# Period and frequency period is the time usually in

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Period and Frequency. Period is the time, usually in seconds, between successive peak excursions in repeating events. Period is associated with harmonic (or sinusoidal) and repetitive time functions as shown in Figures 18a and 18b. Frequency is the reciprocal of period and is usually expressed in Hz (Hertz or cycles per second).
PAGE 21 SYSTEMS Steady State and Transient Motion. If a structural sys- tem is subjected to a continuous harmonic driving force (see Figure 18a), the resulting motion will have a constant frequency and constant maximum amplitude and is referred to as steady state motion. If a real struc- tural system is subjected to a single impulse, damping in the system will cause the motion to subside as illus- trated in Figure 19. This is one type of transient motion. Natural Frequency and Free Vibration. Natural fre- quency is the frequency at which a body or structure will vibrate when displaced and then quickly released. This state of vibration is referred to as free vibration. All structures have a large number of natural frequencies; the lowest or "fundamental" natural frequency is of most concern. Damping and Critical Damping. Damping refers to the loss of mechanical energy in a vibrating system. Damping is usually expressed as the percent of critical damping or as the ratio of actual damping to critical damping. Critical damping is the smallest amount of viscous damping for which a free vibrating system that is displaced from equilibrium and released comes to rest without oscillation. Resonance. If a frequency component of an exciting force is equal to a natural frequency of the structure, resonance will occur. At resonance, the amplitude of the motion can become very large as shown in Figure 20. Step Frequency. Step frequency is the frequency of application of a foot or feet to the floor, e.g., walking, dancing or aerobics. Harmonic . A harmonic multiple is an integer multiple of the frequency of application of a repetitive force (e.g., multiple of step frequency for human activities or mul- tiple of rotational frequency of reciprocating machin- ery). Harmonics can also refer to natural frequencies, e.g., of strings or pipes. Mode Shape. When a floor structure vibrates freely in a particular mode, it moves up and down with a cer- tain configuration or mode shape. Each natural fre- quency has a mode shape associated with it. Figure 21 shows typical mode shapes for a simple beam and for a slab/beam/girder floor system. Figure 18. Types of dynamic loading Figure 19. Decaying vibration with viscous damping Figure 20. Response to sinusoidal force
SYSTEMS PAGE 22 Modal Analysis. Modal analysis refers to a computa- tional analytical or experimental method for determin- ing the natural frequencies and mode shapes of struc- tures, as well as the responses of individual modes to a given excitation.

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