Optimizing material properties of composite plates for sound transmission problem

To calculate the specific transmission loss (TL) of a composite plate, the conjugate gradient optimization method is utilized to estimate and optimize material properties of the composite plate in this study. For an n-layer composite plate, a nonlinear dynamic stiffness matrix based on the thick plate theory is formulated. To avoid huge computational efforts due to the combination of different composite material plates, a transfer matrix approach is proposed to restrict the dynamic stiffness matrix of the composite plate to a 4×4 matrix. Moreover, the transfer matrix approach has also been used to simplify the complexity of the objective function gradient for the optimization method. Numerical simulations are performed to validate the present algorithm by comparing the TL of the optimal composite plate with that of the original plate. Small number of iterations required during convergence tests illustrates the efficiency of the optimization method. The results indicate that an excellent estimation for the composite plate can be obtained for the desired sound transmission.

[1]  W. Lauriks,et al.  Sound transmission through finite lightweight multilayered structures with thin air layers. , 2010, The Journal of the Acoustical Society of America.

[2]  W. Thomson,et al.  Transmission of Elastic Waves through a Stratified Solid Medium , 1950 .

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

[4]  Garret N. Vanderplaats,et al.  Numerical Optimization Techniques for Engineering Design: With Applications , 1984 .

[5]  Jesús Alba,et al.  Improvement of the prediction of transmission loss of double partitions with cavity absorption by minimization techniques , 2004 .

[6]  Jeong-Guon Ih,et al.  Significance of resonant sound transmission in finite single partitions , 2004 .

[7]  Richard Friedrich,et al.  Finite strip method: 30 years A bibliography (1968‐1998) , 2000 .

[8]  Antonio Rodríguez-Ferran,et al.  The finite layer method for modelling the sound transmission through double walls , 2012 .

[9]  Changzheng Huang,et al.  An analytical study of sound transmission through unbounded panels of functionally gradedmaterials , 2011 .

[10]  I. I. Novikov.  Low-frequency sound insulation of thin plates , 1998 .

[11]  Jian-Qiao Sun,et al.  OPTIMIZATION OF ANISOTROPIC SANDWICH BEAMS FOR HIGHER SOUND TRANSMISSION LOSS , 2002 .

[12]  B. Brouard,et al.  A general method of modelling sound propagation in layered media , 1995 .

[13]  A. Trochidis,et al.  Sound transmission through double partitions with cavity absorption , 1986 .

[14]  Gerrit Vermeir,et al.  Low-frequency airborne sound transmission through single partitions in buildings , 1997 .

[15]  Svante Finnveden,et al.  Calculation of wave propagation in rib-stiffened plate structures , 1996 .

[16]  Jean-Louis Guyader,et al.  Prediction of transmission loss of double panels with a patch-mobility method , 2007 .

[17]  Jihong Wen,et al.  Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators , 2012 .

[18]  Atul Bhaskar,et al.  The effect of external mean flow on sound transmission through double-walled cylindrical shells lined with poroelastic material , 2014 .

[19]  B. Aalami,et al.  Waves in Prismatic Guides of Arbitrary Cross Section , 1973 .

[20]  K. Renji.  Sound transmission loss of unbounded panels in bending vibration considering transverse shear deformation , 2005 .

[21]  Sound insulation of composite cylindrical shells , 1999 .

[22]  Jonas Brunskog,et al.  Sound transmission of structures. A finite element approach with simplified room description , 2004 .

[23]  Panayiotis E. Pintelas,et al.  A Descent Dai-Liao Conjugate Gradient Method Based on a Modified Secant Equation and Its Global Convergence , 2012 .

[24]  Seyyed M. Hasheminejad,et al.  Sound Insulation Characteristics of Functionally Graded Panels , 2008 .

[25]  L. Gagliardini,et al.  The use of a functional basis to calculate acoustic transmission between rooms , 1991 .

[26]  Deyu Li,et al.  Effectiveness of T-shaped acoustic resonators in low-frequency sound transmission control of a finite double-panel partition , 2010 .

[27]  Samir N. Y. Gerges,et al.  Numerical simulation and experimental tests of multilayer systems with porous materials , 1999 .

[28]  Y. K. Cheung,et al.  Finite strip method , 1976 .

[29]  Gerrit Vermeir,et al.  A model for estimating the acoustic performances of multilayered systems based on a multiple extension of the transfer matrix method , 2006 .

[30]  A. Belegundu,et al.  Optimization Concepts and Applications in Engineering , 2011 .

[31]  C.-M. Lee,et al.  A modified transfer matrix method for prediction of transmission loss of multilayer acoustic materials , 2009 .

[32]  A. Nouri,et al.  Sound transmission through laminated composite cylindrical shells using analytical model , 2007 .

[33]  C.Y.R. Cheng,et al.  BOUNDARY ELEMENT ANALYSIS OF MUFFLERS WITH AN IMPROVED METHOD FOR DERIVING THE FOUR-POLE PARAMETERS , 1998 .

[34]  M. Crocker,et al.  Sound transmission loss of foam-filled honeycomb sandwich panels using statistical energy analysis and theoretical and measured dynamic properties , 2010 .

[35]  Y. S. Wang,et al.  A prediction method of the acoustical properties of multilayered noise control materials in standing wave-duct systems , 2006 .

[36]  Laurent Maxit,et al.  Non resonant transmission modelling with statistical modal energy distribution analysis , 2014 .

[37]  R. H. Lyon,et al.  Sound Insulation at Low Frequencies , 1972 .

[38]  Osama A B Hassan,et al.  Building Acoustics and Vibration: Theory and Practice , 2009 .