Parametric design sensitivity analysis of high‐frequency structural–acoustic problems using energy finite element method

A design sensitivity analysis of high-frequency structural-acoustic problems is formulated and presented. The energy finite element method (EFEM) is used to predict structural-acoustic responses in the high frequency range, where the coupling between structural junctions and the structural-acoustic interface are modelled using power transfer coefficients. The continuum design sensitivity formulation is derived from the governing equation of EFEM and the discrete method is applied in the variation of the structural-structural and structural-acoustic coupling matrices. The direct differentiation and adjoint variable method are both developed for the sensitivity analysis, where the difficulty of the adjoint variable method is overcome by solving a transposed system equation. Parametric design variables such as panel thickness and material damping are considered for sensitivity analysis, and numerical sensitivity results show excellent agreement as compared to analytical finite difference results.

[1]  Aimin Wang,et al.  Validation of the EFEA Method through Correlation with Conventional FEA and SEA Results , 2001 .

[2]  L. Mongeau,et al.  ENERGY FLOW ANALYSIS OF BEAMS AND PLATES FOR RANDOM DISTRIBUTED LOADING , 1998 .

[3]  Kyung K. Choi,et al.  Design Optimization for Structural-Acoustic Problems Using FEA-BEA With Adjoint Variable Method , 2004 .

[4]  Frank Fahy,et al.  Foundations of engineering acoustics , 2000 .

[5]  Robert J. Bernhard,et al.  Theory and applications of a simplified energy finite element method and its similarity to SEA , 2002 .

[6]  S. H. Sung,et al.  Power Flow Finite Element Analysis of Dynamic Systems: Basic Theory and Application to Beams , 1989 .

[7]  Robert J. Bernhard,et al.  Sensitivity calculations for structural-acoustic EFEM predictions , 1998 .

[8]  Richard H. Lyon,et al.  In-plane Contribution to Structural Noise Transmission , 1986 .

[9]  Robert J. Bernhard,et al.  Prediction of sound fields in cavities using boundary-element methods , 1987 .

[10]  Robert J. Bernhard,et al.  Review of numerical solutions for low-frequency structural-acoustic problems , 1994 .

[11]  N. Vlahopoulos,et al.  A numerical structure-borne noise prediction scheme based on the boundary element method, with a new formulation for the singular integrals , 1994 .

[12]  R. Lyon,et al.  Power Flow between Linearly Coupled Oscillators , 1962 .

[13]  Edward J. Haug,et al.  Design Sensitivity Analysis of Structural Systems , 1986 .

[14]  Paul Bremner,et al.  A Comparison of Test-Based and Analytic SEA Models for Vibro-Acoustics of a Light Truck , 1995 .

[15]  Robert J. Bernhard,et al.  Models of space-averaged energetics of plates , 1992 .

[16]  Robert J. Bernhard,et al.  Structural-acoustic design at high frequency using the energy finite element method , 1999 .

[17]  Kyung K. Choi,et al.  DESIGN SENSITIVITY ANALYSIS OF STRUCTURE-INDUCED NOISE AND VIBRATION , 1997 .

[18]  Oliver Marie Bouthier.  Energetics of vibrating systems , 1992 .

[19]  R. Langley,et al.  Elastic wave transmission through plate/beam junctions , 1990 .

[20]  George A. Borlase,et al.  An energy finite element optimization process for reducing high-frequency vibration in large-scale structures , 2000 .

[21]  K. H. Heron,et al.  The acoustic radiation efficiency of rectangular panels , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[22]  Robert J. Bernhard,et al.  Mechanical energy flow models of rods and beams , 1992 .

[23]  Donald J. Nefske,et al.  Structural-acoustic finite element analysis of the automobile passenger compartment: A review of current practice , 1982 .

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

[25]  Phillip Eung-Ho Cho.  Energy flow analysis of coupled structures , 1993 .

[26]  N. Lalor,et al.  Analysis of interior acoustic fields using the finite element method and the boundary element method , 1995 .

[27]  Nickolas Vlahopoulos,et al.  Numerical Implementation, Validation, and Marine Applications of an Energy Finite Element Formulation , 1999 .

[28]  J. N. Reddy,et al.  Applied Functional Analysis and Variational Methods in Engineering , 1986 .

[29]  R. J. Bernhard,et al.  Computation of acoustic shape design sensitivity using a boundary element method , 1992 .

[30]  Kyung K. Choi,et al.  Energy flow analysis and design sensitivity of structural problems at high frequencies , 2004 .

[31]  Aimin Wang,et al.  High-frequency vibration analysis of thin elastic plates under heavy fluid loading by an energy finite element formulation , 2003 .

[32]  Kyung K. Choi,et al.  Design sensitivity analysis for sequential structural–acoustic problems , 2003 .

[33]  Robert J. Bernhard,et al.  Simple models of the energetics of transversely vibrating plates , 1995 .

[34]  Fernando Bitsie,et al.  The structural -acoustic energy finite -element method and energy boundary -element method , 1996 .

[35]  H. G. Davies.  Sound from Turbulent‐Boundary‐Layer‐Excited Panels , 1969 .

[36]  S. K. Jha,et al.  A simplified finite element method for studying acoustic characteristics inside a car cavity , 1979 .