A proposed theory on biodynamic frequency weighting for hand-transmitted vibration exposure

Applied Force Alters Sensorineural and Peripheral Vascular Function in a Rat Model of Hand-Arm Vibration Syndrome

OBJECTIVE

This study described the effects of applied force (grip) on vascular and sensorineural function in an animal model of hand-arm vibration syndrome (HAVS).

METHODS

Rat tails were exposed to 0, 2, or 4 N of applied force 4 hr/d for 10 days. Blood flow and sensitivity to transcutaneous electrical stimulation and pressure were measured.

RESULTS

Applied force increased blood flow but reduced measures of arterial plasticity. Animals exposed to force tended to be more sensitive to 250-Hz electrical stimulation and pressure applied to the tail.

CONCLUSIONS

Effects of applied force on blood flow and sensation are different than those of vibration. Studies examining co-exposures to force and vibration will provide data that can be used to determine how these factors affect risk of workers developing vascular and sensorineural dysfunction (ie, HAVS).

Problems related to measuring the transmissibility of anti-vibration gloves. Possible efficacy for impact tools used in mining and quarrying activities

AbstractThis commentary takes into account some of the most relevant studies investigating the transmissibility of anti-vibration (AV) gloves. AV gloves are almost useless at the palm level in the low frequencies (less than 31.5 Hz), while they generally start to have an appreciable reduction of the vibration over 400 Hz. In their use with impact tools, having a low dominant vibration frequency usually between 25-60 Hz for chipping hammers and drills, and less than 30 Hz for pneumatic breakers, the average transmissibility reduction at the palm level is 13% (min 2% - max 26%) when used with hammers, and 1% (increment of 4% and reduction of 6%) when used with breakers. The transmissibility at the finger level, especially in the low frequencies, is almost nothing or produces an increase of the vibration. Other problems related to the increase of the applied force and the reduction of dexterity are reported.

A Review of Hand-Arm Vibration Studies Conducted by US NIOSH since 2000

Studies on hand-transmitted vibration exposure, biodynamic responses, and biological effects were conducted by researchers at the Health Effects Laboratory Division (HELD) of the National Institute for Occupational Safety and Health (NIOSH) during the last 20 years. These studies are systematically reviewed in this report, along with the identification of areas where additional research is needed. The majority of the studies cover the following aspects: (i) the methods and techniques for measuring hand-transmitted vibration exposure; (ii) vibration biodynamics of the hand-arm system and the quantification of vibration exposure; (iii) biological effects of hand-transmitted vibration exposure; (iv) measurements of vibration-induced health effects; (iv) quantification of influencing biomechanical effects; and (v) intervention methods and technologies for controlling hand-transmitted vibration exposure. The major findings of the studies are summarized and discussed.

Vibrotactile sensitivity testing for occupational and disease-induce peripheral neuropathies

The International Standard Organization (ISO) standard 13091-1 describes methods and procedures for performing the vibrotactile perception threshold (VPT) testing to diagnose changes in tactile sensory function associated with occupational exposures. However, the VPT test also has been used in the diagnosis of peripheral neuropathies associated with a number of disorders. This review examines the VPT test, variations in procedures that have been used, as well as disorders and diseases in which this test has been reliable for the detection of sensory changes. Mechanisms potentially underlying the changes in VPTs are also discussed along with procedural and subject/patient factors that may affect the interpretation of test results. Based upon the review of the literature, there are also suggestions for where additional research might improve the administration of this test, depending upon the subject/patient population and interpretation of data.

The hand-arm vibration syndrome associated with the grinding of handheld workpieces in a subtropical environment

OBJECTIVES

To study the characteristics and the factors influencing the occurrence of the Hand-Arm Vibration Syndrome (HAVS) for a population grinding handheld workpieces in a subtropical environment.

METHODS

A total of 803 workers grinding handheld workpieces formed the exposure group and 464 workers not exposed to hand-transmitted vibration (HTV) were recruited as the non-exposed group within the same factory in a subtropical climate area. The basic personal information and clinical symptoms reported were collected by trained physicians using a questionnaire and representative measurements were made of the HTV exposure levels and dose.

RESULTS

The average HTV exposure dose A(8) was measured as 5.3 ± 2.0 m/s². The proportion of grinders reporting finger blanching was 15.4% while it was 27.5% for finger numbness. Among the non-exposed group, that proportion was 0% and 6.3% respectively. There was a positive association between the vibration exposure duration and the occurrence of finger blanching, finger numbness and finger coldness. Riding a motorcycle to work was also identified as a factor that could contribute to a higher prevalence of finger blanching among the exposed workers, the OR value was found to be 1.75 (1.12, 2.75).

CONCLUSIONS

Workers exposed to vibration in a subtropical area can also present evidence of finger blanching in addition to neurological symptoms. The reported rate of HAVS was positively associated with the exposure duration. And the levels of the duration of exposure relative to symptoms of vibration white finger in a subtropical temperate environment exposed to a high-frequency vibration might be deemphasized by the current ISO weighting. Motorcycle transportation to work was identified as a factor that could influence the development of the HAVS among the exposed population of grinders.

A Method for Analyzing the Effectiveness of Vibration-Reducing Gloves Based on Vibration Power Absorption

The effectiveness of vibration-reducing (VR) gloves is conventionally assessed based on the vibration transmissibility of the gloves. This study proposed a method for analyzing and assessing the effectiveness of VR gloves based on how gloves affect the vibration power absorption (VPA) of the hand–arm system and its distribution. A model of the entire tool–handle–glove–hand–arm system was used to predict the VPA distributed in the glove and across the substructures of the hand–arm system. The ratio of the gloved-VPA and ungloved-VPA in each group of system substructures was calculated and used to quantify VR glove effectiveness, which was termed the VPA-based glove vibration transmissibility in this study. The VPA-based transmissibility values were compared with those determined using to-the-hand and on-the-hand methods. Three types of gloves (ordinary work glove, gel VR glove, and air bubble VR glove) were considered in the modeling analyses. This study made the following findings: the total VPA-based transmissibility spectrum exhibits some similarities with those determined using the other two methods; the VPA-based transmissibility for the wrist–forearm–elbow substructures is identical to that for the upper–arm–shoulder substructures in the model used in this study; each of them is equal to the square of the glove vibration transmissibility determined using the on-the-wrist method or on-the-upper-arm method; the other substructure-specific VPA-based transmissibility spectra exhibit some unique features; the effectiveness of a glove for reducing the overall VPA in the hand–arm system depends on the glove effectiveness for absorbing the vibration energy, which seems to be associated primarily with the glove cushioning materials; the glove may also help protect the fingers or hand by redistributing the VPA across the hand substructures; this redistribution seems to be primarily associated with the glove structural properties, especially the tightness of fit for the glove.

Organische und funktionelle Durchblutungsstörungen der Hand – differenzialdiagnostische Aspekte

Die Abklärung von venösen und arteriellen Durchblutungsstörungen sowie Lymphödemen gehört zur täglichen Praxisroutine des Gefäßmediziners. Nicht selten werden von chirurgischen Kollegen Patienten mit Beschwerden im Schulter-, Arm- und Handbereich zum Ausschluss einer vaskulären Ursache vorgestellt. Der wohl häufigste Abklärungsgrund im Handbereich ist das Raynaud-Phänomen. Neben arteriosklerotischen Durchblutungsstörungen und der Thrombangiitis obliterans sind das Hypothenar-/Thenar-Hammer-Syndrom und das Vibrationssyndrom in den Fingern eher wenig bekannte Entitäten, deren Kenntnis jedoch neben dem medizinischen Vorgehen auch versicherungsrelevante Konsequenzen haben kann. Während beim Hypothenar-/Thenar-Hammer-Syndrom eine organische Durchblutungsstörung vorliegt, beinhaltet das Vibrationssyndrom der Finger eine funktionell vaskuläre sowie eine nervale Komponente, die eine Trennung vom Karpaltunnelsyndrom erschwert. Bei beiden Entitäten ist eine Berufsanamnese häufig hilfreich. Schon der Verdacht auf eine Berufskrankheit muss nach Gesetzeslage zur Anzeige gebracht werden. Der Artikel beschreibt die wesentlichen pathophysiologischen Mechanismen beider Entitäten und stellt diagnostische und therapeutische Optionen dar. Die Kenntnis beider Erkrankungen erweitert die differenzialdiagnostische Vorgehensweise in der täglichen Praxisroutine bei Patienten mit Schulter-Arm-Hand-Beschwerden und bei Patienten mit Raynaud-Phänomen.

Distributed vibration isolation and manual dexterity of anti-vibration gloves: is there a correlation?

This study focuses on the integrated performance of anti-vibration (AV) gloves in terms of manual dexterity and distributed palm and fingers' vibration transmissibility. Experiments were designed to measure vibration transmission and manual dexterity performance of 10 different gloves using 15 subjects. The results showed all gloves impeded manual dexterity, while five gloves satisfied the AV glove screening criteria. Glove type yielded a significant effect on manual dexterity (p < 0.001) and vibration transmissibility (p ≤ 0.001). Manual dexterity decreased nearly linearly with an increase in glove thickness (p < 0.05), while palm and fingers' vibration transmissibility in high-frequency range was negatively correlated with glove thickness (R² > 0.70). A strong correlation was evident between glove material stiffness and the H-frequency range palm vibration transmissibility (R² ≥ 0.8). While the vibration isolation of a glove is strongly related to material properties at the palm, the dexterity performance is dependent on design factors such as thickness and bulkiness. Practitioner summaryAnti-vibration gloves are used to isolate hand from power tools vibration, while these may adversely affect manual dexterity. Vibration isolation was correlated with material properties and thickness, while dexterity was correlated with thickness alone. Glove thickness is a vital parameter for realising a compromise between vibration isolation and manual dexterity. Abbreviations: HTV: hand-transmitted vibration; AV: anti-vibration; MANOVA: multivariate analysis of variance; TR: vibration transmissibility; ASTM: ASTM F2010 standard test; Minnesota: Two-Hand Turning and Placing Minnesota test; rANOVA: repeated-measures analysis of variance; rms: root mean square; CoV: coefficient of variations; S: score.

The relationships between hand coupling force and vibration biodynamic responses of the hand-arm system

This study conducted two series of experiments to investigate the relationships between hand coupling force and biodynamic responses of the hand-arm system. In the first experiment, the vibration transmissibility on the system was measured as a continuous function of grip force while the hand was subjected to discrete sinusoidal excitations. In the second experiment, the biodynamic responses of the system subjected to a broadband random vibration were measured under five levels of grip forces and a combination of grip and push forces. This study found that the transmissibility at each given frequency increased with the increase in the grip force before reaching a maximum level. The transmissibility then tended to plateau or decrease when the grip force was further increased. This threshold force increased with an increase in the vibration frequency. These relationships remained the same for both types of vibrations. The implications of the experimental results are discussed. Practitioner Summary: Shocks and vibrations transmitted to the hand-arm system may cause injuries and disorders of the system. How to take hand coupling force into account in the risk assessment of vibration exposure remains an important issue for further studies. This study is designed and conducted to help resolve this issue.

Health effects associated with occupational exposure to hand-arm or whole body vibration

Workers in a number of different occupational sectors are exposed to workplace vibration on a daily basis. This exposure may arise through the use of powered-hand tools or hand-transmitted vibration (HTV). Workers might also be exposed to whole body vibration (WBV) by driving delivery vehicles, earth moving equipment, or through use of tools that generate vibration at low dominant frequencies and high amplitudes, such as jackhammers. Occupational exposure to vibration has been associated with an increased risk of musculoskeletal pain in the back, neck, hands, shoulders, and hips. Occupational exposure may also contribute to the development of peripheral and cardiovascular disorders and gastrointestinal problems. In addition, there are more recent data suggesting that occupational exposure to vibration may enhance the risk of developing certain cancers. The aim of this review is to provide an assessment of the occupations where exposure to vibration is most prevalent, and a description of the adverse health effects associated with occupational exposure to vibration. This review will examine (1) various experimental methods used to measure and describe the characteristics of vibration generated by various tools and vehicles, (2) the etiology of vibration-induced disorders, and (3) how these data were employed to assess and improve intervention strategies and equipment that reduces the transmission of vibration to the body. Finally, there is a discussion of the research gaps that need to be investigated to further reduction in the incidence of vibration-induced illnesses and injuries.

Contact area affects frequency-dependent responses to vibration in the peripheral vascular and sensorineural systems

Repetitive exposure to hand-transmitted vibration is associated with development of peripheral vascular and sensorineural dysfunctions. These disorders and symptoms associated with it are referred to as hand-arm vibration syndrome (HAVS). Although the symptoms of the disorder have been well characterized, the etiology and contribution of various exposure factors to development of the dysfunctions are not well understood. Previous studies performed using a rat-tail model of vibration demonstrated that vascular and peripheral nervous system adverse effects of vibration are frequency-dependent, with vibration frequencies at or near the resonant frequency producing the most severe injury. However, in these investigations, the amplitude of the exposed tissue was greater than amplitude typically noted in human fingers. To determine how contact with vibrating source and amplitude of the biodynamic response of the tissue affects the risk of injury occurring, this study compared the influence of frequency using different levels of restraint to assess how maintaining contact of the tail with vibrating source affects the transmission of vibration. Data demonstrated that for the most part, increasing the contact of the tail with the platform by restraining it with additional straps resulted in an enhancement in transmission of vibration signal and elevation in factors associated with vascular and peripheral nerve injury. In addition, there were also frequency-dependent effects, with exposure at 250 Hz generating greater effects than vibration at 62.5 Hz. These observations are consistent with studies in humans demonstrating that greater contact and exposure to frequencies near the resonant frequency pose the highest risk for generating peripheral vascular and sensorineural dysfunction.

Vibration characteristics of golf club heads in their handheld grinding process and potential approaches for reducing the vibration exposure

To control vibration-induced white finger among workers performing the fine grinding of golf club heads, the aims of this study are to clarify the major vibration sources in the grinding process, to identify and understand the basic characteristics of the club head vibration, and to propose potential approaches for reducing the vibration exposure. The vibrations on two typical club heads and two belt grinding machines were measured at a workplace. A simulated test station was also constructed and used to help examine some influencing factors of the club head vibration. This study found that the club head vibration was the combination of the vibration transmitted from the grinding machines and that generated in the grinding process. As a result, any factor that affects the machine vibration, the grinding vibration, and/or the dynamic response of the club head can influence the vibration exposure of the fingers or hands holding the club head in the grinding process. The significant influencing factors identified in the study include testing subject, grinding machine, machine operation speed, drive wheel condition, club head model, mechanical constraints imposed on the club head during the grinding, and machine foot pad. These findings suggest that the vibration exposure can be controlled by reducing the grinding machine vibration, changing the workpiece dynamic properties, and mitigating the vibration transmission in its pathway. Many potential methods for the control are proposed and discussed.

RELEVANCE TO INDUSTRY

Vibrations on handheld workpieces can be effectively transmitted to the hands, especially the fingers. As a result, a major component of the hand-arm vibration syndrome - vibration-induced white finger - has been observed among some workers performing the grinding and/or polishing tasks of the handheld workpieces such as golf club heads. The results of this study can be used to develop more effective methods and technologies to control the vibration exposure of these workers. This may help effectively control this occupational disease.

Human body modeling method to simulate the biodynamic characteristics of spine in vivo with different sitting postures

The aim of this study is to model the computational model of seated whole human body including skeleton, muscle, viscera, ligament, intervertebral disc, and skin to predict effect of the factors (sitting postures, muscle and skin, buttocks, viscera, arms, gravity, and boundary conditions) on the biodynamic characteristics of spine. Two finite element models of seated whole body and a large number of finite element models of different ligamentous motion segments were developed and validated. Static, modal, and transient dynamic analyses were performed. The predicted vertical resonant frequency of seated body model was in the range of vertical natural frequency of 4 to 7 Hz. Muscle, buttocks, viscera, and the boundary conditions of buttocks have influence on the vertical resonant frequency of spine. Muscle played a very important role in biodynamic response of spine. Compared with the vertical posture, the posture of lean forward or backward led to an increase in stress on anterior or lateral posterior of lumbar intervertebral discs. This indicated that keeping correct posture could reduce the injury of vibration on lumbar intervertebral disc under whole-body vibration. The driving posture not only reduced the load of spine but also increased the resonant frequency of spine.

Tool-specific performance of vibration-reducing gloves for attenuating fingers-transmitted vibration

BACKGROUND

Fingers-transmitted vibration can cause vibration-induced white finger. The effectiveness of vibration-reducing (VR) gloves for reducing hand transmitted vibration to the fingers has not been sufficiently examined.

OBJECTIVE

The objective of this study is to examine tool-specific performance of VR gloves for reducing finger-transmitted vibrations in three orthogonal directions (3D) from powered hand tools.

METHODS

A transfer function method was used to estimate the tool-specific effectiveness of four typical VR gloves. The transfer functions of the VR glove fingers in three directions were either measured in this study or during a previous study using a 3D laser vibrometer. More than seventy vibration spectra of various tools or machines were used in the estimations.

RESULTS

When assessed based on frequency-weighted acceleration, the gloves provided little vibration reduction. In some cases, the gloves amplified the vibration by more than 10%, especially the neoprene glove. However, the neoprene glove did the best when the assessment was based on unweighted acceleration. The neoprene glove was able to reduce the vibration by 10% or more of the unweighted vibration for 27 out of the 79 tools. If the dominant vibration of a tool handle or workpiece was in the shear direction relative to the fingers, as observed in the operation of needle scalers, hammer chisels, and bucking bars, the gloves did not reduce the vibration but increased it.

CONCLUSIONS

This study confirmed that the effectiveness for reducing vibration varied with the gloves and the vibration reduction of each glove depended on tool, vibration direction to the fingers, and finger location. VR gloves, including certified anti-vibration gloves do not provide much vibration reduction when judged based on frequency-weighted acceleration. However, some of the VR gloves can provide more than 10% reduction of the unweighted vibration for some tools or workpieces. Tools and gloves can be matched for better effectiveness for protecting the fingers.

The Efficacy of Anti-vibration Gloves

Anyone seeking to control the risks from vibration transmitted to the hands and arms may contemplate the use of anti-vibration gloves. To make an informed decision about any type of personal protective equipment, it is necessary to have performance data that allow the degree of protection to be estimated. The information provided with an anti-vibration glove may not be easy to understand without some background knowledge of how gloves are tested and does not provide any clear route for estimating likely protection. Some of the factors that influence the potential efficacy of an anti-vibration glove include how risks from hand-arm vibration exposure are assessed, how the standard test for a glove is carried out, the frequency range and direction of the vibration for which protection is sought, how much hand contact force or pressure is applied and the physical limitations due to glove material and construction. This paper reviews some of the background issues that are useful for potential purchasers of anti-vibration gloves. Ultimately, anti-vibration gloves cannot be relied on to provide sufficient and consistent protection to the wearer and before their use is contemplated all other available means of vibration control ought first to be implemented.

Review and Evaluation of Hand-Arm Coordinate Systems for Measuring Vibration Exposure, Biodynamic Responses, and Hand Forces

The hand coordinate systems for measuring vibration exposures and biodynamic responses have been standardized, but they are not actually used in many studies. This contradicts the purpose of the standardization. The objectives of this study were to identify the major sources of this problem, and to help define or identify better coordinate systems for the standardization. This study systematically reviewed the principles and definition methods, and evaluated typical hand coordinate systems. This study confirms that, as accelerometers remain the major technology for vibration measurement, it is reasonable to standardize two types of coordinate systems: a tool-based basicentric (BC) system and an anatomically based biodynamic (BD) system. However, these coordinate systems are not well defined in the current standard. Definition of the standard BC system is confusing, and it can be interpreted differently; as a result, it has been inconsistently applied in various standards and studies. The standard hand BD system is defined using the orientation of the third metacarpal bone. It is neither convenient nor defined based on important biological or biodynamic features. This explains why it is rarely used in practice. To resolve these inconsistencies and deficiencies, we proposed a revised method for defining the realistic handle BC system and an alternative method for defining the hand BD system. A fingertip-based BD system for measuring the principal grip force is also proposed based on an important feature of the grip force confirmed in this study.

Theoretical foundation, methods, and criteria for calibrating human vibration models using frequency response functions

While simulations of the measured biodynamic responses of the whole human body or body segments to vibration are conventionally interpreted as summaries of biodynamic measurements, and the resulting models are considered quantitative, this study looked at these simulations from a different angle: model calibration. The specific aims of this study are to review and clarify the theoretical basis for model calibration, to help formulate the criteria for calibration validation, and to help appropriately select and apply calibration methods. In addition to established vibration theory, a novel theorem of mechanical vibration is also used to enhance the understanding of the mathematical and physical principles of the calibration. Based on this enhanced understanding, a set of criteria was proposed and used to systematically examine the calibration methods. Besides theoretical analyses, a numerical testing method is also used in the examination. This study identified the basic requirements for each calibration method to obtain a unique calibration solution. This study also confirmed that the solution becomes more robust if more than sufficient calibration references are provided. Practically, however, as more references are used, more inconsistencies can arise among the measured data for representing the biodynamic properties. To help account for the relative reliabilities of the references, a baseline weighting scheme is proposed. The analyses suggest that the best choice of calibration method depends on the modeling purpose, the model structure, and the availability and reliability of representative reference data.

An examination of an adapter method for measuring the vibration transmitted to the human arms

The objective of this study is to evaluate an adapter method for measuring the vibration on the human arms. Four instrumented adapters with different weights were used to measure the vibration transmitted to the wrist, forearm, and upper arm of each subject. Each adapter was attached at each location on the subjects using an elastic cloth wrap. Two laser vibrometers were also used to measure the transmitted vibration at each location to evaluate the validity of the adapter method. The apparent mass at the palm of the hand along the forearm direction was also measured to enhance the evaluation. This study found that the adapter and laser-measured transmissibility spectra were comparable with some systematic differences. While increasing the adapter mass reduced the resonant frequency at the measurement location, increasing the tightness of the adapter attachment increased the resonant frequency. However, the use of lightweight (≤15 g) adapters under medium attachment tightness did not change the basic trends of the transmissibility spectrum. The resonant features observed in the transmissibility spectra were also correlated with those observed in the apparent mass spectra. Because the local coordinate systems of the adapters may be significantly misaligned relative to the global coordinates of the vibration test systems, large errors were observed for the adapter-measured transmissibility in some individual orthogonal directions. This study, however, also demonstrated that the misalignment issue can be resolved by either using the total vibration transmissibility or by measuring the misalignment angles to correct the errors. Therefore, the adapter method is acceptable for understanding the basic characteristics of the vibration transmission in the human arms, and the adapter-measured data are acceptable for approximately modeling the system.

Antivibration gloves: effects on vascular and sensorineural function, an animal model

Anti-vibration gloves have been used to block the transmission of vibration from powered hand tools to the user, and to protect users from the negative health consequences associated with exposure to vibration. However, there are conflicting reports as to the efficacy of gloves in protecting workers. The goal of this study was to use a characterized animal model of vibration-induced peripheral vascular and nerve injury to determine whether antivibration materials reduced or inhibited the effects of vibration on these physiological symptoms. Rats were exposed to 4 h of tail vibration at 125 Hz with an acceleration 49 m/s(2). The platform was either bare or covered with antivibrating glove material. Rats were tested for tactile sensitivity to applied pressure before and after vibration exposure. One day following the exposure, ventral tail arteries were assessed for sensitivity to vasodilating and vasoconstricting factors and nerves were examined histologically for early indicators of edema and inflammation. Ventral tail artery responses to an α2C-adrenoreceptor agonist were enhanced in arteries from vibration-exposed rats compared to controls, regardless of whether antivibration materials were used or not. Rats exposed to vibration were also less sensitive to pressure after exposure. These findings are consistent with experimental findings in humans suggesting that antivibration gloves may not provide protection against the adverse health consequences of vibration exposure in all conditions. Additional studies need to be done examining newer antivibration materials.

Anti-vibration gloves?

For exposure to hand-transmitted vibration (HTV), personal protective equipment is sold in the form of anti-vibration (AV) gloves, but it remains unclear how much these gloves actually reduce vibration exposure or prevent the development of hand-arm vibration syndrome in the workplace. This commentary describes some of the issues that surround the classification of AV gloves, the assessment of their effectiveness and their applicability in the workplace. The available information shows that AV gloves are unreliable as devices for controlling HTV exposures. Other means of vibration control, such as using alternative production techniques, low-vibration machinery, routine preventative maintenance regimes, and controlling exposure durations are far more likely to deliver effective vibration reductions and should be implemented. Furthermore, AV gloves may introduce some adverse effects such as increasing grip force and reducing manual dexterity. Therefore, one should balance the benefits of AV gloves and their potential adverse effects if their use is considered.

Theoretical relationship between vibration transmissibility and driving-point response functions of the human body

The relationship between the vibration transmissibility and driving-point response functions (DPRFs) of the human body is important for understanding vibration exposures of the system and for developing valid models. This study identified their theoretical relationship and demonstrated that the sum of the DPRFs can be expressed as a linear combination of the transmissibility functions of the individual mass elements distributed throughout the system. The relationship is verified using several human vibration models. This study also clarified the requirements for reliably quantifying transmissibility values used as references for calibrating the system models. As an example application, this study used the developed theory to perform a preliminary analysis of the method for calibrating models using both vibration transmissibility and DPRFs. The results of the analysis show that the combined method can theoretically result in a unique and valid solution of the model parameters, at least for linear systems. However, the validation of the method itself does not guarantee the validation of the calibrated model, because the validation of the calibration also depends on the model structure and the reliability and appropriate representation of the reference functions. The basic theory developed in this study is also applicable to the vibration analyses of other structures.

Modeling of the biodynamic responses distributed at the fingers and palm of the hand in three orthogonal directions

The objectives of this study were to develop models of the hand-arm system in the three orthogonal directions (x_h, y_h , and z_h ) and to enhance the understanding of the hand vibration dynamics. A four-degrees-of-freedom (DOF) model and 5-DOF model were used in the simulation for each direction. The driving-point mechanical impedances distributed at the fingers and palm of the hand reported in a previous study were used to determine the parameters of the models. The 5-DOF models were generally superior to the 4-DOF models for the simulation. Hence, as examples of applications, the 5-DOF models were used to predict the transmissibility of a vibration-reducing glove and the vibration transmissibility on the major substructures of the hand-arm system. The model-predicted results were also compared with the experimental data reported in two other recent studies. Some reasonable agreements were observed in the comparisons, which provided some validation of the developed models. This study concluded that the 5-DOF models are acceptable for helping to design and analyze vibrating tools and anti-vibration devices. This study also confirmed that the 5-DOF model in the z_h direction is acceptable for a coarse estimation of the biodynamic responses distributed throughout the major substructures of the hand-arm system. Some interesting phenomena observed in the experimental study of the biodynamic responses in the three directions were also explained in this study.