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Harris' Shock and Vibration Handbook Part 10

Tham khảo tài liệu 'harris' shock and vibration handbook part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 23.17 FIGURE 23.7 Time-histories of response to shock motions defined in Fig. 23.2 and corresponding shock response spectra. 23.18 CHAPTER TWENTY-THREE ing through the origin. The peak distortion of the structure smax is inversely proportional to frequency. Thus the relative displacement of the mass increases as the natural frequency decreases whereas the equivalent static acceleration has an opposite trend. ACCELERATION STEP The response of a simple structure to the acceleration step in Fig. 23.2B is found by substituting from Eq. 23.5 in Eq. 23.33 and integrating s t wn e - Wn 1 cos adt - sin 1 Z Z 1 23.42 1 - The responses s t are shown in Fig. 23.7B for Z 0 0.1 and 0.5. The response overshoots the value w0 wn2 and then oscillates about this value as a mean with diminishing amplitude as energy is dissipated by damping. An overshoot to 2w0 wn2 occurs for zero damping. A response s w0 wn2 would result from a steady application of the acceleration w0. The response maxima and minima occur at the times t in ad i 0 providing the first minimum and i 1 the first maximum. The maximum values of the relative displacement response are Smax Wn Z 1 exp - y 2 j i odd 23.43 The largest positive response occurs at the first maximum i.e. where i 1 and is shown by the solid symbols in Fig. 23.7B. The equivalent static acceleration in the positive direction is obtained by substitution of Eq. 23.43 into Eq. 23.34 with i 1 A q W Z y 1 exp - x Z A 23.44a The greatest negative response is zero it occurs at t 0 independent of the value of damping as shown by open symbols in Fig. 23.7B. Thus the equivalent static acceleration in the negative direction is A-q W Z 0 23.44b Since the equivalent static acceleration is independent of natural frequency the shock response spectrum curves shown in Fig. 23.7B are horizontal lines. The symbols shown on the shock response spectra correspond to the responses shown. The equivalent static acceleration for an undamped simple structure is twice the .