汽车声品质研究经典论文.pdf

Subjective evaluations of sound radiated by impacted plates using the design of experiments method Miloudi Abdelhamid a Hamzaoui Nacerb Guyader Jean Louisb aLaboratoire de M canique Avanc e LMA Universit des Sciences et de la Technologie Houari Boum di ne BP 32 El Alia 16111 Bab Ezzouar Alger Algeria bLaboratoire de Vibrations Acoustique LVA INSA de Lyon B t Antoine de Saint Exup ry 25 bis Avenue Jean Capelle 69621 Villeurbanne Cedex France a r t i c l ei n f o Article history Received 25 July 2008 Received in revised form 22 December 2009 Accepted 24 December 2009 Available online xxxx Keywords Impacted plate Sound perception Acoustical radiation Temporal acoustic a b s t r a c t This study combines physical and subjective approaches to evaluate the sound quality of impacted plates A numerical model based on the Hertz law of contact has been used to determine the sound pressure level at any point in space resulting from an impact Sounds synthesized using this model and those from experiments can then be exploited in a physical analysis and or a subjective analysis of the effects asso ciated with variations in parameters Here the infl uence of certain physical parameters on the sound per ception of impacted plates is evaluated through a design of experiments method and a subjective test of preference The subjective test is based on an estimate of preference between two pairs of synthetic sounds by varying several structural parameters at the same time This differs from other studies that vary only one parameter at a time and fi x the other parameters 2009 Elsevier Ltd All rights reserved 1 Introduction Usually studies of acoustic radiation of structures are limited to the physical characteristics of acoustic signals The share taken by perceptive analysis in these studies is still quite limited although it could very usefully complement physical studies Indeed such analysis helps to evaluate the infl uence of physical parameters and geometry in terms of subjective criteria and thus choose the right answers to a technical problem of noise The sound quality of industrial products has been the subject of several acoustics studies and this new orientation does not only concern pressure level and its reduction but also the auditory sensation character ized by subjective experiments performed with a group of listeners Sound is not simply a phenomenon that can be explained by the physical characteristics of acoustic waves propagated through the air but also by the mechanical characteristics of the vibrating sys tems producing it Their different effects on sound levels are well known but few studies on sound perception have been carried out It would be interesting to know for example the subjective sound effect of a change made to the thickness of a vibrating structure converted into the frequency spectrum of sound pressure The subjective characterization of sound and the characteristics of the latter in relation to the positive perception of the listener is an increasingly important factor for a growing number of industrial sectors There are an increasing number of psychomechanic studies see Ref 1 i e studies that combine the vibroacoustic and psychoa coustic aspects of radiation problems Roussarie 2 used a model designed by Chaigne and Lambourg 3 and discussed different perceptive attributes of synthetic sounds simulating the radiation of impacted bars and plates One of the pioneers in this area was Freed 4 who conducted tests of listening to sounds emitted by metal objects struck by a hammer highlighting the fact that listen ers could feel and evaluate the hardness of the hammer A similar topic was dealt with in the articles of Lutfi 5 6 respectively de voted to the auditory discrimination of changes in the material composing clamped bars and to the auditory detection of a hollow portion in a vibrating solid stem Marquis Favre et al 7 tested the transmission of white noise through a plate model in which they analysed density Young mod ulus and damping independently of variations in thickness These studies focused on both the transmission effi ciency and quality of the transmitted noise In their studies Can vet et al 8 performed auditory analyses of the acoustic radiation of clamped plates in the form of brief sig nals caused by transient excitations The model used is based on a development of radiated pressure on a series of resonance modes a method particularly well adapted to the time domain and therefore transient domains The subjective tests developed concerned dis similarity and overall sound quality depending on the type of exci tation on the plate the excitation point and the damping of the constitutive material Hamzaoui et al 9 estimated preference between several synthetic sounds emitted by the radiation of vibrating plates by 0003 682X see front matter 2009 Elsevier Ltd All rights reserved doi 10 1016 j apacoust 2009 12 006 Corresponding author Tel 33 4 72 43 80 81 fax 33 4 72 43 87 12 E mail address nacer hamzaoui insa lyon fr H Nacer Applied Acoustics xxx 2010 xxx xxx Contents lists available at ScienceDirect Applied Acoustics journal homepage ARTICLE IN PRESS Please cite this article in press as Abdelhamid M et al Subjective evaluations of sound radiated by impacted plates using the design of experiments meth od Appl Acoust 2010 doi 10 1016 j apacoust 2009 12 006 varying several structural parameters simultaneously Different listening tests have confi rmed the preponderance of damping and structure thickness on auditory preference In this context the work of Marquis Favre and Faure 10 deserves particular attention regarding this type of approach because they emphasized the importance of the damping and thickness of a steel plate baf fl ed and subject to a plane wave in sound perception The studies of Demirdjian 11 established relations between the mechanical and geometrical parameters of plates the acoustic parameters of sounds and the perceptive attributes used by listen ers during psychoacoustic tests Indeed the results proved that changing the point of impact and its duration infl uence the signal tones on the resonant part and acuity on the transient part Also sounds corresponding to high impact duration and excitations at the plate center were found to be more enjoyable by all listeners Our study focuses on the analysis of mechanical and geometri cal parameters in relation to physical and sound perception To this end we propose a theoretical model developed in the time domain focusing on the noise radiated by a vibrating plate subjected to im pact forces An experimental bench is used to evaluate the ap proachandprovidesabasisforproducingsoundsamples obtained by parametric variations related to the material the im pact point and the listening point The originality of this work resides in the theoretical approach used to model the impact force spherical striker head incorporating the Hertz contact law in the general approach that includes sound perception to simultaneously assess the infl uence of subjective and objective parameters such as damping boundaries conditions materials and plate thickness by using the design of experiments method The evaluation of the theoretical model can be then performed by the measurements supplied by the experimental bench Structural damping has been observed several times cf 7 9 11 to be the most dominant parameter in the sound perception of vibrating plates To implement this simultaneous multi parameter analysis using the design of experiments method we chose to remove the damping and keep only the parameters subject to little discussion material impact point position and listening point position By using this approach we can also incorporate sound percep tion to adjust the parameters to calculate for example the number of modes sampling time acquisition time etc We therefore chose to analyse the material boundary condition and impact point position parameters for the stimuli resulting from the calculation and the material impact point position and listening point position parameters as it is very diffi cult to change the boundary conditions experimentally for the stimuli resulting from the experimental bench 2 Plate vibration response The vibration response of a rectangular clamped plate to an im pact can be calculated by solving the classical equation governing the fl exural motion of the plate qh 2w t2 k w t DD2w P t d x x0 d y y0 1 where w x y t is the transverse displacement of the plate at point x y and P t is the applied force at point x0 y0 In this equation the constants are D Eh3 12 1 t2 is the fl exural rigidity qis the density h is the thickness of the plate E is the Young modulus tis the Poisson ratio andgis the internal loss factor of the plate D2 4 x4 2 4 x2 y2 4 y4 is the Laplace operator 2 1 The impact force Studying the dynamic behaviour of the impacted plates requires knowledge of the temporal evolution of the impact force The latter has been the subject of several studies using numerical and exper imental approaches but calculating the unknown data exactly re mains diffi cult The expression of contact force P developed during the elastic impact of a spherical striker of radius R with a rigid plane surface of a semi infi nite solid was given by Hunter 12 as a function of the relative approach of the striker and the impacted plane surface see Fig 1 P kca3 2 2 whereais the relative approach between the striker and the im pacted plane surface given by a zI t w x0 y0 t 3 and kcis the contact stiffness that depends on the geometrical and rheological characteristics of the two bodies in contact given by kc 4 3 ffi ffi ffi R p 1 t2 1 E1 1 t2 2 E2 4 t1 t2and E1 E2are respectively the Poisson ratios and elasticity moduli of the sphere and the impacted object respectively x0and y0are the coordinates of the point of impact The contact force given in Eq 2 is an extension of the well known Hertz contact theory developed for the static contact of curved bodies 2 2 Response of the plate to impact In the case of an impact between a sphere and a thin plate the evolution of the impact force is determined by combining Eq 2 with the equation of motion Eq 1 of the plate The resulting non linear differential equation can be solved numerically The numerical model proposed by us is simple effi cient and gives very satisfactory results It takes into account several modes in the impact force and dynamic plate response calculations It also calls on Hertz s contact law and classical plate theory At the fi rst h I V RI MI a z w x Before impact t0 Median Plan Fig 1 Transverse impact at the plate center 2M Abdelhamid et al Applied Acoustics xxx 2010 xxx xxx ARTICLE IN PRESS Please cite this article in press as Abdelhamid M et al Subjective evaluations of sound radiated by impacted plates using the design of experiments meth od Appl Acoust 2010 doi 10 1016 j apacoust 2009 12 006 instant of contact the spherical striker of mass MIand velocity VI knocks a thin plate with an impact force P According to the action and reaction principle the plate applies a force equal to P on the sphere but in the opposite direction The dynamic balance of the spherical striker and the plate is gi ven respectively by MI zI P 0 zI 0 0and zI 0 VI 5 and qh w Dr4w P d x x0 d y y0 w x y 0 w x y 0 0 6 In Eq 5 it is assumed that load P x y t due to the interaction between the plate and the striker is governed by Hertz s contact law Thereafter we solve both equations of motion simultaneously by an iterative numerical method using modal decomposition for the transverse defl exion of the plate and a Newmark integration scheme for the contact force 13 From the temporal evolution of the impact force we can calcu late the vibratory characteristics of the plate in any point by modal superposition 3 Radiated acoustic pressure In the time domain the sound pressure radiated by a vibrating plate inserted in an infi nite baffl e is calculated by using the Ray leigh integral where each surface element of the plate is considered as a monopolar source P X t q0 2 Z Z S 1 r cnQ t r C dS 7 wherecn Q t is the normal acceleration of the plate r is distance from each elemental area to the calculated pressure point X is point where the acoustic pressure is calculated Q is point of the plate sur face t is time at which the pressure is calculated C is the acoustic sound speed The proper time delay due to the distance from the receiver to the different parts of the plate is accounted for by the term td t r C 8 Once the space distribution of acceleration is known we can ob tain the acoustic pressure at any point in space by Eq 6 In the present approach the fl uid loading on the plate is ne glected which is a simplifi cation generally performed for radiation in air and known as the light fl uid approximation 4 Experimental study Measurements of acoustical pressure are performed on rectan gular plates in a semi anechoic room The plates are clamped ver tically on the wall by 38 bolts see Fig 5 in order to avoid transmission losses In this series of experiments the plate was vi brated by a spherical ended striker The pressure signal was re corded at a distance of approximately 0 5 m from the plate In order to assess the validity of the acoustic calculation in the case of plate impact radiation we compared the acoustic pressures measured and calculated during a time interval of 1 s The results obtained are illustrated in Fig 5 where we show the evolution of the acoustic pressure time history at the listening point The impact is produced by a pendulum at a given angle from its equilibrium position see Fig 2 Measurements corresponding to the present theoretical analy sis were carried out to obtain plate vibration responses and radi ated acoustic pressures from an impacted plate The experimental set up is shown in Figs 3 and 4 Impact veloc ity can be calculated from the distance travelled It should be noted that this method led to relatively high uncertainties especially for a low initial speed Impact speed is therefore given by Vi ffi ffi ffi ffi ffi ffi ffi ffi 2gh p 9 The plate was fastened to the wall by 38 bolts distributed around the plate contour as shown in Fig 4 This type of fastening cannot ensure totally clamped boundary conditions Thus the boundary conditions vary from clamped and simply supported For the experimental study presented here sound signals were measured for clamped aluminium and thin steel plates of dimen sions 0 6 m length 0 4 m width and 0 001 m thickness Each signal was measured with a sampling frequency of 11 025 Hz over dura tion of 1 5 s The spectrum extended on a frequency band up to 5500 Hz The pressure fi eld was measured at two distances from the plate d 0 5 m and d 0 25 m We chose to vary three parameters excitation point coordinates listening point coordinates the material 4 1 Evaluation of the calculated sound pressure We performed a comparison between the vibration calculation and the measurements To do this we chose simply supported and clampedboundaryconditionsattheplateedgesforthe O x y z h Pressure M O Acceleration Measure room Excitation room Fig 2 Scheme of the experimental device Fig 3 During impact M Abdelhamid et al Applied Acoustics xxx 2010 xxx xxx3 ARTICLE IN PRESS Please cite this article in press as Abdelhamid M et al Subjective evaluations of sound radiated by impacted plates using the design of experiments meth od Appl Acoust 2010 doi 10 1016 j apacoust 2009 12 006 calculations The fi rst eigenfrequencies for a steel plate are grouped in the Table 1 Analysis of these results showed that the experimental results are closer to the clamped case than the simply supported one as mentioned in Table 1 Therefore the clamped boundary conditions were chosen for all the edges of the vibration model 4 2 Comparison between measured and calculated sound pressure In order to validate acoustic calculation of radiation from an im pacted plate we compared the acoustic pressures measured and calculated during a 1 s time interval The results obtained are illus trated in Fig 5 in which the time history of the acoustic pressure at the listening point is shown The results of the simulated sound pressure obtained in the case of impact are close to the experimental results despite a slight dif ference for the fi rst moments This difference is due to the trunca tion of higher modes in the calculation which also occur in the experiment and the difference of boundary conditions between the model and the measurement Objectively our goal is not to up date the calculation with the measure but rather to assess the cal culation parameters in subjective terms Fig 7 reveals the similarity of listening to these two stimuli The model appears suffi ciently representative of reality to be used for sound quality studies 4 3 Utilisation of experimental results Initially it seemed interesting to examine the infl uence of the plate material impact point position and listening point position Fig 4 Pressure measurement of clamped plate Table 1 Steel plate eigenfrequencies OrderCalculation resultsExperimental results SSSSCCCC 122 2742 2140 38 242 8265 1961 91 368 51103 5389 50 477 08104 0797 57 589 07124 89111 70 Table 2 Tested factors and their levels FactorsLevel 1Level 2 A materialSteelAluminium B impact point 0 3 0 2 0 41 0 11 C receiver point 0 3 0 2 0 5 0 45 0 11 0 5 Fig 5 Comparison between the calculated and simulated acoustic pressure at point 0 3 0 2 0 5 during 1 s 4M Abdelhamid et al Applied Acoustics xxx 2010 xxx xxx ARTICLE IN PRESS Please cite this article in press as Abdelhamid M et al Subjective evaluations of sound radiated by impacted plates using the design of experiments meth od Appl Acoust 2010 doi 10 1016 j apacoust 2009 12 006 at the global level of sound pressure radiated by an impacted plate To this end we opted for design of experiment based Tagushi methods 14 in order to determine the infl uence of the different parameters studied by carrying out a