F 2PV M

where f = frequency, cycles/s or Hz

K = EA/L = spring stiffness, lb/in (N/mm) E = Young's modulus of elasticity of support beam, lb/in2 (Pa) A = cross-sectional area of support beam, in2 (mm2) L = length of support beam in (mm) M = mass lb • s2/in (N • s2/mm)

/////////// FIGURE 8 Single-degree-of-freedom oscillator

With this idealization, the frequency of the SDF oscillator may be varied by changing the length of the beam element and maintaining E, A, and M constant (Figure 8). A horizontal degree of freedom would be used in conjunction with beam bending and shearing.

Damping effects are simulated by a dashpot, which can be assigned different damping ratios. Although there is little effect on the frequency of the SDF oscillator when the dash-pot is assigned damping ratios below 10 or 15% of critical damping, there is a significant effect when higher values are used. Thus, if the dashpot is assigned 100% of critical damping, the oscillator will behave as a rigid body, duplicating, without amplification, the support input motion.

Test Response Spectrum (TRS) The TRS is a response spectrum that is either theoretically constructed or derived using spectrum analysis based on the actual motion of the shake table (during dynamic testing).

Time History Analysis The time history analysis is an analysis performed in the time domain using time history vibratory input. A direct integration or modal analysis may be performed.

Time History of Acceleration The time history of acceleration is a variation of acceleration as a function of time during the postulated duration of the seismic event.

Zero Period Acceleration (ZPA) The ZPA is a response acceleration at frequencies above 33 Hz.

Although these definitions will facilitate the understanding of the seismic considerations discussed herein, the reader is encouraged to review the works listed at the end of this subsection for a more complete list of terms and definitions used in the process of dynamic qualifications.

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