Abstract
In the present paper a lumped single degree-of-freedom nonlinear model is used to study biodynamic responses of the hand arm system (HAS) under harmonic vibrations. Then, the harmonic balance method is implemented to derive the vibration transmissibility. Furthermore,Padé approximations are used in the identification process of biodynamic characteristics of the HAS model. This process is based on minimizing the distance between the theoretical and the experimentally measured transmissibilities. The proposed identification workflow is applied to vibrations at the wrist in two cases: 1) the transmissibility versus the grip force for fixed excitation frequencies, and 2) the transmissibility versus the excitation frequency for fixed grip force.
Highlights
The viscoelastic characteristics of the hand-arm system (HAS) are modelled by restoring and dissipative forces that are assumed to be nonlinearly related to the displacement and the velocity, respectively
It is worth pointing out that the linear transmissibility (8) is independent of the imposed handle motion amplitude Y, while the nonlinear transmissibility (6) is dependent on it
The model parameters identification process is based on experimental measurements of the HAS vibration transmissibility, along the forearm direction i.e., Zh axis, that were performed on nine subjects under various hand forces and excitation frequencies [4]
Summary
The imposed harmonic displacement at the handle is denoted y(t) = Y cos(Ω t), where t is time, Y and Ω are the amplitude and the frequency (measured in rad/s), respectively. A first order approximation of the periodic solution of Eq(1), having the same frequency Ω as the imposed harmonic displacement of the handle, is obtained using the harmonic balance method (HBM) [5]. Where a is the the relative displacement amplitude of the mass. It is solution of the following sixth order algebraic equation It is worth pointing out that the linear transmissibility (8) is independent of the imposed handle motion amplitude Y, while the nonlinear transmissibility (6) is dependent on it. Based on vibration measurements on the HAS, Adewusi et al [3] found experimentally, using two different magnitudes of broad-band random vibrations of the handle, that the excitation magnitude affects the transmissibility, around the characteristic frequencies
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