Foreword to series |
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xi | |
Introduction |
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xv | |
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xvii | |
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1 | (40) |
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Static effects/dynamic effects |
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1 | (2) |
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Behaviour under dynamic load (impact) |
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3 | (3) |
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5 | (1) |
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Elements of a mechanical system |
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6 | (26) |
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6 | (1) |
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7 | (1) |
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7 | (1) |
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Equivalent spring constant |
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8 | (3) |
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Stiffness of various parts |
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11 | (3) |
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14 | (1) |
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15 | (1) |
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15 | (2) |
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17 | (1) |
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18 | (5) |
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23 | (1) |
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24 | (1) |
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25 | (1) |
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26 | (1) |
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27 | (2) |
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Static modulus of elasticity |
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29 | (1) |
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Dynamic modulus of elasticity |
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30 | (2) |
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32 | (9) |
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32 | (1) |
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33 | (1) |
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34 | (1) |
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35 | (2) |
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37 | (1) |
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Linear one-degree-of-freedom mechanical systems |
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37 | (1) |
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Setting an equation for n-degrees-of-freedom lumped parameter mechanical system |
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38 | (3) |
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Response of a linear single-degree-of-freedom mechanical system to an arbitrary excitation |
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41 | (48) |
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41 | (2) |
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Excitation defined by force versus time |
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43 | (4) |
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Excitation defined by acceleration |
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47 | (2) |
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49 | (4) |
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Excitation defined by a force on a mass or by an acceleration of support |
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49 | (1) |
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Excitation defined by velocity or displacement imposed on support |
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50 | (3) |
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Solution of the differential equation of movement |
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53 | (10) |
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53 | (1) |
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53 | (1) |
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General expression for response |
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53 | (2) |
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55 | (1) |
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56 | (1) |
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56 | (1) |
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57 | (1) |
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General expression for response |
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57 | (1) |
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58 | (1) |
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59 | (1) |
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60 | (2) |
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62 | (1) |
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Natural oscillations of a linear single-degree-of-freedom system |
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63 | (26) |
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64 | (4) |
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68 | (3) |
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71 | (1) |
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71 | (4) |
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Points of contact of the response with its envelope |
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75 | (1) |
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Reduction of amplitude: logarithmic decrement |
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75 | (8) |
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Number of cycles for a given reduction in amplitude |
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83 | (2) |
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Influence of damping on period |
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85 | (1) |
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Particular case of zero damping |
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86 | (2) |
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88 | (1) |
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Impulse and step responses |
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89 | (42) |
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Response of a mass-spring system to a unit step function (step or indicial response) |
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89 | (13) |
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Response defined by relative displacement |
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89 | (1) |
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89 | (4) |
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93 | (2) |
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First excursion of response to unit value |
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95 | (2) |
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Response defined by absolute displacement, velocity or acceleration |
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97 | (1) |
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97 | (1) |
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98 | (3) |
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First passage of the response by the unit value |
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101 | (1) |
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Response of a mass-spring system to a unit impulse excitation |
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102 | (10) |
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Response defined by relative displacement |
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102 | (1) |
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102 | (4) |
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106 | (2) |
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Response defined by absolute parameter |
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108 | (1) |
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108 | (2) |
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110 | (2) |
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Use of step and impulse responses |
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112 | (7) |
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Transfer function of a linear one-degree-of-freedom system |
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119 | (11) |
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119 | (2) |
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Calculation of H(h) for relative response |
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121 | (1) |
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Calculation of H(h) for absolute response |
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122 | (3) |
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Other definitions of transfer function |
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125 | (1) |
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125 | (1) |
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125 | (1) |
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126 | (1) |
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126 | (4) |
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Measurement of transfer function |
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130 | (1) |
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131 | (12) |
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131 | (8) |
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131 | (1) |
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132 | (1) |
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Mean square value -- rms value |
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133 | (2) |
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135 | (3) |
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138 | (1) |
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Periodic and sinusoidal vibrations in the real environment |
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139 | (1) |
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Sinusoidal vibration tests |
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139 | (4) |
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Response of a linear single-degree-of-freedom mechanical system to a sinusoidal excitation |
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143 | (54) |
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General equations of motion |
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144 | (11) |
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144 | (3) |
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147 | (2) |
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149 | (1) |
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150 | (2) |
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Response to periodic excitation |
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152 | (1) |
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Application to calculation for vehicle suspension response |
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153 | (2) |
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155 | (4) |
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155 | (4) |
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159 | (1) |
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159 | (2) |
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159 | (1) |
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160 | (1) |
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161 | (14) |
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Variations of velocity amplitude |
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162 | (1) |
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162 | (2) |
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164 | (1) |
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Energy dissipated during a cycle |
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165 | (3) |
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168 | (2) |
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170 | (4) |
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Variations in velocity phase |
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174 | (1) |
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175 | (14) |
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Variation in response amplitude |
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175 | (1) |
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Dynamic amplification factor |
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175 | (4) |
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Width of H(h) for HRD = HRDmax/√2 |
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179 | (1) |
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180 | (9) |
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Responses, y/xm, y/xm, y/xm and FT/Fm |
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189 | (5) |
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Movement transmissibility |
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189 | (1) |
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190 | (2) |
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192 | (2) |
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Graphical representation of transfer functions |
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194 | (3) |
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197 | (30) |
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Damping observed in real structures |
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197 | (1) |
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Linearization of non-linear hysteresis loops -- equivalent viscous damping |
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198 | (4) |
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202 | (8) |
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Damping force proportional to the power b of the relative velocity |
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202 | (1) |
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203 | (2) |
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Damping force proportional to the square of velocity |
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205 | (1) |
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Damping force proportional to the square of displacement |
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206 | (1) |
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Structural or hysteretic damping |
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207 | (1) |
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Combination of several types of damping |
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208 | (1) |
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Validity of simplification by equivalent viscous damping |
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209 | (1) |
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Measurement of damping of a system |
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210 | (14) |
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Measurement of amplification factor at resonance |
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210 | (2) |
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212 | (1) |
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Decreased rate method (logarithmic decrement) |
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213 | (7) |
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Evaluation of energy dissipation under permanent sinusoidal vibration |
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220 | (4) |
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224 | (1) |
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224 | (3) |
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227 | (24) |
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227 | (2) |
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227 | (1) |
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Octave -- number of octaves in a frequency interval (f1, f2) |
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228 | (1) |
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228 | (1) |
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`Swept sine' vibration in the real environment |
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229 | (1) |
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`Swept sine' vibration in tests |
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229 | (2) |
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Origin and properties of main types of sweepings |
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231 | (20) |
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231 | (3) |
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Case no1: sweep where time Δt spent in each interval Δf is constant for all values of f0 |
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234 | (11) |
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Case no2: sweep with constant rate |
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245 | (1) |
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Case no3: sweep ensuring a number of identical cycles ΔN in all intervals Δf (delimited by the half-power points) for all values of f0 |
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246 | (5) |
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Response of a one-degree-of-freedom linear system to a swept sine vibration |
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251 | (30) |
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251 | (1) |
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Response of a linear one-degree-of-freedom system to a swept sine excitation |
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252 | (17) |
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Methods used for obtaining response |
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252 | (1) |
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Convolution integral (or Duhamel's integral) |
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253 | (2) |
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Response of a linear one-degree-of-freedom system to a linear swept sine excitation |
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255 | (10) |
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Response of a linear one-degree-of-freedom system to a logarithmic swept sine |
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265 | (4) |
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Choice of duration of swept sine test |
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269 | (1) |
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270 | (1) |
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271 | (10) |
Appendix. Laplace transformations |
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281 | (14) |
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281 | (1) |
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282 | (3) |
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282 | (1) |
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A.2.2. Shifting theorem (or time displacement theorem) |
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282 | (1) |
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A.2.3. Complex translation |
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283 | (1) |
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A.2.4. Laplace transform of the derivative of f(t) with respect to time |
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283 | (1) |
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A.2.5. Derivative in the p domain |
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283 | (1) |
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A.2.6. Laplace transform of the integral of a function f(t) with respect to time |
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284 | (1) |
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A.2.7. Integral of the transform F(p) |
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284 | (1) |
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284 | (1) |
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A.2.9. Theorem of damping or rule of attenuation |
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285 | (1) |
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A.3 Application of Laplace transformation to the resolution of linear differential equations |
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285 | (2) |
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A.4 Calculation of inverse transform: Mellin-Fourier integral or Bromwich transform |
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287 | (2) |
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289 | (3) |
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A.6 Generalized impedance -- the transfer function |
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292 | (3) |
Vibration tests: a brief historical background |
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295 | (2) |
Bibliography |
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297 | (12) |
Index |
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309 | |