The transmission of vertical vibration through seats: Influence of the characteristics of the human body

The transmission of vibration through a seat depends on the impedance of the seat and the apparent mass of the seat occupant. This study was designed to determine how factors affecting the apparent mass of the body (age, gender, physical characteristics, backrest contact, and magnitude of vibration) affect seat transmissibility. The transmission of vertical vibration through a car seat was measured with 80 adults (41 males and 39 females aged 18-65) at frequencies between 0.6 and 20 Hz with two backrest conditions (no backrest and backrest), and with three magnitudes of random vibration (0.5, 1.0, and 1.5 m s^-2 rms). Linear regression models were used to study the effects of subject physical characteristics (age, gender, and anthropometry) and features of their apparent mass (resonance frequency, apparent mass at resonance and at 12 Hz) on the measured seat transmissibility. The strongest predictor of both the frequency of the principal resonance in seat transmissibility and the seat transmissibility at resonance was subject age, with other factors having only marginal effects. The transmissibility of the seat at 12 Hz depended on subject age, body mass index, and gender. Although subject weight was strongly associated with apparent mass, weight was not strongly associated with seat transmissibility. The resonance frequency of the seat decreased with increases in the magnitude of the vibration excitation and increased when subjects made contact with the backrest. Inter-subject variability in the resonance frequency and transmissibility at resonance was less with greater vibration excitation, but was largely unaffected by backrest contact. A lumped parameter seat-person model showed that changes in seat transmissibility with age can be predicted from changes in apparent mass with age, and that the dynamic stiffness of the seat appeared to increase with increased loading so as to compensate for increases in subject apparent mass associated with increased sitting weight.     

The apparent mass and mechanical impedance of the hand and the transmission of vibration to the fingers, hand, and arm

Although hand-transmitted vibration causes injury and disease, most often evident in the fingers, the biodynamic responses of the fingers, hand, and arm are not yet well understood. A method of investigating the motion of the entire finger-hand-arm system, based on the simultaneous measurement of the biodynamic response at the driving point and the transmissibility to many points on the finger-hand-arm system, is illustrated. Fourteen male subjects participated in an experiment in which they pushed down on a vertically vibrating metal plate with their right forearm pronated and their elbow bent at 90°. The apparent mass and mechanical impedance of the finger-hand-arm system were measured for each of seven different contact conditions between the plate and the fingers and hand. Simultaneously, the vibration of the fingers, hand, and arm was measured at 41 locations using a scanning laser Doppler vibrometer. Transmissibilities showed how the vibration was transmitted along the arm and allowed the construction of spectral operating deflection shapes showing the vibration pattern of the fingers, hand, and arm for each of the seven contact conditions. The vibration patterns at critical frequencies for each contact condition have been used to explain features in the driving point biodynamic responses and the vibration behaviour of the hand-arm system. Spectral operating deflection shapes for the upper limb assist the interpretation of driving point biodynamic responses and help to advance understanding required to predict, explain, and control the various effects of hand-transmitted vibration.     

Vibration transmissibility characteristics of the human hand-arm system under different postures, hand forces and excitation levels

Biodynamic responses of the hand-arm system have been mostly characterized in terms of driving-point force-motion relationships, which have also served as the primary basis for developing the mechanical-equivalent models. The knowledge of localized vibration responses of the hand-arm segments could help derive more effective biodynamic models. In this study, the transmission of z_h-axis handle vibration to the wrist, elbow and the shoulder of the human hand and arm are characterized in the laboratory for the bent-arm and extended arm postures. The experiments involved six subjects grasping a handle subject to two different magnitudes of broad-band random vibration, and nine different combinations of hand grip and push forces. The vibration transmissibility data were acquired in the z_h- and y_h-axis at the wrist and shoulder, and along all the three axes around the elbow joint. The results show that the human hand-arm system in an extended arm posture amplifies the vibration transmitted to the upper-arm and the whole-body at frequencies below 25 Hz, but attenuates the vibration above 25 Hz more effectively than the bent-arm posture, except at the shoulder. The magnitudes of transmitted vibration under an extended arm posture along the y_h-axis were observed to be nearly twice those for the bent-arm posture in the low frequency region. The results further showed that variations in the grip force mostly affect vibration transmissibility and characteristic frequencies of the forearm, while changes in the push force influenced the dynamic characteristics of the entire hand-arm system. The magnitudes of transmitted vibration in the vicinity of the characteristic frequencies were influenced by the handle vibration magnitude.     

EVALUATION OF FREQUENCY WEIGHTING (ISO 2631-1) FOR ACUTE EFFECTS OF WHOLE-BODY VIBRATION ON GASTRIC MOTILITY

The aim of this study was to investigate the effects of exposure to whole-body vibration (WBV) and the ISO 2631/1-1997 frequency weighting on gastric motility. The gastric motility was measured by electrogastrography (EGG) in nine healthy volunteers. Sinusoidal vertical vibration at a frequency of 4, 6·3, 8, 12, 16, 31·5, or 63 Hz was given to the subjects for 10 min. The magnitude of exposure at 4 Hz was 1·0m/s² (r.m.s.). The magnitudes of the other frequencies gave the same frequency-weighted acceleration according to ISO 2631/1-1997. The pattern of the dominant frequency histogram (DFH) was changed to a broad distribution pattern by vibration exposure. Vibration exposure had the effect of significantly reducing the percentage of time for which the dominant component had a normal rhythm and increasing the percentage of time for which there was tachygastria (p<0·05). Vibration exposure generally reduced the mean percentage of time with the dominant frequency in normal rhythm component. There was a significant difference between the condition of no vibration and exposure to 4 and 6·3 Hz of vibration frequency (p<0·05). The frequency weighting curve given in ISO 2631/1-1997 was not adequate for use in evaluating the physiological effects of WBV exposure on gastric motility.     

A BODY MASS DEPENDENT MECHANICAL IMPEDANCE MODEL FOR APPLICATIONS IN VIBRATION SEAT TESTING

A three degree-of-freedom model is proposed to predict the biodynamic responses of the seated human body of different masses. A baseline model is initially derived to satisfy both the mean apparent mass and seat-to-head transmissibility responses proposed in ISO/DIS 5982:2000 applicable for mean body mass of 75 kg. The validity of the resultant generic mass dependent model is verified by comparing the apparent mass and driving-point mechanical impedance responses computed for total body masses of 55, 75 and 90 kg with the range of idealized values proposed for body masses within the 49-93 kg range. Considering the lack of data that could be found to define the apparent mass/mechanical impedance of subjects with different body masses when applying the experimental conditions defined in ISO/DIS 5982:2000, an attempt is made to adapt the parameters of the base model to fit the measured apparent mass data applicable to groups of automobile occupants within different mass ranges. This is achieved through constrained parametric optimization which consists of minimizing the sum of squared errors between the computed response and the mean apparent mass data measured for automobile occupants within four mass groups: less than 60 kg, 60·5-70·5 kg, 70·5-80 kg and above 80 kg. The results show a reasonably good agreement between the model responses and the measured apparent mass data, particularly at frequencies below 10 Hz. The results suggest that the proposed mass dependent model can effectively predict the apparent mass responses of automobile occupants over a wide range of body masses and for two different postures: passenger (hands-in-lap) and driver (hands-on-steering wheel) postures.     

Vibration modelling of helical springs with non-uniform ends

Helical springs constitute an integral part of many mechanical systems. Usually, a helical spring is modelled as a massless, frequency independent stiffness element. For a typical suspension spring, these assumptions are only valid in the quasi-static case or at low frequencies. At higher frequencies, the influence of the internal resonances of the spring grows and thus a detailed model is required. In some cases, such as when the spring is uniform, analytical models can be developed. However, in typical springs, only the central turns are uniform; the ends are often not (for example, having a varying helix angle or cross-section). Thus, obtaining analytical models in this case can be very difficult if at all possible. In this paper, the modelling of such non-uniform springs are considered. The uniform (central) part of helical springs is modelled using the wave and finite element (WFE) method since a helical spring can be regarded as a curved waveguide. The WFE model is obtained by post-processing the finite element (FE) model of a single straight or curved beam element using periodic structure theory. This yields the wave characteristics which can be used to find the dynamic stiffness matrix of the central turns of the spring. As for the non-uniform ends, they are modelled using the standard finite element (FE) method. The dynamic stiffness matrices of the ends and the central turns can be assembled as in standard FE yielding a FE/WFE model whose size is much smaller than a full FE model of the spring. This can be used to predict the stiffness of the spring and the force transmissibility. Numerical examples are presented.     

Suppression of brake squeal noise applying finite element brake and pad model enhanced by spectral-based assurance criteria

An enhanced dynamic finite element (FE) model with friction coupling is applied to analyze the design of disc brake pad structure for squeal noise reduction. The FE model is built-up from the individual brake component representations. Its interfacial structural connections and boundary conditions are determined by correlating to a set of measured frequency response functions using a spectral-based assurance criterion. The proposed friction coupling formulation produces an asymmetric system stiffness matrix that yields a set of complex conjugate eigenvalues. The analysis shows that eigenvalues possessing positive real parts tend to produce unstable modes with the propensity towards the generation of squeal noise. Using a proposed lumped parameter model and eigenvalue sensitivity study, beneficial pad design changes can be identified and implemented in the detailed FE model to determine the potential improvements in the dynamic stability of the system. Also, a selected set of parametric studies is performed to evaluate numerous design concepts using the proposed dynamic FE model. The best pad design attained, which produces the least amount of squeal response, is finally validated by comparison to a set of actual vehicle test results.     

Experimental Investigation of Nonlinear Vibration Isolator with Fluidic Actuators (NLVIFA)

This paper elaborates a nonlinear fluidic low frequency vibration isolator designed with the characteristics of quasi-zero stiffness (QZS). The existing model of QZS vibration isolator enhances amplitude of vibration and attenuating vibration frequencies. This concern with displacement plays a vital role in the performance and instability of oblique spring setup reduces the isolator performance in horizontal non-nominal loads, in this accordance; this paper associates double acting hydraulic cylinder (fluidic actuators in short) in oblique and helical coil spring. An approximate expression of unique analytical relationship between the stiffness of vertical spring and bulk modulus of the fluid is derived for Quasi – Zero Stiffness Non-Linear Vibration Isolator with Fluidic Actuators (NLVIFA in short) system and the force transmissibility is formulated and damping ratio are discussed for characteristic analysis. Modal analysis carried out and compared with analytical results and an experimental prototype is developed and investigated. The performance of the NLVIFA reduces the external embarrassment more at low frequencies and the series of experimental studies showing that the soft nonlinearity causes limitation in the resonant frequency thereupon the isolation will be enhanced and NLVIFA greatly outperform some other type of nonlinear isolators.     

A new multi-objective approach to finite element model updating

The single objective function (SOF) has been employed for the optimization process in the conventional finite element (FE) model updating. The SOF balances the residual of multiple properties (e.g., modal properties) using weighting factors, but the weighting factors are hard to determine before the run of model updating. Therefore, the trial-and-error strategy is taken to find the most preferred model among alternative updated models resulted from varying weighting factors. In this study, a new approach to the FE model updating using the multi-objective function (MOF) is proposed to get the most preferred model in a single run of updating without trial-and-error. For the optimization using the MOF, non-dominated sorting genetic algorithm-II (NSGA-II) is employed to find the Pareto optimal front. The bend angle related to the trade-off relationship of objective functions is used to select the most preferred model among the solutions on the Pareto optimal front. To validate the proposed approach, a highway bridge is selected as a test-bed and the modal properties of the bridge are obtained from the ambient vibration test. The initial FE model of the bridge is built using SAP2000. The model is updated using the identified modal properties by the SOF approach with varying the weighting factors and the proposed MOF approach. The most preferred model is selected using the bend angle of the Pareto optimal front, and compared with the results from the SOF approach using varying the weighting factors. The comparison shows that the proposed MOF approach is superior to the SOF approach using varying the weighting factors in getting smaller objective function values, estimating better updated parameters, and taking less computational time.     

Tactile information transfer: a comparison of two stimulation sites

Two experiments on the discrimination of time-varying tactile stimuli were performed, with comparison of stimulus delivery to the distal pad of the right index finger and to the right wrist (palmar surface). Subjects were required to perceive differences in short sequences of computer-generated stimulus elements (experiment 1) or differences in short tactile stimuli derived from a speech signal (experiment 2). The pulse-train stimuli were distinguished by differences in frequency (i.e., pulse repetition rate) and amplitude, and by the presence/absence of gaps (approximately 100-ms duration). Stimulation levels were 10 dB higher at the wrist than at the fingertip, to compensate for the lower vibration sensitivity at the wrist. Results indicate similar gap detection at wrist and fingertip and similar perception of frequency differences. However, perception of amplitude differences was found to be better at the wrist than at the fingertip. Maximum information transfer rates for the stimuli in experiment 1 were estimated at 7 bits s(-1) at the wrist and 5 bits s(-1) at the fingertip.     

A new type of semi-active hydraulic engine mount using controllable area of inertia track

Automotive engine mounts function to constrain the engine shake motion resulting at low-frequencies, as well as to isolate noises and vibrations generated by the engine with unbalanced disturbances at the high frequencies. The property of the mount depends on vibration amplitude and excitation frequency. It means that the excitation amplitude is large in low excitation frequency range and small in high frequency range. In this paper, a new hydraulic engine mount with a controllable area of inertia track is proposed and investigated. Theoretical works with the mount model to isolate the engine-related vibrations were conducted by an optimal algorithm to control the area of the inertia track under shocks and multi-signal force excitations. This research clearly gives an analysis of the considerable changes in the mount dynamic properties according to the changes in the inertia track area. Consequently, when the inertia track area is tuned, the transmissibility of the mount is effectively reduced.     

Experimental Investigation and Semi-Active Control Design of A Magnetorheological Engine Mount

In this paper; the dynamic characteristics of a semi-active magnetorheological fluid (MRF) engine mount are studied. To do so, the performance of the MRF engine mount is experimentally examined in higher frequencies (50~170 Hz) and the various amplitudes (0.01 ~ 0.2 mm). In such an examination, an MRF engine mount along with its magnetically biased is fabricated and successfully measured. In addition, the natural frequencies of the system are obtained by standard hammer modal test. For modelling the behavior of the system, a mass-spring-damper model with tuned PID coefficients based on Pessen integral of absolute error method is used. The parameters of such a model including mass, damping ratio, and stiffness are identified with the help of experimental modal tests and the recursive least square method (RLS). It is shown that using PID controller leads to reducing the vibration transmissibility in the resonance frequency (=93.45 Hz) with respect to the typical passive engine mount by a factor of 58%. The average of the vibration transmissibility decreasing is also 43% within frequency bandwidth (50~170 Hz).     

Effects of isolators internal resonances on force transmissibility and radiated noise

Vibration isolators have been extensively used to reduce the vibration and noise transmitted between the components of mechanical systems. Although some previous studies on vibration isolation considered the inertia of isolators, they only examined its effects on the vibration of single degree-of-freedom (d.o.f.) systems. These studies did not emphasize the importance of the isolators’ inertia, especially from the perspective of noise reduction. This paper shows that the internal dynamics of the isolator, which are also known as internal resonances (IRs) or wave effects, can significantly affect the isolator performance at high frequencies. To study the IR problem, a model of a primary mass connected to a flexible foundation through three isolators is used. In this model, the isolator is represented as a one-dimensional continuous rod that accounts for its internal dynamics. The primary mass is modelled as a rigid body with three d.o.f.'s. The effects of the IRs on the force transmissibility and the radiated sound power from the foundation are examined. It is shown that the IRs significantly increase the force transmissibility and the noise radiation level at some frequencies. These effects cannot be predicted using a traditional model that neglects the inertia of the isolator. The influence of the foundation flexibility on the IRs is also investigated. It is shown that the foundation flexibility greatly affects the noise radiation level but it affects only slightly the force transmissibility, especially at high frequencies where the IRs occur.     

MR detection of mechanical vibrations using a radiofrequency field gradient

A new method for NMR characterization of mechanical waves, based upon radiofrequency field gradient for motion encoding, is proposed. A binomial B1 gradient excitation scheme was used to visualize the mobile spins undergoing a periodic transverse mechanical excitation. A simple model was designed to simulate the NMR signal as a function of the wave frequency excitation and the periodicity of the NMR pulse sequence. The preliminary results were obtained on a gel phantom at low vibration frequencies (0-200 Hz) by using a ladder-shaped coil generating a nearly constant RF field gradient along a specific known direction. For very small displacements and/or B1 gradients, the NMR signal measured on a gel phantom was proportional to the vibration amplitude and the pulse sequence was shown to be selective with respect to the vibration frequency. A good estimation of the direction of vibrations was obtained by varying the angle between the motion direction and the B1 gradient. The method and its use in parallel to more conventional MR elastography techniques are discussed. The presented approach might be of interest for noninvasive investigation of elastic properties of soft tissues and other materials.     

Improved eigenvalues for combined dynamical systems using a modified finite element discretization scheme

New approaches are presented to discretize an arbitrarily supported linear structure carrying various lumped attachments. Specifically, the exact eigendata, i.e., the exact natural frequencies and mode shapes, of the linear structure without the lumped attachments are first used to modify its finite element mass and stiffness matrix so that the eigensolutions of the discretized system coincide with the exact modes of vibration. This is achieved by identifying a set of minimum changes in the finite element system matrices and enforcing certain constraint conditions. Once the updated matrices for the linear structure are found, the finite element assembling technique is then used to include the lumped attachments by adding their parameters to the appropriate elements in the modified mass and stiffness matrices. Numerical experiments show that for the same number of elements, the proposed scheme returns higher natural frequencies that are substantially more accurate than those given by the finite element model. Alternatively, the proposed discretization scheme allows one to efficiently and accurately determine the higher natural frequencies of a combined system without increasing the number of elements in the finite element model.     

Sensor fusion for active vibration isolation in precision equipment

Sensor fusion is a promising control strategy to improve the performance of active vibration isolation systems that are used in precision equipment. Normally, those vibration isolation systems are only capable of realizing a low transmissibility. Additional objectives are to increase the damping ratio of internal vibration modes and to provide a high support stiffness. It is shown that these three objectives cannot be realized simultaneously if only acceleration or force feedback is used. An active hard mount suspension with a feedback strategy based on sensor fusion is proposed that uses the acceleration signal at low frequencies and the force signal at high frequencies. Using sensor fusion, the three objectives can be achieved simultaneously. Experiments on a single-axis setup show that this feedback strategy provides an excellent performance.     

Fore-and-aft transmissibility of backrests: Variation with height above the seat surface and non-linearity

The transmissibility of a seat depends on the dynamic response of the human body (which varies between individuals, body locations, and vibration magnitudes) and the dynamic response of the seat (which varies according to seat design). In the fore-and-aft direction, the transmissibility of a seat backrest was therefore expected to vary with vertical position on the backrest. This experimental study with 12 subjects investigated how backrest transmissibility varied with both the vertical measurement position and the magnitude of vibration. The transmissibilities of the backrest of a car seat and a block of solid foam were measured at five heights above the seat surface with random fore-and-aft vibration at five magnitudes (0.1, 0.2, 0.4, 0.8 and 1.6 ms⁻² rms) over the range 0.25–20 Hz. The median transmissibilities exhibited resonances in the range 4–5 Hz for the car seat and in the range 3–6 Hz for the foam. The backrests showed clear changes in transmissibility with vertical position, but there were minimal changes in the resonance frequencies. For both backrests, the transmissibilities were greatest at the middle of the backrest. The least transmissibility was measured at the top of the car seat but at the bottom of the foam backrest. At each measurement position on both backrests, the transmissibility was non-linear with vibration magnitude: the resonance frequencies and transmissibilities at resonance decreased with increasing vibration magnitude. The variations in backrest transmissibility with vertical position and with vibration magnitude were sufficiently great to affect assessments of backrest dynamic performance. The results suggest that the fore-and-aft transmissibilities of backrests should be evaluated from more than one measurement location.     

Development and analysis of a longitudinal and torsional type ultrasonic motor with two stators

In this paper, a new longitudinal and torsional type ultrasonic motor with two stators is presented and investigated. Normally, such a motor consists of one rotor and one stator, and two types of transducers that are longitudinal PZT and torsional PZT are used to generate the desired elliptical locus on the stator surface. The operating frequency is at the resonance frequency of torsional transducer. In order to enhance the efficiency of the motor, however, the resonance frequencies of both transducers should be closed to each other. For the purpose of matching the resonance frequencies, a symmetrical structure is adopted in design of the motor. Furthermore, two rings are added to the stators in order to adjust the resonance frequencies of these two transducers. A finite element model is developed and ANSYS software is used to analyze the resonance frequencies of longitudinal vibration and torsional vibration as well as optimize the motor geometry. According to the FE results, an experimental prototype is fabricated and the experimental results agree well with the theoretical predictions.     

Transfer function method for investigating the complex modulus of acoustic materials: Spring-like specimen

The complex modulus of acoustic materials has to be known as a function of frequency. Among many methods for investigating the complex modulus, it is advantageous to use the transfer function method for detailed frequency analysis. In this method, a cylindrical or prismatic specimen is excited into longitudinal vibration at one end, the other end being loaded by a mass. The complex modulus can be calculated after having measured the transfer function: i.e., the vibration amplitudes of the specimen ends and the phase angle between them. In this paper the transfer function and its measurability are investigated theoretically and experimentally in that frequency range where the specimen can essentially be modelled by lumped parameter mechanical elements. The role of the measurement errors is analyzed and it is shown that the smaller the loss factor the higher the measurement accuracy that is needed. Furthermore, it is shown that disregarding the longitudinal wave motion of the specimen at higher frequencies leads to an apparent increase of the dynamic modulus and to an apparent decreases of the loss factor. This effect may be compensated up to a certain frequency by the lateral wave motion of the specimen. Experimental results supporting the theoretical predictions are presented.