Acceleration Transmissibility Research Articles

Platform accelerations of three different whole-body vibration devices and the transmission of vertical vibrations to the lower limbs

Physical whole-body vibration (WBV) exercises become available at various levels of intensity. In a first series of measurements, we investigated 3-dimensional platform accelerations of three different WBV devices without and with three volunteers of different weight (62, 81 and 100 kg) in squat position (150° knee flexion). The devices tested were two professional devices, the PowerPlate and the Galileo-Fitness, and one home-use device, the PowerMaxx. In a second series of measurements, the transmission of vertical platform accelerations of each device to the lower limbs was tested in eight healthy volunteers in squat position (100° knee flexion). The first series showed that the platforms of two professional devices vibrated in an almost perfect vertical sine wave at frequencies between 25–50 and 5–40 Hz, respectively. The platform accelerations were slightly influenced by body weight. The PowerMaxx platform mainly vibrated in the horizontal plane at frequencies between 22 and 32 Hz, with minimal accelerations in the vertical direction. The weight of the volunteers reduced the platform accelerations in the horizontal plane but amplified those in the vertical direction about eight times. The vertical accelerations were highest in the Galileo (∼15 units of g) and the PowerPlate (∼8 units of g) and lowest in the PowerMaxx (∼2 units of g). The second series showed that the transmission of vertical accelerations at a common preset vibration frequency of 25 Hz were largest in the ankle and that transmission of acceleration reduced ∼10 times at the knee and hip. We conclude that large variation in 3-dimensional accelerations exist in commercially available devices. The results suggest that these differences in mechanical behaviour induce variations in transmissibility of vertical vibrations to the (lower) body.

Transmission of Vertical Whole Body Vibration to the Human Body

According to experimental studies, low-amplitude high-frequency vibration is anabolic to bone tissue, whereas in clinical trials, the bone effects have varied. Given the potential of whole body vibration in bone training, this study aimed at exploring the transmission of vertical sinusoidal vibration to the human body over a wide range of applicable amplitudes (from 0.05 to 3 mm) and frequencies (from 10 to 90 Hz). Vibration-induced accelerations were assessed with skin-mounted triaxial accelerometers at the ankle, knee, hip, and lumbar spine in four males standing on a high-performance vibration platform. Peak vertical accelerations of the platform covered a range from 0.04 to 19 in units of G (Earth's gravitational constant). Substantial amplification of peak acceleration could occur between 10 and 40 Hz for the ankle, 10 and 25 Hz for the knee, 10 and 20 Hz for the hip, and at 10 Hz for the spine. Beyond these frequencies, the transmitted vibration power declined to 1/10th-1/1000 th of the power delivered by the platform. Transmission of vibration to the body is a complicated phenomenon because of nonlinearities in the human musculoskeletal system. These results may assist in estimating how the transmission of vibration-induced accelerations to body segments is modified by amplitude and frequency and how well the sinusoidal waveform is maintained. Although the attenuation of vertical vibration at higher frequencies is fortunate from the aspect of safety, amplitudes >0.5 mm may result in greater peak accelerations than imposed at the platform and thus pose a potential hazard for the fragile musculoskeletal system.

Application of Momentum Exchange Impact Dampers to Forging Machine

This paper proposes an impact control method for a forging machine using a momentum exchange impact damper. This method is based on momentum conservation of two colliding bodies. A conventional added mass control method fails to suppress the acceleration and force transmission simultaneously. By using the momentum exchange impact damper, it is shown that the bed acceleration and the transmitted force to the floor are reduced. This paper presents a theoretical analysis of an impact damper and an optimum condition that leads to a minimization of the energy of a forging machine. An experimental analysis is shown to validate the simulation results.

Research on parametric optimum design for a multi medium coupling shock absorber based on dual demand for resisting violent impact and attenuating vibration

The aim of this paper is to provide a method to perform parameters matching selection for a multi medium coupling shock absorber. A model considers the coupling of quadratic damping, viscosity damping, coulomb damping and spring is investigated. Two style excitations on the system as inputs are discussed respectively. The approximate theoretical formulae include output response of the system, break-loose frequency, absolute acceleration transmissibility are deduced. The analytical results are compared with numerical solution. The impact characteristic of the model is also analysed. An optimum model for parameters is built. An example is illustrated to confirm the validity of the modelling and the solution.

Assessments of two dynamic manikins for laboratory testing of seats under whole-body vibration

The aptness of two anthropodynamic manikins for assessing vibration isolation effectiveness of suspension seats is evaluated through laboratory measurements. The evaluations were performed using five different suspension seats exposed to idealized white noise (0.5–20 Hz) and target vehicle excitations along the vertical axis using a whole-body vehicular vibration simulator. The measurements were performed to derive acceleration transmissibility and seat effective amplitude transmissibility (SEAT) characteristics of seats loaded with: human subjects of body masses in the vicinity of 55, 75 and 98 kg; manikins configured to same masses; and equivalent rigid masses. The dynamic responses of the manikins were also measured under different magnitudes of white-noise excitations and expressed in terms of apparent mass. The relative applicability of the manikins for selected seats was evaluated by comparing the measures with those obtained for the seat–human and seat–mass systems. The comparisons suggested that the SEAT measures attained with manikins are comparable with those obtained with equivalent rigid mass, irrespective of the body mass, for the low natural frequency seats (⩽2 Hz) considered in the study. Both the manikins and the equivalent rigid masses, however, provided an overestimate of isolation effectiveness of seats, when compared to those with human subjects. The manikins resulted in better estimates of SEAT values for high natural frequency seats than the rigid mass. The dynamic responses of manikins were also compared with the ranges of standardized values reported in ISO-5982 and DIN-45676. The results revealed considerable differences between the biodynamic responses of manikins and the standardized ranges.

On dry friction modelling and simulation in kinematically excited oscillatory systems

This paper deals with the analysis and simulation of a general single degree of freedom (sdof) oscillatory system with idealised linear viscous damper and dry friction. For dry friction modelling the phenomenological macro-slip approach is employed, described in mathematical form either by the signum function approach or by the physically correct stick–slip approach assuming switching phenomena on a short time scale. Both approaches are illustrated first using a steady-state harmonic acceleration excitation with constant amplitude and then a stationary random acceleration excitation, corresponding to a field-measured excitation in a vehicle. The differences in the two approaches are highlighted, indicating that the physically correct stick–slip approach describes the friction phenomenon better than the standard signum approach. The signum approach is prone to false numerical oscillations completely distorting the acceleration response signal in comparison to measured suspension system response. The acceleration transmissibility response is analysed in respect to the dry friction force magnitude, employing stationary random excitation. A sdof oscillatory system without viscous damping, subjected to both stationary random acceleration and harmonic acceleration is analysed, too. It is shown that such a system can be used without serious practical problems; however, no implications on its performance from the analysis under harmonic constant amplitude acceleration excitation can be made.

A systematic approach on computational analysis and optimization design: for a nonlinear coupling shock absorber

The aim of this article is to provide a systematic approach to perform computational simulation and optimization design of parameters matching selection for a nonlinear coupling shock absorber. A theoretical mathematical model with nonlinear coupling for shock absorber is induced based on relative literature. The model considers the coupling of quadratic damping, viscosity damping, coulomb damping and nonlinear spring. Approximate computational solution is deduced by introducing harmonic balance method and Fourier transform method. These approximate theoretical solutions include output response of the system, absolute acceleration transmissibility in vibration or impact, and the maximum relative displacement in impact process, etc. The approximate computational results are compared with those obtained by numerical integration to confirm the validity of the mathematical model. In the meantime, an optimization design model for parameters is built. The design example is illustrated to confirm the validity of the modeling method and the theoretical solution.

고무와 압전작동기를 이용한 하이브리드 마운트의 설계 및 진동제어 응용

This paper presents active vibration control using a hybrid mount which consists of rubber element and the piezostack actuator. After identifying stiffness and damping properties of the rubber element and piezoelectric elements, a mechanical model of the hybrid mount is established. The mount model is then incorporated with the vibration system, and the governing equation of motion is obtained in a state space. A sliding mode controller and LQG controller are designed in order to actively attenuate the vibration of the system subjected to various frequencies and small magnitude excitations. Control responses such as acceleration and force transmission through the hybrid mount are evaluated by computer simulation.

Dynamic investigation and optimal design of a novel fluid coupling shock absorber for dual demand of vibration and impact safety of precision systems

The aim of this article is to provide a systematic investigation to the design or optimal design of the shock absorber for the protection of a precision system as electronic packaging system in harsh vibration-impact environment. To get the dual demand of resisting violent impact and attenuating vibration in vibration-impact-safety for precision equipment or components, a novel micro fluid coupling damping shock absorber is designed and manufactured through coupling the oil, rubber ball and spring by ingenious tactics. The physical mechanism of the actual shock absorber is systematically investigated. The experimental results of the key-model machine in dynamic tests show complex nonlinear dynamic characteristics. Based on the test, the nonlinear dynamic model for the shock absorber is presented by analyzing the internal fluid dynamic phenomenon with respect to the shock absorber. Comparisons with experimental data confirm the validity of the model. The model is integrated by introducing normalization measure in progress. The approximate formulae are deduced by introducing some transformation tactics. These approximate theoretical formulae include the output response of the system, absolute acceleration transmissibility in vibration or impact, and the maximum relative displacement in impact process etc. So the optimal model for parameters matching the design is built. The parameters matching the design are discussed based on an approximate solution in progress. Finally, an example of the applied product is described.

Changes in Muscle Activity in Response to Different Impact Forces Affect Soft Tissue Compartment Mechanical Properties

Electromyographic (EMG) activity is associated with several tasks prior to landing in walking and running including positioning the leg, developing joint stiffness and possibly control of soft tissue compartment vibrations. The concept of muscle tuning suggests one reason for changes in muscle activity pattern in response to small changes in impact conditions, if the frequency content of the impact is close to the natural frequency of the soft tissue compartments, is to minimize the magnitude of soft tissue compartment vibrations. The mechanical properties of the soft tissue compartments depend in part on muscle activations and thus it was hypothesized that changes in the muscle activation pattern associated with different impact conditions would result in a change in the acceleration transmissibility to the soft tissue compartments. A pendulum apparatus was used to systematically administer impacts to the heel of shod male participants. Wall reaction forces, EMG of selected leg muscles, soft tissue compartment and shoe heel cup accelerations were quantified for two different impact conditions. The transmissibility of the impact acceleration to the soft tissue compartments was determined for each subject/soft tissue compartment/shoe combination. For this controlled impact situation it was shown that changes in the damping properties of the soft tissue compartments were related to changes in the EMG intensity and/or mean frequency of related muscles in response to a change in the impact interface conditions. These results provide support for the muscle tuning idea--that one reason for the changes in muscle activity in response to small changes in the impact conditions may be to minimize vibrations of the soft tissue compartments that are initiated at heel-strike.

Broadband noise reduction of piezoelectric smart panel featuring negative-capacitive-converter shunt circuit

A broadband noise reduction of a piezoelectric smart panel featuring a negative capacitance converter (NCC) shunt circuit is experimentally investigated. Piezoelectric shunt damping utilized on the panel structure is attractive for noise reduction especially at low resonance frequencies of the structure. To achieve a broadband noise reduction, however, a multimode shunt is necessary. The NCC circuit can be an ideal broadband shunt circuit by nullifying the capacitance of the piezoelectric patch with the circuit. Since the intrinsic capacitance of the patch is not constant with the frequency, the broadband shunt performance of the NCC can be deteriorated. Thus, we introduce the dual-patch NCC circuit on the smart panel. The proposed concept is explained and the tuning and implementation procedures are addressed. The noise reduction performance of the panel is tested in terms of transmission loss according to the standard transmitted noise measurement. The broadband damping performance of the smart panel featuring a dual-patch NCC shunt is compared with the panels featuring resonant shunt circuit and ordinary NCC shunt circuit in terms of acceleration and noise transmission loss. It is found that the dual-patch NCC shunt is more efficient than ordinary NCC and resonant shunt for achieving broadband noise reduction with smart panels.

On the significance of body mass and vibration magnitude for acceleration transmission of vibration through seats with horizontal suspensions

Seats with horizontal suspensions can help to reduce detrimental effects of whole-body vibration (WBV) on health, comfort and performance. Two seats were used to examine the effect of body mass and WBV-magnitude on the transmission of WBV from the seat base to the cushion. Both seats have suspension in the x-direction while Seat 2 has suspension also in the y-direction. Twelve subjects with a body mass ranging from 59.0 to 97.3 kg volunteered for the study. A set of anthropometric characteristics was acquired. Three magnitudes of WBV were used with a truck-like signal (Seat 1, 0.3–0.59 m s −2 w d -weighted rms values at the seat base, x-direction) and a tractor-like signal (Seat 2, 0.55–1.09 m s −2 w d -weighted rms values at the seat base, x-direction, 0.52–1.07 m s −2 w d -weighted rms values, y-direction). The magnitude of WBV had a significant effect on the transmissibility characterized by SEAT-values. A significant influence of the body mass on SEAT-values was found for the y-direction only. Other anthropometric characteristics proved to be more important for the prediction of SEAT values by multiple regressions. There was no significant correlation of SEAT-values, x-direction, with the body mass. Other anthropometric characteristics enabled a satisfactory prediction of SEAT values also for x-direction in several cases. Tests with only two subjects of extreme body mass are not suited to obtain comparable and representative results required for a comparison of different seats with a suspension in the x-direction. The effect of the WBV-magnitude on the WBV-transmissibility should be considered with the design, testing and application of suspended seats.

Estimation of the Transmissibility of Anti-Vibration Gloves when Used with Specific Tools

Anti-vibration gloves are increasingly being used as personal protective equipment to help reduce the hazards of hand-transmitted vibration. A vibration transfer function method for estimating the tool-specific performance of anti-vibration gloves has been proposed to help select appropriate gloves for particular tools and to assess the potential risks posed by tool vibration. This study evaluates the validity of the method by comparing the predicted vibration transmissibility with the measured value. Two typical vibration-attenuating gloves (air-bladder and visco-elastic material gloves) were used in the study. Two series of experiments were performed for the evaluation. In the first series, the isolation efficiency of selected anti-vibration gloves was evaluated in the laboratory under synthesized handle vibration spectra of six different tools. The second series of tests involved the measurement of the glove transmissibility, while operating two different pneumatic chipping hammers. The results of the study show reasonably good agreements between the predicted and measured acceleration transmissibility values of the candidate gloves. It is thus concluded that the transfer function method provides a reasonably good estimate of vibration attenuation performance of gloves for specific tools.

Experimental Modal Analysis by Base Excitation (Vibration Analysis of ADE)

For Above Deck Equipment (ADE) on a ship, it is necessary to perform experimental modal analysis (EMA) by base excitation. Existing EMA tools are designed to perform curve-fitting on the frequency response function of displacement or acceleration at measuring point to an excitation force. However, in case of experiment by base excitation, transmissibility of acceleration, that is, the ratio of accelerations between measuring point and base is to be used for modal analysis. A method, which makes modal analysis for base excitation possible by performing curve-fitting on the transmissibility of acceleration using existing EMA tools, is proposed in this paper. First, the relation of transmissibility of acceleration using modal parameters in case of base excitation is derived. Based on the relation, a new method for modal analysis is given and its feasibility for one D. O. F. system is shown by numerical calculation. Finally, the method is applied to the modal analysis of an ADE, and its effectiveness is shown by comparing experimental results with simulation results using the modal parameters obtained by the method.

The application of a programmable servo controller to state control of an electrohydraulic active suspension

Fully active electrohydraulic control of a 1/4 car test rig is considered from both a modelling and experimental point of view. Both pole assignment (PA) and linear quadratic control (LQC) techniques are used to design the state feedback gains with a view to achieving an optimum body acceleration characteristic, based on a validated linearized mathematical model. Computer simulation of the complete system suggests that the LQ control design approach gives the better performance characteristic. An industrial programmable servo controller (PSC) is implemented to drive two servo valves, one used for the road input actuator and the other used for the active control actuator. Programmable features are introduced, such as gain scheduling and state gain switching to achieve improved control. It is shown that although body displacement compensation is naturally achieved for road input changes, the global optimum design for acceleration transmissibility could not be achieved, due to practical limitations caused by the predicted low transducer gain between wheel and body. A further feature of the programmable controller approach was the ability to change state feedback gains during operation. This was found necessary to move the suspension from its initial rest position to its operating position. However, an improved performance in body acceleration amplitude control was still possible compared with the optimum passive suspension theoretical predictions.

Transmission of vibration to the backrest of a car seat evaluated with multi-input models

The transmission of vibration to the occupant of a car seat has been studied using the multiple vibration inputs to the seat. Twelve input signals at the seat base (tri-axial vibration at the four corners) and six output signals (tri-axial vibration at the backrest and seat pan) were measured while driving. The results showed that vibration inputs to the seat varied between the four positions at the seat base. The two fore-aft input accelerations at the left-hand side of the seat base and the two fore-aft input accelerations at the right-hand side of the seat base were highly correlated with each other. There was also a high correlation between the two pairs of lateral acceleration inputs at the front and rear of the seat base. A computer program for studying seat vibration transmission via multi-input channels was developed to allow the calculation of seat transmissibility with up to 12 different inputs. The transmission of multi-axis seat base vibration to fore-aft seat backrest vibration was investigated using single-input, two-input, six-input and eight-input models. Results showed that the fore-aft vibration and the vertical vibration, but not lateral vibration, at the four corners of the seat base contributed to fore-aft vibration of the backrest. The primary peak of the fore-aft backrest transmissibility occurred around 4–5 Hz. The coherency was improved when using the multi-input models, although the characteristics of the transmissibility remained similar. The transmission of lateral vibration at the seat base to lateral vibration at the backrest was studied using single-input and two-input models. With single-input models, the transmission of lateral acceleration at the seat base to lateral acceleration at the backrest was amplified between 18 and 35 Hz, with a peak at 26 Hz. Coherency was greater at frequencies above 20 Hz than at lower frequencies. The coherency at low frequencies was increased with a two-input model. The transmission of vertical vibration to vertical vibration at the backrest was investigated using single-input, four-input and six-input models. The results showed that vertical acceleration at the four corners of the seat base was highly correlated with vertical acceleration at the backrest. The results are consistent with previous findings that a single-input model is not sufficient to study the transmission of vibration to the seat back in the horizontal directions, while for the transmission of vertical vibration a single-input model is probably sufficient, especially when low frequencies are of main concern.

Optimization of Classical Hydraulic Engine Mounts Based on RMS Method

Based on RMS averaging of the frequency response functions of the absolute acceleration and relative displacement transmissibility, optimal parameters describing the hydraulic engine mount are determined to explain the internal mount geometry. More specifically, it is shown that a line of minima exists to define a relationship between the absolute acceleration and relative displacement transmissibility of a sprung mass using a hydraulic mount as a means of suspension. This line of minima is used to determine several optimal systems developed on the basis of different clearance requirements, hence different relative displacement requirements, and compare them by means of their respective acceleration and displacement transmissibility functions. In addition, the transient response of the mount to a step input is also investigated to show the effects of the optimization upon the time domain response of the hydraulic mount.

The effect of localized leg muscle fatigue on tibial impact acceleration

Objective. The objective of this study was to assess the effect of localized leg muscle fatigue on tibial acceleration following impact. Background. Peak tibial accelerations measured just distal to the knee joint during running have been shown to increase with general body fatigue. However, the role that local leg muscle fatigue plays in shock attenuation is not clear. Methods. The unshod, dominant foot of 24 healthy women in two different age groups was impacted into a vertical force plate, using a human pendulum method. Impact velocity and force approximated that found in running. EMG activity of the gastrocnemius and tibialis anterior muscles was monitored during fatiguing isometric exercise to assess fatigue, and quantified at impact as a measure of muscle activation level. A skin-mounted uni-axial accelerometer, was located at the tibial tubercle under pre-load, to measure tibial acceleration at impact. Results. There was a significant decrease in peak tibial acceleration ( P=0.008) and acceleration slope ( P=0.033) following fatigue. There were no significant main effects or interactions for age group or muscle group for all tibial response variables. Conclusion. The reduction in peak tibial acceleration following fatigue (for the test performed) is contrary to the response documented following whole-body fatigue. Relevance A decrease in tibial acceleration transmission may have a protective effect on the weight-bearing joints proximal to the ankle. Thus, local muscle fatigue may not be detrimental to the joints in those people participating in weight-bearing, ballistic activities or for those with neurological peripheral weakness.

Modelling the static stiffness and dynamic frequency response characteristics of a leaf spring truck suspension

The suspension characteristics of a 10 ton truck with a highly non-linear leaf spring suspension have been investigated. The acceleration transmissibility frequency response characteristics of the truck were first investigated. Results showed that whereas the bounce (sprung mass) resonant frequency was quite close to that expected, the wheel-hop (unsprung mass) resonant frequencies were roughly twice that expected. As no obvious mechanism for this effect was evident, the static stiffness characteristics of the suspension were measured in an attempt to understand this phenomenon. A simple plot of the resulting suspension-generated force against suspension deflection showed that two distinct stiffness regimes were present; the first, which was associated with small suspension deflections of between 2 and 4 mm, was significantly greater than the second, which was associated with larger suspension deflections. A state-variable linear 5 degree-of-freedom spring mass damper model of the vehicle was created within MATLAB in an attempt to predict the frequency response characteristics of the vehicle. The state-variable model predictions were close to those seen experimentally for the sprung mass at frequencies below 3 Hz, but were quite incorrect for both the sprung and unsprung masses above this frequency. The state-variable model was then used again with increased values of suspension stiffness and results showed that using these higher values led to a more accurate predicted response for both the sprung and unsprung masses above 3 Hz, whereas below this frequency their responses were clearly incorrect. Comparison of experimental and predicted results showed that the vehicle frequency response was dominated above 3 Hz by the low suspension deflection-high stiffness regime identified in the static stiffness results, whereas below this frequency, the high suspension deflection- low stiffness regime tended to dominated the response. To overcome the problem of the transition from the low to the high stiffness regimes when predicting the frequency response characteristics, a non-linear model was created using MATLAB and SIMULINK. Results showed that the model was able to capture this transition, with resulting frequency response curves for both the sprung and unsprung masses being very similar to the experimental results. Further refinements to the model were able to account for additional discrepancies between predictions and experimental results. The non-linear nature of the spring stiffnesses, resulting in a very useful hysteresis damping effect at the sprung mass resonant frequency, meant that for most normal road conditions the vehicle would ride on a near solid suspension. The apparent advantages of the extra damping would therefore be o set by a significant decrease in ride quality, and this was especially evident in respect to road noise and vibration-a finding borne out in practice. This paper establishes the principal characteristics of the truck suspension and goes on to describe the linear state-variable and non-linear models created to simulate the frequency response characteristics of the vehicle suspension.

A comparison of semi-active damping control strategies for vibration isolation of harmonic disturbances

Active vibration isolation systems are less commonly used than passive systems due to their associated cost and power requirements. In principle, semi-active isolation systems can deliver the versatility, adaptability and higher performance of fully active systems for a fraction of the power consumption. Various semi-active control algorithms have been suggested in the past, many of which are of the “on–off” variety. This paper studies the vibration isolation characteristics of four established semi-active damping control strategies, which are based on skyhook control and balance control. A semi-active damper is incorporated into a single-degree-of-freedom (s.d.o.f.) system model subject to base excitation. Its performance is evaluated in terms of the root-mean-square (r.m.s.) acceleration transmissibility, and is compared with those of a passive damper and an ideal skyhook damper. The results show that the semi-active system always provides better isolation at higher frequencies than a conventional passively damped system.