Human Body Models in Structural Vibration

The body model of a standing person in the vertical direction

The tests demonstrate that a standing person acts as a mass-spring-damper rather than an inert mass in vertical structural vibration while a walking or jumping person acts solely as loading on structures.

Fig. 19-6: Test set-up for identifying human body models in vertical structural vibration

Fig. 19-6a shows a simply supported reinforced concrete beam with an accelerometer placed at the centre of the beam. Striking the middle of the beam vertically with a rubber hammer caused vertical vibrations of the beam. The acceleration-time history recorded from the beam and the frequency spectrum abstracted from the record are shown in Figs. 19-7a and 19-7b. It can be observed that the simply supported beam has a vertical natural frequency of 18.7 Hz and the system has a very small damping ratio shown by the decay of the free vibrations which lasts more than eight seconds.

Fig. 19-7: Measurements of the identification tests in vertical directions

A person then stood on the centre of the beam as shown in Fig. 19-6b and a human-structure system was created. A rubber hammer was again used to induce vibrations. Figs. 19-7c and 19-7d show the acceleration-time history and frequency spectrum of the beam with the person. Comparing the two sets of measurements in Fig. 19-7 shows that:

• the measured vertical natural frequency of the beam with the person was 20.0 Hz which is larger than that of the beam alone (Figs 19-7b and 19-7d). This observation coincides with Relationship 3, i.e. .
• the beam with the person possesses a much larger damping ratio than the beam alone as the free vibration of the beam with the person decays very quickly (Fig. 19-7c). This is also evident from Fig. 19-7d as the peak in the spectrum of the beam with the person has a much wider spread than that of the beam alone (Fig. 19-7a).

Further tests were conducted to identify the effects qualitatively of human bodies in structural vibration, including tests on the beam with a dead weight and the beam occupied by a person who moved, both jumping and walking. The measured frequencies for these cases are listed in Table 19-1, which shows:

• the dead weights, which were placed centrally on the beam for two tests, reduced the natural frequency as expected. This can be accurately predicted using Eq. 19-1.
• the test with the person standing on the beam showed an increase in the measured natural frequency. This observation cannot be explained using the inert mass model or Eq. 19-1. Thus it is clear that the standing human body does not act as an inert mass in structural vibration.
• the measured frequency for the vibrations when the person sat on a stool on the beam was also higher than that of the beam alone.
• significant damping contributions from the human whole-body were observed for both standing and sitting positions, as can be appreciated from Fig. 19-7 for the standing person.
• jumping and walking also provided interesting results in that they did not affect either natural frequency or damping. The unchanged system characteristics would appear to be because the moving human body is not vibrating with the beam.

Table 19-1: Natural frequencies observed on the beam [19.2]

Two concepts can be identified from the above tests:

• A stationary person, e.g. sitting or standing, acts as a mass-spring-damper rather than as an inert mass in structural vibration.
• A walking or jumping person acts solely as loading on structures.

The body model of a standing person in the lateral directions

The tests demonstrate that a standing person acts as a mass-spring-damper rather than an inert mass in lateral structural vibration [19.8].

Fig. 19-8: Test set-up for identifying human body models in lateral structural vibration

Fig. 19-8a shows a single degree-of-freedom rig for both vertical and horizontal directions used for identification tests of human body models in structural vibration. The test rig consists of two circular top plates bolted together, three identical springs supporting the plates and a thick base plate. The test procedure is simple and is the same as that conducted in Section 19.3.1. The free vibration test of the test rig alone was first conducted using a rubber hammer to generate an impact on the rig in the lateral direction. Then a person stood on the test rig and an impact was applied in the lateral direction parallel to the shoulder of the test person as shown in Fig. 19-8b. Fig. 19-9 shows the displacement-time histories and the corresponding spectra of the test rig alone and the human-occupied test rig in the lateral directions. It can be noted from Fig. 19-9 that:

Fig. 19-9: Measurements of the identification tests in lateral directions

• The standing body contributes significant damping to the test rig in the lateral direction (Figs. 19-9a and 19-9c).
• There is one single resonance frequency recorded on the test rig alone (Fig. 19-9b) but two resonance frequencies are observed from the human-structure system in the lateral direction (Fig. 19-9d).
• The single resonance frequency of the test rig alone is between the two resonance frequencies of the human occupied test rig (Relationship 3 in Section 19.2.2)
• Human whole body damping in the lateral directions is large but less than that in the vertical direction as shown by the vibration time history of the human-structure system in the lateral directions which is longer than that in the vertical directions (Fig. 19-7c), although the test structures are different.

The experimental results of the identification tests conducted in the lateral directions clearly indicate that a standing human body acts in a similar manner to a mass-spring-damper rather than an inert mass in lateral structural vibration.

Further identification tests have been conducted on the same test rig with a bouncing person who maintains contact with the structure. It is observed that:

• A bouncing person acts as both loading and a mass-spring-damper on structures in vertical structural vibration.
• The interaction between a bouncing person and the test rig is less significant than that between a standing person and the test rig.

The effect of stationary spectators on a grandstand

Fig. 19-11: Response spectra of the North Stand, Twickenham

Measurements were taken to determine the dynamic behaviour of the North Stand (Fig. 19-10) at the Rugby Football Union ground at Twickenham. The grandstand has three tiers and two of them are cantilevered. Dynamic tests were performed on the roof and cantilevered tiers of the stand, with further measurements of the response of the middle-cantilevered tier to dynamic loads induced by spectators during a rugby match [19.2].

Spectra for the empty and full grandstand are given in Fig 19-11. Fig. 19-11a shows a clearly defined fundamental mode of vibration for the empty structure. Instead of the expected reduction in natural frequency of the stand as the crowd assembled, the presence of the spectators appeared to result in the single natural frequency changing into a two natural frequencies (Fig. 19-11b). Fig. 19-11 shows that the dynamic characteristics of the grandstand changed significantly when a crowd was involved and that the structure and the crowd interacted. This pattern was also noted in two other locations of the stand where measurements were taken.

Comparing the spectra for the empty stand and fully occupied stand, three significant phenomena are apparent:

• an additional frequency was observed in the occupied stand.
• the natural frequency of the empty stand is between the two natural frequencies of the occupied stand.
• the damping increases significantly when people were presented.

Considering human bodies simply as masses cannot explain the above observations. The observations suggest that the crowd acted as a mass-spring-damper rather than just as a mass. When the crowd is modelled as a single degree-of-freedom system, the structure and the crowd form a two-degree-of-freedom system. Based on this model, the above observations can be explained. These observations complement the laboratory tests described in Section 19.3.

Calculation of the natural frequencies of a grandstand

It is common for a grandstand, either permanent or temporary, to be full of spectators during a sports event or a pop concert as shown in Fig. 19-12. In this situation, the human mass can be of the same order as the mass of the structure. When calculating the natural frequencies of a grandstand for design purposes, it is necessary to consider how the human mass should be represented. It is recommended in BS6399: Part 1: Loading for Buildings [19.6] and the Interim Guidance [19.7] that empty structures should be used for calculating their natural frequencies. i.e., the human mass should not be included. This is because the worst situation for design consideration is when people move rather than when people are stationary. Therefore engineers will not under-estimate the natural frequencies of grandstands through adding the mass of a crowd to the structural mass.

Dynamic response of a structure used at pop concerts

During a pop concert, it is rare that everyone moves in the same way following the music. Some people will move enthusiastically, jumping or bouncing, some will sway and some will remain stationary, either sitting or standing. Those who are stationary will provide significant damping to the structure as observed from the previous demonstrations and thus will alter the dynamic characteristics of the structure and effectively damp the level of vibration induced by the movements of the others. This in part explains why the predicted structural vibrations induced by human movements, where stationary people are not considered, are often much larger than vibrations measured on site.

The effect of stationary people in structural vibration has been considered in the new version of the Interim Design Guidance [19.7] for predicting the response of grandstands used for pop concerts.

Indirect measurement of the fundamental natural frequency of a standing person

If a stationary person should be modelled as a single degree-of-freedom (SDOF) system in structural vibration, what are the natural frequency, damping ratio and the modal mass of the human SDOF system?

The natural frequency of a human body cannot be obtained directly using traditional methods and tools of structural dynamics, such as sensors (accelerometers) which cannot be conveniently mounted on a human body. However, a method has been developed to estimate the natural frequency of a standing person by experiment without touching the person whilst still using the methods of structural dynamics.

A simple formula can be derived based on the three frequency relationships derived in Section 19.2.2 using the measurements of the natural frequency of the empty structure and the resonance frequency/frequencies of the human-structure system as demonstrated in Section 19.3. For example, the demonstration given in Section 19.3.2 shows the natural frequency of the test rig alone of 6.10 Hz and the two resonance frequencies of the human-rig system of 5.20 Hz and 7.30 Hz respectively in Figure 19-9. Using Eq. 19-8 gives an estimated natural frequency of the standing person of 6.22 Hz in the lateral direction. It should be noted that this is an approximation because:

• the measurements in Fig. 19-9d are the resonance frequencies which include the effect of human body damping while Eq. 19-8 does not consider any effect of damping.
• the simple mass-spring-damper model is good enough for identifying the models of human body in structural vibration qualitatively. However, this body model is developed on fixed ground rather than on a vibrating structure.

The indirect measurement method needs to be improved; nevertheless it uses the methods of structural dynamics to study the biomechanics properties of a human body, which is fundamentally different from the methods of body biomechanics where shaking tables are used.

Indirect measurement of the fundamental natural frequency of a chicken

Six hundred million chickens are consumed each year in the UK. It has been observed sometimes during transportation that healthy chickens become ill and are unable to stand. Possible causes for this have been found to arise from the effect of resonance associated with the transportation.

In order to prevent the resonance in which a natural frequency of the truck matches the body natural frequency of chickens, the natural frequency of a typical chicken needs to be identified. When studying body biomechanics to determine the characteristics of a human body, a subject is asked to sit or to stand on a shaking table for a short period of vibration. However, this technique cannot be applied to studying the natural frequency of a chicken, as the chicken will fly off when the shaking table moves.

The method developed for indirectly measuring human body natural frequencies could be used to obtain the natural frequency of a chicken. Fig. 19-13 shows a chicken perched on a wooden beam. A slight impact on the beam can generate vibration of the beam and the chicken, which will not cause anxiety in the chicken. When the frequencies of the bare beam and the beam with the chicken are measured, the natural frequency of the chicken can be estimated from the two measurements and a simple equation.