Human response of vertical and pitch motion to vertical vibration on whole body according to sitting posture

Transcription

1 Journal of Mechanical Science and Technology 26 (8) (2012) 2477~ DOI /s x Human response of vertical and pitch motion to vertical vibration on whole body according to sitting posture Min-Seok Kim 1, Gyeoung-Jin Jeon 2, Jae-Young Lee 2, Se-Jin Ahn 3,*, Wan-Suk Yoo 2 and Weui-Bong Jeong 2 1 Construction Equipment Research Department, Product Development Research Institute, Hyundai Heavy Industries, 1 Jeonha-dong, Dong-gu, Ulsan, , Korea 2 School of Mechanical Engineering, Pusan National University, 30 Jangjeon-dong, Geumjeong-gu, Busan , Korea 3 Vehicle Quality Engineering Department, Renault Samsung Motors Company, 185 Shinho-dong, Gangso-gu, Busan , Korea (Manuscript Received October 31, 2011; Revised March 15, 2012; Accepted April 3, 2012) Abstract When a whole body is exposed to vertical vibration, the body s asymmetric shape affects the response to translational and rotational motion. The degree of asymmetry of a body on a seat is affected by posture. In our study, sixteen male subjects sitting on a seat were used to obtain a response to vertical vibration over a frequency range of 3 to 40 Hz. Two kinds of magnitude of the vibration at each frequency were applied (0.224 m/s 2 and m/s 2 RMS). Without a backrest, three kinds of sitting postures (average P1, supported P2, and minimum P3) were set by adjusting the height of the footrest and by using an inclined seat pan. The vertical and rotational responses were measured using a force plate mounted on a rigid seat. The apparent eccentric mass (AEM) is defined in this study as rotational response of body to vertical whole body vibration exposure. In the result, the AEM of P2 posture was bigger than that of P1 and P3 posture, especially in a frequency range of 20 to 40 Hz where idle vibration of the passenger vehicle exists. The apparent mass (AM) was even changed by the three kinds of sitting posture, but the difference was not as much as in the case of the AEM. The bigger difference of the AEM is assumed that the sitting posture mainly affects the asymmetry of the fore-andaft direction, which is more strongly correlated with the rotational pitch response. Keywords: Whole body vibration; Apparent mass; Apparent eccentric mass; Sitting posture effect; Human response; Idle vibration Introduction The apparent mass (AM) and impedance of a human body exposed to whole body vibration imply frequency characteristics of vibration of the body [1]. In ISO 5982, the AM of a whole body postured on a seat is presented [2]. Most previous studies used sinusoidal or random vibration in a frequency range of 0.2 to 20 Hz with a magnitude of 0.25 to 3.0 m/s 2 root mean square (RMS) to study human response to vibration. Studies have shown that the main peak of human body resonance exists at 4 to 6 Hz, and a secondary peak appears at about 8 to 13 Hz [3-5]. Holmlund et al. and Matsumoto et al. showed a softening effect of the human body to explain the observation that the greater the magnitude of vibration, the lower the frequency of the body resonance. They also used the softening effect to support an assumption of nonlinearity in the human body response to vibration [6, 7]. Unlike previous studies that used a sinusoidal or random * Corresponding author. Tel.: address: Sejin.ahn@renaultsamsungm.com Recommended by Editor Yeon June Kang KSME & Springer 2012 signal for input vibration, Ahn et al. used a shock-type signal to obtain a quasi-apparent mass of the human body. The nonlinearity of the human body with respect to vibration magnitude also was found to occur in the quasi-apparent mass at a higher frequency range rather than the human body resonance range (4 to 5 Hz). The quantity of the nonlinearity regarding magnitude showed to be affected by the parameters of shocktype input signal, such as attenuation ratio and phase. The shock-type vibration was also used to investigate discomfort felt by fifteen subjects. More discomfort was found at low frequencies below 1 Hz, and at the resonance frequency of the human body from 4 to 10 Hz [8-10]. Yoo et al. found the correlations between the measured accelerations transmitted to the hands and the subjective ratings of 14 people using Stevens power law. The subjective ratings were found to be more highly correlated with the root mean quad values of the frequency-weighted acceleration [11]. Nawayseh et al. focused on the fore-and-aft response of a seated human body exposed to vertical vibration to describe a biodynamic model s vibration response in more detail, rather than by only using vertical response. The fore-and-aft re-

2 2478 M.-S. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2477~2484 sponse to vertical input, defined as cross-axis AM, was found to have a nonlinear characteristic caused by the asymmetry of the human body. In their study, the supported of the sitting posture had greater cross-axis AM than the average [12, 13]. Kitazaki et al. and Matsumoto et al. took several models into account to describe the cross-axis movements of a body induced by vertical excitation using measurements of the transmissibility to the upper body [14, 15]. Kitazaki reported that a principal resonance at about 7 Hz corresponded to a rotational mode of the pelvis. The rotational mode of the pelvis was found in both the sixth and seventh modes, but it was more dominant in the seventh mode. In the measured sixth and seventh modes, the lower lumbar spine below L2 appeared to deform axially with pelvic rotation. However, the model achieved the pelvic rotation with no axial deformation of the lumbar spine by assigning a lower bending stiffness to the lowest spine and adjusting the location of the pelvic mass, and the axial and bending stiffnesses for the buttocks tissue beams [14]. Matsumoto et al. used two models with four and five degrees of freedom (DOFs) that gave more reasonable representations than other models. Mechanical parameters obtained with median and individual experimental data were consistent for vertical DOFs, but varied for rotational DOFs. The resonance of the AM at about 5 Hz can be attributed to a vibration mode consisting of a vertical motion of the pelvis and leg, a pitch motion of the upper body above the pelvis, a bending motion of the spine, and a vertical motion of the viscera [15]. Wang et al. performed measurements for various sitting postural configurations realized through variations in hand position, seat height, and seat design factors involving pan orientations and back support conditions. The measurements showed that a higher seat yielded higher peak magnitude of response; this was attributed to the relatively larger portion of the body mass supported by the seat [16]. When a passenger sits on the seat of a vehicle that is vibrating in the vertical direction, the human body responds to the movement in various directions due to asymmetrical characteristics of the body: for instance, vertical, fore-and-aft, pitching, and rolling responses. In this study, a pitching movement of a body responding to vertical vibration was additionally analyzed more than the vertical movement like AM. When a subject sat on the vibration seat, the height of the footrest and the angle of the seat plate were controlled as parameters for changing asymmetry amount of a seated human body. A difference in the footrest height varies the ratio of weight loaded on the seat and footrest, and the seat angle made a difference in the force on the seat plate. The AM and apparent eccentric mass (AEM) were used to investigate the response of a human body depending on sitting posture, where AEM is defined as the pitching moment of a body activated by vertical vibration. Two hypotheses were posed in our study. The first is that the height of the footrest, which changes the amount of body asymmetry, should affect human responses (AM and AEM) to vertical whole-body vibration. For this hypothesis, three kinds Table 1. Specifications of shaker generating controlled vibration. Model IMV i-220 Type Electro-dynamic Rated force 5.6 kn (random) Frequency range DC ~ 3,300 Hz Maximum displacement 51 mm peak-peak Maximum payload 200 kg Force Platform of sitting postures were examined: the average, supported, and minimum. The second hypothesis is that the magnitude of vibration should also affect the human response. Two magnitudes (0.224 m/s 2 and m/s 2 RMS, 107 db and 117 db, ref: 10-6 m/s 2 ) considered for the vibration of a passenger vehicle at idle condition were used to correlate with the human response [17]. 2. Method Accelerometer Electro-dynamic Type Vibration Shaker 2.1 Apparatus Force Signal Strain Gauge Amplifier Acceleration Signal Control system Power Amplifier Low Pass Filter Low Pass Filter Signal generator Fig. 1. Schematic diagram of experimental set-up. Data Acquisition/ Processing System Vertical vibration was generated using an electro-dynamic one-axis shaker (i-220, IMV Corporation, Japan). As shown in Fig. 1, the shaker was designed to implement feedback control by a signal from a one-axis accelerometer (8310B, Kistler, Switzerland) mounted on the platform of the shaker. The frequency and magnitude of actual vibration was kept at the control value by the feedback control system. Detailed specifications of the shaker are presented in Table 1. The strain-type force plate (OR 6-7, Advanced Mechanical Technology, Inc., USA) installed on the top of the shaker measured three translational forces and three rotational moments induced on the human body. The actual acceleration generated by the exciter was measured using a strain gage-type ICP accelerometer, which normally has stable output performance in the low frequency range. LabVIEW (Ver. 10.5, National Instruments, USA) was used to acquire acceleration data and perform digital signal processing. The processed data were evaluated using MATLAB software (Ver. 7.7, The MathWorks, Inc., USA). To control the sitting posture of the subject, two footrest heights and a sloped seat plate were used as shown in Fig. 2. For P1 posture, the height of the footrest was adjusted for each subject to keep an average. The P2 posture was implemented using a sloped seat plate and by adjusting the

3 M.-S. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2477~ Table 2. Physical data of the sixteen subjects employed in the experiment. Item Average Standard deviation Max/Min Weight (kg) /60 Height (cm) /170 Age (yr) /25 (a) P1 Posture (b) P2 posture (c) P3 Posture Fig. 2. Schematic diagram of three kinds of sitting postures: (P1) average ; (P2) supported ; (P3) minimum thigh contact. the subject was not allowed to have intentional movement. Most studies of human response have focused on the frequency range below 20 Hz where major resonance peaks of the human body exist. In this way, the passenger vehicle driver is exposed to vibration at higher frequencies than 20 Hz. In the study, the frequency range of excitation was expanded from 3 to 40 Hz to include the frequency range of idle vibration in the passenger vehicle (20 to 40 Hz). Two vibration magnitudes (0.224 m/s 2 and m/s 2 RMS) were used to reflect idle vibration on the passenger vehicle. The period of each excitation for a sitting posture was set to 80 s. To eliminate transient data, 10 s of data at the beginning and at the end of the full period was discarded. Thus, only 60 s in the center of the excitation period was used to calculate the human response. The time data were processed with a frequency span of 100 Hz and frequency resolution of 0.5 Hz for spectrum analysis. A spectrum average was calculated after applying a Hanning window to enhance processing reliability. 2.3 Analysis A whole-body coordinate system based on ISO was employed to describe the vertical force (F z ) and pitching moment (M y ) that are induced by the fore-and-aft directional asymmetry of the human body [20]. For a general analysis of human response to vertical vibration, the acceleration and reaction force of the rigid plate on which the subject is sitting was measured. In the case of random excitation, the AM is defined as follows [1]: Sa ( ) Z f f Z AM ( f ) = S ( f) (1) azaz Fig. 3. Vibration shaker and subject sitting on the rigid seat. footrest height to keep the normal, which we considered to be the posture of a passenger sitting in a vehicle seat. Finally, for the P3 posture, only the sloped seat plate was deleted from the P2 posture for minimum. The rigid seat and the sloped plate were made of a hard wood material. Although it has been found that the backrest is one of the major factors affecting human response [18], it was not considered in this study to simplify the experiment and reduce the diversity of the hypothesis. The backrest effect could be discussed and developed in a future study. 2.2 Experiment Sixteen randomly-selected male subjects took part in the experiment. Their physical data are statistically shown in Table 2. As shown in Fig. 3, each subject sat with his hands on his knees naturally, with the back straight and eyes looking forward. Once the excitation began, for stable data acquisition, where SaZ a is the power spectrum of acceleration of the vertical excitation and SaZ f Z represents the cross spectrum of the Z reaction force related to the acceleration. In this study, the AEM was originally introduced to define response of pitching moment to vertical vibration. The apparent eccentric mass, AEM ( f ), was calculated as follows: Sa ( ) Zm f Y AEM ( f ) = S ( f) (2) azaz where my is the rotational moment of pitching motion against the Y direction as defined in Fig. 3, and SaZ m represents the Y cross spectrum of the pitching moment related to the vertical acceleration. 3. Results 3.1 Apparent mass (AM) Fig. 4 shows the median values of the AMs for sixteen subjects exposed to two different magnitudes of excitation according to the three sitting postures. The main peak of body

4 2480 M.-S. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2477~2484 (a) P1 posture (a) P1 posture (b) P2 posture (b) P2 posture (c) P3 posture (c) P3 posture Fig. 4. Apparent mass of sixteen subjects according to excitation magnitude (gray lines: individual results from two magnitudes, thick solid line: median for m/s 2, thick dotted line: median for m/s 2 ). Fig. 5. P-values of sign test according to excitation magnitude (AM). resonance exists at around 6 Hz, and the secondary peak is near 12 Hz. The frequencies and amplitudes of the peaks were affected by the excitation magnitude as well as the sitting posture. However, for frequencies over about 18 Hz, the excitation magnitude did not have much effect. In the lower frequency range, below 18 Hz, as the excitation magnitude increased, the apparent mass and main peak frequency decreased. This phenomenon is a result of the softening effect of the human body exposed to a high magnitude of vibration, which has been reported by Holmlund et al. and Matsumoto et al. [6, 7]. We used the sign test, which is a nonparametric statistical technique, to analyze the significance of the effect of excitation magnitude at each sitting posture. Fig. 5 shows p-values calculated using the sign test [20, 21]. The lower p-value means a more significant effect on the parameter. For sitting postures P1 and P3, there is statistical significance (p < ) in the low frequency range below 18 Hz, except at the main peak of 6 Hz and the secondary peak of Hz. In the case of P2, the exception is only at 6 Hz. For the higher frequency range over 18 Hz, significance with a low p-value under is shown for most of the frequencies with some exceptions, depending on sitting posture. The median values of the apparent masses of the sixteen subjects were rearranged to compare the effect of sitting posture for the two magnitudes, as shown in Fig. 6. The frequency and magnitude of the main peak were not significantly affected by sitting posture. Over 10 Hz, including the secon-

5 M.-S. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2477~ Table 3. Frequency and magnitude of main peak of AM according to two excitation magnitudes and three sitting postures. Excitation magnitude (m/s 2 RMS) Average (P1), magnitude (kg) Supported (P2) Minimum (P3) , , , , , , 92.2 P-value(Friedman test) (a) m/s 2 RMS P-value(Friedman test) (a) m/s 2 RMS. (b) m/s 2 RMS Fig. 7. P-values of Friedman test according to sitting posture (AM). peak was significantly moved from 7.0 Hz to 5.5 Hz when the excitation increased. (b) m/s 2 RMS. Fig. 6. Median of AM of 16 subjects according to sitting posture (solid line: P1 posture; chain line: P2 posture; dotted line: P3 posture). dary peak, there seems to be a significant effect according to sitting posture. The Friedman test was used to determine the significance of the effect of sitting posture on the two excitation magnitudes [20, 21]. Fig. 7 shows the results of the test: the posture effect is significant, showing p-values under at all frequencies over 10 Hz. Especially, between 20 Hz and 40 Hz (the frequency range of idle vibration), the effect was so much significant with p-values under. Table 3 shows the frequency and magnitude of the main peak versus the excitation magnitude and sitting posture. We found that the main peak frequency decreased and the peak magnitude decreased in the case of greater excitation. The P1 and P2 postures had main peaks at the same frequency of 6.5 Hz with a lower excitation, and 6.0 Hz with a greater excitation. In the case of P3, the frequency and magnitude of the main peaks were different than those of P1 and P2, and the 3.2 Apparent eccentric mass (AEM) Fig. 8 shows the median values of the AEMs of the sixteen subjects according to two excitation magnitudes at three sitting postures. With a variation related to sitting posture, the main peak frequency was about 7 Hz, and the secondary peak was about 12 Hz. Although the effect of excitation magnitude seems to be clear at the low frequency range below 20 Hz, very little or no effect occurred above 20 Hz. The AEM decreased and the frequency of the main peak decreased when the excitation magnitude increased. This phenomenon is very similar to that of the aforementioned apparent mass. A sign test was performed at each frequency from 3 to 40 Hz to analyze the significance of the effect of excitation magnitude on the three sitting postures. Fig. 9 shows the p-values of the sign test, which indicate no significance of the effect at most of the frequencies. Thus, the AEM was only slightly affected by excitation magnitude. The median values of the AEMs were rearranged to show the difference according to sitting posture for the same excitation magnitude, as shown in Fig. 10. A noticeable difference occurred in the median AEM at the two different excitation magnitudes. In particular, in the higher frequency range over the main peak, the AEM for the P2 posture is consistently the greatest, and the next is P1 followed by P3.

6 2482 M.-S. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2477~ (a) P1 posture (b) P2 posture (c) P3 posture 10-1 Fig. 8. AEM of 16 subjects according to excitation magnitude (gray lines: individual results of two kinds of magnitude, thick solid line: median of m/s 2, dotted line: median of m/s 2 ). (a) P1 posture (b) P2 posture (c) P3 posture Fig. 9. P-values of sign test according to excitation magnitude (AEM). (a) m/s 2 RMS (b) m/s 2 RMS Fig. 10. Median AEM of 16 subjects according to sitting posture (solid line: P1 posture; chain line: P2 posture; dotted line: P3 posture). P-value(Friedman test) P-value(Friedman test) (a) m/s 2 RMS (b) m/s 2 RMS Fig. 11. P-values of Friedman test according to sitting posture (AEM).

7 M.-S. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2477~ Table 4. Frequency and magnitude of main peak of AEM according to two excitation magnitudes and three sitting postures. Excitation magnitude (m/s 2 RMS) A Friedman test was performed at each frequency to analyze the effect of sitting posture. The p-values from the test at two excitation magnitudes are presented in Fig. 11. The effect of sitting posture on the AEM is highly significant (p < ) at all frequencies over 8 Hz. The frequency and magnitude of the main peak of the AEM are presented in Table 4. The results show that the higher the excitation magnitude, the lower the frequency of the main peak. 4. Discussion Average (P1), magnitude (kgm) Supported (P2) Minimum (P3) , , , , , , 3.9 The studies by Mansfield et al., Matsumoto et al., and Rakheja et al. examined the biodynamic response of a human body exposed to whole-body vibration. The main peak of body resonance occurs at 4-6 Hz, and the secondary peak occurs at 8-12 Hz [3-5]. Kitazaki et al. reported that a principal resonance of the human body at about 5 Hz consisted of an entire body mode in which the skeleton moved vertically due to axial and shear deformations of buttocks tissue [14]. Matsumoto et al. concluded that the resonance frequency at around 5 Hz could be attributed to a vibration mode consisting of vertical motion of the pelvis and legs and a pitch motion of the pelvis, both of which cause vertical motion of the upper body above the pelvis, a bending motion of the spine, and vertical motion of the viscera [15]. We confirmed that the main peak of the apparent mass is near 6 Hz, which is not dependent on the sitting posture and excitation magnitude. The secondary peak is near 12 Hz with a small dependence due to sitting posture. Holmlund et al. and Matsumoto et al. explained the softening effect as a nonlinearity of the human body that causes decreasing peak frequency of body resonance by increasing the excitation magnitude. In this study, the softening effect is confirmed when the main peak frequency of both the AM and AEM decreases with greater excitation magnitude in all the three sitting postures [6, 7]. Nawayseh et al. reported that apparent mass in a sitting posture of supported is greater than the average [12]. Wang et al. found that the higher portion of body mass on seat according to seat height, the higher peak magnitude on human response, such as apparent mass [16]. The greatest magnitude of AM was found in the supported (P2) of this study, wherein we assumed that a greater mass of the body is supported on the seat rather than on the footrest, as previous researchers have reported. While greater magnitude of AEM on P1 than P2 is shown at near main peak frequency, the order of magnitude is P2, P1 and P3 at the rest frequency range. The highest magnitude on P2 and the lowest on P3 was assumed to be caused by the difference of momentum-resisting pitch motion according to a different on the seat plate. We found that the AEM was much more sensitive to the sitting posture than to the AM, which means that the sitting posture mainly affects the asymmetry of the fore-and aft direction, which is more strongly correlated with the rotational pitch response. At higher frequencies over 15 Hz (including the idle vibration frequency of a passenger vehicle), the effect of sitting posture is quite consistent. 5. Conclusion With an experimental hypothesis that sitting posture should affect human response excited on a rigid seat, the AM and AEM were studied using three sitting postures controlled by the height of the footrest and the angle of the seat plate. We conclude that the AM and AEM are relatively greater when the human body is more tightly in contact with the seat, such as in the case of the sitting posture of supported thigh contact. While the AEM showed a clear and consistent effect of sitting posture over most of the frequency range, the AM had little effect. For an idle vibration frequency of 20 to 40 Hz, the AEM was greater on the supported posture than on average, and the lowest AEM was consistently on minimum. We found that the softening effect with high magnitude was common in the AM as well as in the AEM, but its quantity was affected by sitting posture. Our results clearly show that sitting posture is one of the significant factors that affect human response to whole-body vibration, especially in the frequency range of idle vibration from 20 to 40 Hz. References [1] M. J. Griffin, Handbook of human vibration, Elsevier Academic Press, London (1990). [2] ISO 5982, Mechanical vibration and shock - Range of idealized values to characterize seated-body biodynamic response under vertical vibration, International Organization for Standardization, Geneva (2001). [3] N. J. Mansfield and M. J. Griffin, Non-linearities in apparent mass and transmissibility during exposure to whole-body vertical vibration, Journal of Biomechanics, 33 (2000) [4] Y. Matsumoto and M. J. Griffin, Non-linear characteristics in the dynamic responses of seated subjects exposed to vertical whole-body vibration, Journal of Biomechanical Engineering, 124 (2002) [5] S. Rakheja, I. Stiharu and P. E. Boileau, Seated occupant apparent mass characteristics under automotive postures and vertical vibration, Journal of Sound and Vibration, 253 (2002)

8 2484 M.-S. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2477~2484 [6] P. Holmlund, R. Lundström and L. Lindberg, Mechanical impedance of the human body in vertical direction, Applied Ergonomics, 31 (2000) [7] Y. Matsumoto and M. J. Griffin, Effect of muscle tension on non-linearities in the apparent masses of seated subjects exposed to vertical whole-body vibration, Journal of Sound and Vibration, 253 (2002) [8] S. J. Ahn, M. J. Griffin, W. S. Yoo and W. B. Jeong, Nonlinearity of biodynamic response to shock-type vertical whole-body vibration, Transactions of the KSME A, 31 (2) (2007) (in Korean). [9] S. J. Ahn and M. J. Griffin, Effects of frequency, magnitude, damping, and direction on the discomfort of vertical wholebody mechanical shocks, Journal of Sound and Vibration, 311 (2008) [10] S. J. Ahn, Discomfort of vertical whole-body shock-type vibration in the frequency range of 0.5 to 16Hz, International Journal of Automotive Technology, 11 (6) (2010) [11] W. S. Yoo, S. D. Na and M. S. Kim, Relationship between subjective and objective evaluations of steering wheel vibration, Journal of Mechanical Science and Technology, 25 (7) (2011) [12] N. Nawayseh and M. J. Griffin, Non-linear dual-axis biodynamic response to vertical whole-body vibration, Journal of Sound and Vibration, 268 (2003) [13] N. Nawayseh and M. J. Griffin, A model of the vertical apparent mass and the fore-and-aft cross-axis apparent mass of the human body during vertical whole-body vibration, Journal of Sound and Vibration, 319 (2009) [14] S. Kitazaki and M. J. Griffin, A modal analysis of whole-body vertical vibration, using a finite element model of the human body, Journal of Sound and Vibration, 200 (1) (1997) [15] Y. Matsumoto and M. J. Griffin, Modelling the dynamic mechanisms associated with the principal resonance of the seated human body, Clinical Biomechanics, 16 Supplement (1) (2001) S31-S44. [16] W. Wang, S. Rakheja and P. E. Boileau, Effects of sitting postures on biodynamic response of seated occupants under vertical vibration, International Journal of Industrial Ergonomics, 34 (2004) [17] D. W. Park, S. J. Ahn and W. S. Yoo, Study on relationship between discomfort and body pressure distribution on the seat under height of footrest and angle of seat pan, Transactions of the KSAE, 15 (6) (2007) (in Korean). [18] N. Nawayseh and M. J. Griffin, Tri-axial forces at the seat and backrest during whole-body vertical vibration, Journal of Sound and Vibration, 277 (2004) [19] ISO , Mechanical vibration and shock - Evaluation of human exposure to whole-body vibration Part 1: General requirements, International Organization for Standardization, Geneva (1997). [20] D. Howitt and D. Cramer, Introduction to statistics in psychology, Pearson Education limited, Essex (2005). [21] S. Siegel and N. J. Castellan, Nonparametric statistics for the behavioral sciences, McGraw Hill, New York, Min-Seok Kim received his B.S., M.S., and Ph.D degrees from Pusan National University in 2003, 2005, and 2010, respectively. Dr. Kim is currently a full time Research Engineer at the Research Institute of Mechanical Technology at Pusan National University. His research interests are in human vibration and multi-body dynamics. Gyeoung-Jin Jeon received his B.S. degree from Yeungnam University in He is currently a candidate for the M.S. degree in Pusan National University from the Department of Mechanical Engineering. His research interest is in human vibration and computer aided engineering analysis of radiated noise. Jae-Young Lee received his B.S. degree from Pusan National University in He is currently a candidate for the M.S. degree in Pusan National University from the Department of Mechanical Engineering. His research interest is in human vibration. Se-Jin Ahn received his B.S., M.S., and Ph.D. degrees from Pusan National University in 1994, 1996, and 2003, respectively. Dr. Ahn is currently a Senior Manager in the Vehicle Quality Engineering Department of the Renault Samsung Motors Company. His research interest is in human vibration. Wan-Suk Yoo received his B.S. degree from Seoul National University in 1976, the M.S. degree from Korea Advanced Institute of Science and Technology in 1978, and the Ph.D degree from the University of Iowa in Dr. Yoo is currently a Professor in the School of Mechanical Engineering at Pusan National University, and served as President of Korean Society of Mechanical Engineers in His main interests are in flexible multi-body dynamics and vehicle dynamics. Weui-Bong Jeong received his B.S. degree from Seoul National University in 1978, the M.S. degree from Korea Advanced Institute of Science and Technology in 1980, and his Ph.D from Tokyo Institute of Technology in Dr. Jeong is currently a Professor in the Department of Mechanical Engineering at Pusan National University, Busan, Korea.