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Research Papers

Modal Damping Ratio and Optimal Elastic Moduli of Human Body Segments for Anthropometric Vibratory Model of Standing Subjects

[+] Author and Article Information
Manoj Gupta

Department of Mechanical Engineering,
Malaviya National Institute of Technology,
Jaipur 302017, India
e-mail: mngupt@gmail.com

T. C. Gupta

Department of Mechanical Engineering,
Malaviya National Institute of Technology,
Jaipur 302017, India
e-mail: tcgmnit@gmail.com

Manuscript received February 1, 2017; final manuscript received July 19, 2017; published online August 16, 2017. Assoc. Editor: Guy M. Genin.

J Biomech Eng 139(10), 101006 (Aug 16, 2017) (13 pages) Paper No: BIO-17-1037; doi: 10.1115/1.4037403 History: Received February 01, 2017; Revised July 19, 2017

The present study aims to accurately estimate inertial, physical, and dynamic parameters of human body vibratory model consistent with physical structure of the human body that also replicates its dynamic response. A 13 degree-of-freedom (DOF) lumped parameter model for standing person subjected to support excitation is established. Model parameters are determined from anthropometric measurements, uniform mass density, elastic modulus of individual body segments, and modal damping ratios. Elastic moduli of ellipsoidal body segments are initially estimated by comparing stiffness of spring elements, calculated from a detailed scheme, and values available in literature for same. These values are further optimized by minimizing difference between theoretically calculated platform-to-head transmissibility ratio (TR) and experimental measurements. Modal damping ratios are estimated from experimental transmissibility response using two dominant peaks in the frequency range of 0–25 Hz. From comparison between dynamic response determined form modal analysis and experimental results, a set of elastic moduli for different segments of human body and a novel scheme to determine modal damping ratios from TR plots, are established. Acceptable match between transmissibility values calculated from the vibratory model and experimental measurements for 50th percentile U.S. male, except at very low frequencies, establishes the human body model developed. Also, reasonable agreement obtained between theoretical response curve and experimental response envelop for average Indian male, affirms the technique used for constructing vibratory model of a standing person. Present work attempts to develop effective technique for constructing subject specific damped vibratory model based on its physical measurements.

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Figures

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Fig. 1

Anthropometric human body model showing ellipsoidal elements [34]

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Fig. 2

Ellipsoidal segment of human body showing semi-axes

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Fig. 3

Anthropometric vibratory model of standing human subjected to vertical excitation of platform

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Fig. 4

Response of single DOF system (a) for forced vibration and (b) under support excitation

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Fig. 5

Sample plot for response of single DOF system under support excitation

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Fig. 6

Experimental data for average platform-to-head TR of U.S. male [17]

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Fig. 7

Comparison of TR for vibratory model (modified Ei) and average experimental TR

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Fig. 8

Comparison of TR for vibratory model (optimal Ei) and average experimental TR

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Fig. 9

Comparison of TR for vibratory model (optimal Ei and modified ξ4) and average experimental TR

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Fig. 10

TR from vibratory model (optimal Ei) and experimental TR envelop [39] for Indian male

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Fig. 11

Apparent mass of U.S. male from vibratory model (optimal Ei) and experimental apparent mass envelop [40]

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