Dynamics: Resonance

Avoidance of resonance - design of structures used for pop concerts

Figure 16-14: At a pop concert

British Standard BS 6399: Part 1, Loading for Buildings [16.7], introduced in September 1996, included a new section on synchronised dance loading. It stated that any structure that might be subjected to this form of loading should be designed in one of two ways: to withstand the anticipated dynamic loads or to avoid significant resonance effects. The first method requires dynamic analysis to assess the structural response to the loading in order to calculate a safety margin. The second method requires that the structure should be designed to be sufficiently stiff so that the lowest relevant natural frequency of the structure is above the range of load frequencies considered. The second approach is simpler and only requires the calculation of natural frequencies. However, both approaches need knowledge of the load frequencies.

Dance-type activities, such as keep-fit exercises, aerobics and audience movements at pop-concerts, are more common now than ever before. These activities are likely to be held on grandstands, dance floors and in sports centres. Therefore, the use and/or design of these structures should consider the effect of the human induced dance-type loads. Fig.16-14 shows a pop concert where people moved, jumped, bobbed and swayed, in time to the music.

Dance is movement with rhythmic steps and actions, usually to accompanying music. Efforts have been made to study dance-type loads since prediction of the response of a structure subject to this loading requires an understanding of the loading. Dance-type loads are functions of the type of dance activity, the density and distribution of the dancers, the frequency of the music, load factors and the dynamic crowd effect.

There are many different types of dancing and a wide range of beat frequencies for dance music, however, dance frequencies tend to be in the range of 1.5-3.5Hz for individuals and 1.5-2.8Hz for groups of people.

Fig.16-15: Structural response to the music beat frequency at a pop concert [16.8]

Fig. 16-15 shows an autospectrum obtained from accelerometers monitoring vertical motions of a grandstand during a pop concert [16.8]. The vertical axis indicates the normalised acceleration squared per Hz, while the horizontal axis shows frequency. It can be seen that the frequencies corresponding to the peaks of responses are the beat frequency of the music and integer multiples of the beat frequency. This phenomenon has been observed in a number of measurements taken during pop concerts and can be explained theoretically. As spectators at pop concerts move with the music beat, the frequency of dance-type loads can be determined from the beat frequency of music played on these occasions. The beat frequencies of 210 modern songs have been determined [16.9].

Fig.16-16: Frequency distribution of the 210 modern songs [16.9]

The 210 songs consisted of 30 songs from each of the 1960's, the 1970's and the 1980's, and 120 songs from the 1990's. The 1990s music was further classified into four main types, dance, indie, pop and rock, with 30 songs for each group. All the songs selected had been popular in their time and thus provided a good sample of popular music. The frequency distribution of the 210 songs surveyed is given in Fig. 16-16. It can be seen that the majority of songs (202 out of 210) are in the frequency range of 1.0 - 2.8 Hz.

Human loading, such as jumping, bobbing and walking, contains several harmonic components with the load frequency, two times the frequency, three times the frequency and so on. However, only the first two or three components are significant and need to be considered in design. For example, if the load or music frequency is not larger than 2.8 Hz and the first three load components are considered for a floor subject to jumping type loading, the highest frequency in the load to be considered will not be larger than 2.8 x 3 =8.4 Hz. This corresponds to the threshold value of natural frequency in BS6399: Part 1 of 8.4 Hz in the vertical direction, for which no dynamic analysis of the structure is required [16.7].

The video chip shows how severe the vibration of a grandstand is which was incluced by spectators jumping during a football match.

(Courtesy of Prof. M Kasperski, Ruhi-University Bochum, Germany)
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