Sine -- 8.1. Definitions -- 8.1.1. Swept sine -- 8.1.2. Octave - number of octaves in frequency interval (f1, f2) -- 8.1.3. Decade -- 8.2. "Swept sine" vibration in the real environment -- 8.3. "Swept sine" vibration in tests -- 8.4. Origin and properties of main types of sweepings -- 8.4.1. The problem -- 8.4.2. Case 1: sweep where time Δt spent in each interval Δf is constant for all values of f0 -- 8.4.3. Case 2: sweep with constant rate -- 8.4.4. Case 3: sweep ensuring a number of identical cycles ΔN in all intervals Δf (delimited by the half-power points) for all values of f0 -- Chapter 9. Response of a Linear One-Degree-of-Freedom System to a Swept Sine Vibration -- 9.1. Influence of sweep rate -- 9.2. Response of a linear one-degree-of-freedom system to a swept sine excitation -- 9.2.1. Methods used for obtaining response -- 9.2.2. Convolution integral (or Duhamel's integral) -- 9.2.3. Response of a linear one-degree-of freedom system to a linear swept sine excitation -- 9.2.4. Response of a linear one-degree-of-freedom system to a logarithmic swept sine -- 9.3. Choice of duration of swept sine test -- 9.4. Choice of amplitude -- 9.5. Choice of sweep mode -- Appendix. Laplace Transformations -- Vibration Tests: a Brief Historical Background -- Bibliography -- Index -- Summary of Other Volumes in the Series.