Reduction of Sound Radiation from Automotive-Type Panels

The problem of the effect of structural modifications on sound radiation from a structure is very important with many applications in the design of a variety of products. In practise, for the design of acoustically optimum structures simplified theoretical models are used which can lead to unexpected behaviour of the real structures. Alternatively, measurements or numerical simulation can be used. The disadvantage of these two methods is that the study of alternative structures (structures with different properties) is not easy since for every modification a new structure must be manufactured or a new numerical model must be created. Moreover, these two methods do not easily give an insight into the physical mechanisms of sound radiation from modified structures. In the first part of this thesis the problem of vibration and sound radiation from a plate with an attached beam stiffener is studied theoretically. This extends the current theories of vibroacoustic behaviour of infinite plates with an infinitely long beam discontinuity and infinite plates with an infinite number of equidistant beam discontinuities forming a periodic structure. Firstly, the propagation of flexural waves and the subsequent sound radiation from an infinitely long plate strip is considered. The scattering of plate flexural waves by a finite beam across its width is considered. Changes to the mean square velocity, sound power and radiation efficiency of the plate strip due to the introduction of the beam stiffener are identified. Simplified approximate analytical expressions for the low-frequency range, well below the critical frequency, are also presented. This model is extended for the case of a finite rectangular plate by incorporating wave reflection from the two additional boundaries of the plate. Expressions for the radiation efficiency and the mean squared velocity of the stiffened plate are derived. The results are compared with results derived using well established numerical methods. For structures with more complicated modifications the derivation of analytical expressions is not easy. For this reason numerical optimisation is often used. In this thesis numerical optimisation is used to optimise the modes of a structure in order to radiate acoustic energy weakly into the acoustic medium. The effectiveness of point mass and line stiffener modification to create acoustically optimum modeshapes in a flat simply supported plate is firstly studied. The results show significant reduction in the sound power radiated by the optimised structural modes. These results are also verified experimentally. This optimisation method has certain advantages when it is used on automotive panels. The main advantage is that the panel under consideration can be isolated from the rest of the automotive structure and it can be optimised alone. This drastically reduces the time required and makes the optimisation practically applicable. A simplified car model is used and the proposed optimisation is applied to one of its floor panels. Firstly, point masses and line stiffeners are used as structural modifications to create weakly radiating modeshapes. Then more commonly used geometrical modifications are used on the floor panel. Two such modifications are studied; swages and domes. The results show a significant reduction in the radiation effciency and sound power radiated by the optimised panel.

[1]  Frank Fahy,et al.  Wave propagation in damped, stiffened structures characteristic of ship construction , 1976 .

[2]  R. M. Grice,et al.  A METHOD FOR THE VIBRATION ANALYSIS OF BUILT-UP STRUCTURES, PART I: INTRODUCTION AND ANALYTICAL ANALYSIS OF THE PLATE-STIFFENED BEAM , 2000 .

[3]  K. Cunefare,et al.  The radiation modes of baffled finite plates , 1994 .

[4]  Richard H. Lyon.  Sound Radiation from a Beam Attached to a Plate , 1962 .

[5]  E. E. Ungar,et al.  Structure-borne sound , 1974 .

[6]  Yitshak M. Ram,et al.  Constructing a Finite Element Model of a Vibratory Rod from Eigendata , 1994 .

[7]  S. Marburg.  A general concept for design modification of shell meshes in structural-acoustic optimization: part I: Formulation of the concept , 2002 .

[8]  Raphael T. Haftka,et al.  Sensitivity analysis and optimization of nodal point placement for vibration reduction , 1987 .

[9]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[10]  Ulrich Seiffert,et al.  Handbook of automotive engineering , 2005 .

[11]  Peter Hagedorn,et al.  Identification of boundary conditions as a part of model correction , 1995 .

[12]  G. Koopmann,et al.  GLOBAL OPTIMUM ACTIVE NOISE CONTROL : SURFACE AND FAR-FIELD EFFECTS , 1991 .

[13]  Per-Olof Persson,et al.  A Simple Mesh Generator in MATLAB , 2004, SIAM Rev..

[14]  John E. Mottershead,et al.  Boundary condition identification by solving characteristic equations , 2001 .

[15]  Gary H. Koopmann,et al.  Designing Quiet Structures: A Sound Power Minimization Approach , 1997 .

[16]  Manfred Heckl,et al.  Wave Propagation on Beam‐Plate Systems , 1961 .

[17]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[18]  F. Fahy,et al.  Sound and Structural Vibration: Radiation, Transmission and Response , 1987 .

[19]  Miguel C. Junger,et al.  Sound, Structures, and Their Interaction , 1972 .

[20]  Gary H. Koopmann,et al.  A Design Method for Minimizing the Sound Power Radiated from Plates by Adding Optimally Sized, Discrete Masses , 1995 .

[21]  Li Li,et al.  Vibroacoustic Optimization of Two Cross Stamped Ribs in a Plate , 2005 .

[22]  Semyung Wang,et al.  Acoustic Design Sensitivity Analysis and Optimization for Reduced Exterior Noise , 2001 .

[23]  Benjamin A. Cray,et al.  Acoustic radiation from periodic and sectionally aperiodic rib‐stiffened plates , 1994 .

[24]  K. Graff.  Wave Motion in Elastic Solids , 1975 .

[25]  Deng Xiaolong,et al.  Genetic Algorithms for the Vibroacoustic Optimization of the Stamped Rib in a Plate , 2004 .

[26]  C. Wallace.  Radiation Resistance of a Rectangular Panel , 1972 .

[27]  Jason C. Brown,et al.  Motor Vehicle Structures: Concepts and Fundamentals , 2001 .

[28]  F. Fahy.  Sound and structural vibration , 1985 .

[29]  Stephen A. Hambric.  Approximation Techniques for Broad-Band Acoustic Radiated Noise Design Optimization Problems , 1993 .

[30]  J. Zhu,et al.  Estimation of boundary parameters of plate structures , 1995 .

[31]  K. Cunefare,et al.  On the exterior acoustic radiation modes of structures , 1994 .

[32]  Kazuo Takahashi,et al.  Free vibrations of plate structures with intermediate frames , 1978 .

[33]  M. L. Rumerman,et al.  Vibration and wave propagation in ribbed plates , 1971 .

[34]  Alain Berry,et al.  Use of genetic algorithms for the vibroacoustic optimization of a plate carrying point-masses , 1998 .

[35]  Stephen A. Hambric.  Sensitivity Calculations for Broad-Band Acoustic Radiated Noise Design Optimization Problems , 1996 .

[36]  V. A. Zarutskii,et al.  Influence of discrete ribs on the vibrations of rectangular plates , 2006 .

[37]  S. Hayek,et al.  Acoustic radiation from an insonified elastic plate with a line discontinuity , 1989 .

[38]  W. H. Vogel,et al.  Transmission of free waves across a rib on a panel , 1976 .

[39]  Ronald N. Bracewell,et al.  The Fourier Transform and Its Applications , 1966 .

[40]  J. S. Lamancusa,et al.  Numerical optimization techniques for structural-acoustic design of rectangular panels , 1993 .

[41]  M. S. Howe,et al.  Sound radiation from plates with density and stiffness discontinuities , 1972 .

[42]  A. Berry,et al.  Structural acoustics and vibration behavior of complex panels , 1994 .

[43]  K. Kelkel.  Green's function and receptance for structures consisting of beams and plates , 1987 .

[44]  Fredrik Holmström.  STRUCTURE-ACOUSTIC ANALYSIS USING BEM/FEM; IMPLEMENTATION IN MATLAB , 2001 .

[45]  D. M. Mead,et al.  WAVE PROPAGATION IN CONTINUOUS PERIODIC STRUCTURES: RESEARCH CONTRIBUTIONS FROM SOUTHAMPTON, 1964–1995 , 1996 .

[46]  Y. Ram.  Inverse mode problems for the discrete model of a vibrating beam , 1994 .

[47]  Kessissoglou.  Active control of the plate energy transmission in a semi-infinite ribbed plate , 2000, The Journal of the Acoustical Society of America.

[48]  W. Soedel,et al.  The receptance method applied to the free vibration of continuous rectangular plates , 1984 .

[49]  Frank Fahy,et al.  Sound and Structural VibrationRadiation, Transmission and Response , 2007 .

[50]  G. M. L. Gladwell.  THE INVERSE MODE PROBLEM FOR LUMPED-MASS SYSTEMS , 1986 .

[51]  S. Marburg.  Developments in structural-acoustic optimization for passive noise control , 2002 .

[52]  Tian Ran Lin,et al.  A closed form solution for the dynamic response of finite ribbed plates , 2006 .

[53]  John William Nicholson.  Free Vibration of Stiffened Rectangular Plates Using Green's Functions and Integral Equations , 1986 .

[54]  Chai Gin Boay,et al.  Free vibration of rectangular isotropic plates with and without a concentrated mass , 1993 .

[55]  Sound radiation by a plate reinforced by a set of projecting stiffener ribs subjected to a periodic system of forces , 1982 .

[56]  Eric E. Ungar.  Transmission of Plate Flexural Waves through Reinforcing Beams; Dynamic Stress Concentrations , 1961 .

[57]  Wim Desmet,et al.  A wave-based substructuring approach for fast modification predictions and industrial vehicle optimization , 2006 .

[58]  G. Maidanik,et al.  Response of Ribbed Panels to Reverberant Acoustic Fields , 1962 .

[59]  Jie Pan,et al.  An analytical investigation of the active attenuation of the plate flexural wave transmission through a reinforcing beam , 1997 .

[60]  Malcolm J. Crocker,et al.  Handbook of noise and vibration control , 2007 .

[61]  A. Belegundu,et al.  Material tailoring of structures to achieve a minimum radiation condition , 1992 .

[62]  Osman Kopmaz,et al.  FREE VIBRATIONS OF A RECTANGULAR PLATE CARRYING A DISTRIBUTED MASS , 2002 .

[63]  Steffen Marburg,et al.  Case studies on structural-acoustic optimization of a finite beam , 2006 .

[64]  Luiz C. Wrobel,et al.  Boundary Element Method, Volume 1: Applications in Thermo-Fluids and Acoustics , 2003 .

[65]  G. P. Eatwell,et al.  The response of a fluid-loaded, beam-stiffened plate , 1982 .