Fore-and-aft apparent mass of the back: Nonlinearity and variation with vertical location

The dynamic interaction between the human back and a backrest is complex: the forces at the back–backrest interface depend on the dynamic characteristics of both the back and the backrest, which vary with location over the backrest. This experimental study was designed to investigate the variation in the ratio of the force to acceleration (referred to as the apparent mass) at the back associated with variations in the vertical position and the magnitude of fore-and-aft vibration. Twelve male subjects were exposed to random fore-and-aft vibration in the frequency range 0.25–10 Hz at five vibration magnitudes (0.1, 0.2, 0.4, 0.8 and 1.6 m s−2 rms). The fore-and-aft forces were measured at five vertical locations (using a flat vertical contact area 120 mm in height) and with a flat vertical backrest covering the entire back. At all locations, but not for all subjects, three resonances were observed in the fore-and-aft apparent mass of the back. The first resonance around 1–2 Hz was most visible at the middle and lower back. A clearer, second resonance was exhibited between 4 and 5 Hz (in the upper back) and between 5 and 8 Hz (in the middle and lower back). A third resonance around 7 Hz was most apparent in the middle back. The forces at the back were highly dependent on the location: the lower back produced greater forces than the middle and the upper back. The apparent mass of the entire back showed three resonances at similar frequencies: around 2 Hz, between 4 and 6 Hz and between 7 and 8 Hz. The first and the third resonances were observed in most subjects, but not all. With the entire back, the forces were similar to those with the middle back. With variations in vibration magnitude, a nonlinearity in the apparent mass of the back was evident at all locations and with the entire back. It is concluded that biodynamic models of seated persons in contact with a backrest and excited by fore-and-aft vibration should allow for the effects of vibration magnitude and the location of excitation.