Abstract
The pears in carton box on vibrator being asumed to be a Voigt-body rod atached to a foundation that vibrates the rod axially, the following differential equation and boundary conditions are derived:
∂2u/∂t2-gγ/ρ∂2u/∂x2-ηg/ρ∂3u/∂t∂x2=Aω2cosωt (1)
Stress=∂u/∂x=0 where x=λ (2)
u=Acosωt where x=0 (3)
where t: the time (sec), u: the displacement of the point in the vertical direction (m), x: coordinate in the vertical direction (m), g=9.8m/sec2, ρ: the density (kg/m3), η: the viscosity of the pears (kgs/m2), A: the amplitude of the vibrator (m), ω: the circular frequency of the vibrator (sec-1), γ: the elastisity of the pears (kg/m2), λ: the effective depth of the carton box (m).
Using this solution, the elastisity and viscosity fo the pears are both calculated from the acceleration measured by the accelerometers in the pears (TABLE 1).
