Mechanical Engineering

Afinite element model aimed at predicting the in-plane and out-of-plane static mechanical behavior of atightened bowisdeveloped. It takes into account the prestress due to hair tension and the nonlinear behavior due to large displacements. An non-destructive procedure to determine the input parameters of the model from measurements on abow is described. Numerical and experimental results are then compared in the case of twobows, showing good agreement between the simulated and measured mechanical behavior.Finally,hair tension and camber are shown to influence the proportion between lateral and vertical compliances of the tightened bow. PACS no. 43.75.De 640 ©S.Hirzel Verlag · EAA Ablitzer et al.:A djustment of violin bows ACTA ACUSTICA UNITED WITH ACUSTICA Vol. 98 (2012)

Porous materials are widely used for noise control. Often attached to a structure subjected to vibration, the porous layer contributes to diminish vibration by increasing structural damping and also reduce noise level in cavities by sound absorption. For optimal design, it is often necessary to know the viscoelastic properties of these materials in the frequency range relevant to their application. At these frequencies and for most of porous materials the viscoelastic properties can not be determined by standard methods because of the strong coupling with air. The method proposed is based on measurements representative of industrial use (car, aircraft, train): acoustic radiation of vibrating coated panel and transmission loss of coated panel. The use of an inverse methode based on analytical models to determined the viscoelatic properties insure a good simulation of the porous material behaviour in the required context.

Damping using an instability of a fluid film in contact with a vibrating structure is investigated. Waves induced in the fluid film is the source of the added damping. A model based on the theory of Faraday instability is applied to a clamped circular plate covered by a fluid film. It is shown that this original technique can provide a significant damping. It depends of the viscosity of the fluid, the local amplitude of the vibration, the threshold of the instability and the amplitude of the induced waves. The non linear relation between the amplitude of the waves and the plate acceleration induces a non linear damping. Theoretical and experimental results are compared. The model slightly overestimates the added damping. Comparison with viscoelastic and porous material treatments shows that damping are of the same order.

This paper investigates the feasibility to use an electrodynamic loudspeaker to determine viscoelastic properties of sound absorbing materials in the audible frequency range. The loudspeaker compresses the porous sample in a cavity and a measurement of its electrical impedance allows to determine the mechanical impedance of the sample: no additional sensors are required. Viscoelastic properties of the material are then estimated by inverting a 1D Biot model. The method is applied to two sound absorbing materials (glass wool and polymer foam). Results are in good agreement with classical compression quasistatic method.

This paper presents an analytical model for calculating the shape and the radial stiffness of ferrofluid seals used as radial bearings and this theoretical value of the radial stiffness is compared to measured values. This approach is interesting for the design of loudspeakers. Moreover, the concept of magnetic pressure is used to determine the seal shape as well as its energy. This paper corresponds to the case in which the ferrofluid seal is submitted to a high magnetic field. Furthermore, the calculation of the seal shape when the moving part is decentred is discussed. Indeed, the variation of the seal energy is evaluated with a three-dimensional analytical approach and both the restoring force exerted by the seal and the radial stiffness are calculated. The results obtained with an experimental setting confirm the validity of the model.

To predict noise in enclosure containing treated vibrating panels, porous layer effect has to be taken into account. This study propose an analytical model of the effects of a porous layer on a vibrating plate by separating the acoustical and vibratory behaviours. This paper deals with acoustic coupling by means of surface impedance derived by a one-dimensional model using "Biot-Allard" theory. It is shown that this impedance is different from that calculated when the porous is backed by an impervious rigid wall. The total radiation efficiency of a circular plate characterized by the surface impedance, clamped in a rigid infinite baffle, is computed and compared with experimental measurements. This model shows good agreement with experimental datas.

A straightforward criterion to determine the limp model validity for porous materials is addressed here. The limp model is an "equivalent fluid" model which gives a better description of the porous behavior than the well known "rigid frame" model. It is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the Frame Stiffness Influence FSI based on porous material properties. The critical values of FSI under which the limp model can be used, are determined using a 1D analytical modeling for a specific boundary set: radiation of a vibrating plate covered by a porous layer.

The use of finite element modeling for porous sound absorbing materials is often limited by the numerical cost of the resolution scheme. To overcome this limitation, an alternative finite element formulation for poroelastic materials modelled with the Biot-Allard theory is first presented. This formulation is based on the solid and total displacement fields of the porous medium. Three resolution methods (one semi-analytical and twon umerical) based on normal modes are proposed secondly.These methods takebenefitfrom the decoupling properties of normal modes. The semi-analytical method is associated with problems in which the shear wave can be neglected. The numerical methods are ad irect and an iterative scheme. The direct method allows ar eduction by 2o ft he number of degrees without making anya pproximation. The iterative method provides an approximation corresponding to acontrolled tolerance. The finite element formulation is validated by comparison with an analytical model in twom ono-dimensional configurations corresponding to as ingle and am ultilayered problem. The efficiencyo ft he twon umerical resolution methods is also illustrated in term of computation time in comparison with classical formulations, such as the mixed displacement-pressure formulation.

Finite element (FE) models of long bones are widely used to analyze implant designs. Experimental validation has been used to examine the accuracy of FE models of cadaveric femurs; however, although convergence tests have been carried out, no FE models of an intact and implanted human cadaveric tibia have been validated using a range of experimental loading conditions. The aim of the current study was to create FE models of a human cadaveric tibia, both intact and implanted with a unicompartmental knee replacement, and to validate the models against results obtained from a comprehensive set of experiments. Seventeen strain rosettes were attached to a human cadaveric tibia. Surface strains and displacements were measured under 17 loading conditions, which consisted of axial, torsional, and bending loads. The tibia was tested both before and after implantation of the knee replacement. FE models were created based on computed tomography (CT) scans of the cadaveric tibia. The models consisted of ten-node tetrahedral elements and used 600 material properties derived from the CT scans. The experiments were simulated on the models and the results compared to experimental results. Experimental strain measurements were highly repeatable and the measured stiffnesses compared well to published results. For the intact tibia under axial loading, the regression line through a plot of strains predicted by the FE model versus experimentally measured strains had a slope of 1.15, an intercept of 5.5 microstrain, and an R 2 value of 0.98. For the implanted tibia, the comparable regression line had a slope of 1.25, an intercept of 12.3 microstrain, and an R 2 value of 0.97. The root mean square errors were 6.0% and 8.8% for the intact and implanted models under axial loads, respectively. The model produced by the current study provides a tool for simulating mechanical test conditions on a human tibia. This has considerable value in reducing the costs of physical testing by pre-selecting the most appropriate test conditions or most favorable prosthetic designs for final mechanical testing. It can also be used to gain insight into the results of physical testing, by allowing the prediction of those variables difficult or impossible to measure directly.

The validity of using the limp model for porous materials is addressed in this paper. The limp model is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. Being an equivalent fluid model accounting for the motion of the frame, it has fewer limitations than the usual equivalent fluid model assuming a rigid frame. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the frame stiffness influence ͑FSI͒, based on porous material properties. The critical values of FSI under which the limp model can be used are determined using a one-dimensional analytical modeling for two boundary sets: absorption of a porous layer backed by a rigid wall and radiation of a vibrating plate covered by a porous layer. Compared with other criteria, the criterion associated with FSI provides information in a wider frequency range and can be used for configurations that include vibrating plates.

This paper presents a measurement setup for determining the mechanical properties of porous materials at low and medium frequencies by extending toward higher frequencies the quasistatic method based on a compression test. Indeed, classical quasistatic methods generally neglect the inertia effect of the porous sample and the coupling between the surrounding fluid and the frame; they are restricted to low frequency range (<100 Hz) or specific sample shape. In the present method, the porous sample is placed in a cavity to avoid a lateral airflow. Then a specific electrodynamic ironless transducer is used to compress the sample. This highly linear transducer is used as actuator and sensor; the mechanical impedance of the porous sample is deduced from the measurement of the electrical impedance of the transducer. The loss factor and the Young's modulus of the porous material are estimated by inverse method based on the Biot's model. Experimental results obtained with a polymer foam show the validity of the method in comparison with quasistatic method. The frequency limit has been extended from 100 Hz to 500 Hz. The sensitivity of each input parameter is estimated in order to point out the limitations of the method.

A straightforward criterion to determine the limp model validity for porous materials is addressed here. The limp model is an "equivalent fluid" model which gives a better description of the porous behavior than the well known "rigid frame" model. It is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the Frame Stiffness Influence FSI based on porous material properties. The critical values of FSI under which the limp model can be used, are determined using a 1D analytical modeling for a specific boundary set: radiation of a vibrating plate covered by a porous layer.

The validity of using the limp model for porous materials is addressed in this paper. The limp model is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. Being an equivalent fluid model accounting for the motion of the frame, it has fewer limitations than the usual equivalent fluid model assuming a rigid frame. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the frame stiffness influence ͑FSI͒, based on porous material properties. The critical values of FSI under which the limp model can be used are determined using a one-dimensional analytical modeling for two boundary sets: absorption of a porous layer backed by a rigid wall and radiation of a vibrating plate covered by a porous layer. Compared with other criteria, the criterion associated with FSI provides information in a wider frequency range and can be used for configurations that include vibrating plates.

Cet article propose une méthode de caractérisation des propriétés viscoélastiques des matériaux poreux pour des applications de type automobile (plafonnier, tablier,...) ou aéronautique (garnissage de carlingue, habitacle pilote). Le systèmeétudié se compose d'une plaque vibrante recouverte d'une couche poreuse. L'objectif est de modéliser le rayonnement de cette structure puis d'ajuster les simulations sur des données expérimentales pour déterminer les propriétés viscoélastiques de la couche poreuse. Le modèle analytique proposé décrit le rayonnement de la structure en considérant le découplage des comportements acoustiques et vibratoires. L'effet de la couche poreuse sur le rayonnement acoustique de la structure estétudié en tenant compte des couplages entre le fluide environnant et le squelette du matériau poreux. Pour cela, un modèle unidimensionnel de propagation d'ondes dans la couche poreuse aété développé en utilisant la théorie de "Biot-Allard". Ce modèle est ensuite appliqué au rayonnement d'une plaque circulaire encastrée vibrant dans unécran rigide. Le recalage par rapportà des données expérimentales permet alors de déterminer les propriétés viscoélastiques du matériau poreux.

Modeling a porous layer mounted on a vibrating structure using acoustic impedance is investigated in this paper. It is shown that the use of surface impedance usually measured with the impedance tube method can provide an inaccurate estimation of the acoustic pressure radiated by the covered structure. The paper focuses on the derivation of an impedance, denoted the "transfer impedance", which describes accurately the dynamic movement of the porous layer. Biot's theory is used in the model to account for deformations in the thickness of the layer.

Porous materials are widely used for noise control. Often attached to a structure subjected to vibration, the porous layer contributes to diminish vibration by increasing structural damping and also reduce noise level in cavities by sound absorption. For optimal design, it is often necessary to know the viscoelastic properties of these materials in the frequency range relevant to their application. At these frequencies and for most of porous materials the viscoelastic properties can not be determined by standard methods because of the strong coupling with air. The method proposed is based on measurements representative of industrial use (car, aircraft, train): acoustic radiation of vibrating coated panel and transmission loss of coated panel. The use of an inverse methode based on analytical models to determined the viscoelatic properties insure a good simulation of the porous material behaviour in the required context.

Damping using an instability of a fluid film in contact with a vibrating structure is investigated. Waves induced in the fluid film is the source of the added damping. A model based on the theory of Faraday instability is applied to a clamped circular plate covered by a fluid film. It is shown that this original technique can provide a significant damping. It depends of the viscosity of the fluid, the local amplitude of the vibration, the threshold of the instability and the amplitude of the induced waves. The non linear relation between the amplitude of the waves and the plate acceleration induces a non linear damping. Theoretical and experimental results are compared. The model slightly overestimates the added damping. Comparison with viscoelastic and porous material treatments shows that damping are of the same order.

This paper investigates the feasibility to use an electrodynamic loudspeaker to determine viscoelastic properties of sound absorbing materials in the audible frequency range. The loudspeaker compresses the porous sample in a cavity and a measurement of its electrical impedance allows to determine the mechanical impedance of the sample: no additional sensors are required. Viscoelastic properties of the material are then estimated by inverting a 1D Biot model. The method is applied to two sound absorbing materials (glass wool and polymer foam). Results are in good agreement with classical compression quasistatic method.

This paper presents an analytical model for calculating the shape and the radial stiffness of ferrofluid seals used as radial bearings and this theoretical value of the radial stiffness is compared to measured values. This approach is interesting for the design of loudspeakers. Moreover, the concept of magnetic pressure is used to determine the seal shape as well as its energy. This paper corresponds to the case in which the ferrofluid seal is submitted to a high magnetic field. Furthermore, the calculation of the seal shape when the moving part is decentred is discussed. Indeed, the variation of the seal energy is evaluated with a three-dimensional analytical approach and both the restoring force exerted by the seal and the radial stiffness are calculated. The results obtained with an experimental setting confirm the validity of the model.