NUMERICAL SHAPE OPTIMIZATION IN STRUCTURAL ACOUSTICS
CONTENTS INTRODUCTION BACKGROUND AND MOTIVATION LITERATURE REVIEW OPTIMIZATION IN (STRUCTURAL) ACOUSTICS NUMERICAL OPTIMIZATION STRUCTURAL OPTIMIZATION TOPOLOGY OPTIMIZATION AND FULLY STRESSED DESIGN ACTIVE CONTROL OTHER TOPICS SCOPE AND OBJECTIVES OF THIS STUDY ISSUES THAT ARE OBJECTIVES ISSUES THAT ARE NOT OBJECTIVES FURTHER CONSIDERATIONS OUTLINE STRUCTURAL ACOUSTICS FUNDAMENTAL EQUATION OF MACHINE ACOUSTICS LEVEL OF STRUCTURE BORNE SOUND LS MEAN LEVEL OF STRUCTURE BORNE SOUND MLS OPTIMIZATION ALGORITHMS GENERAL ASPECTS OF NUMERICAL OPTIMIZATION METHODS COBYLA ALGORITHM MOTIVATION FOR USING COBYLA THE SIMPLEX ALGORITHM DESCRIPTION OF THE COBYLA ALGORITHM PIKAIA ALGORITHM MOTIVATION FOR USING PIKAIA BASIC CONCEPTS OF A GENERAL GENETIC ALGORITHM PIKAIA—A SPECI?C IMPLEMENTATION OF A GENETIC ALGORITHM OPTIMIZATION PROCEDURE OPTIMIZATION PROCEDURE IN GENERAL START OF OPTIMIZATION PROCEDURE CALCULATION OF OBJECTIVE FUNCTION AND CONSTRAINTS EVALUATION OF MODI?ED DESIGN OPTIMIZATION PROCEDURE USING COBYLA OBJECTIVE FUNCTION AND CONSTRAINTS CONVERGENCE CRITERION FEASIBLE RESULTS AND TOLERABLE CONSTRAINT VIOLATIONS OPTIMIZATION PROCEDURE USING PIKAIA CALCULATION OF FITNESS CONTROL PARAMETER SETTING FINITE ELEMENT MODELS COMMON PROPERTIES RECTANGULAR PLATE RE?NED DISCRETIZATION COARSE DISCRETIZATION DISCRETIZATION ERROR AND NUMERICAL POLLUTION TWO PLATES JOINED AT 90? HALF-CYLINDER GEARBOX EMPLOYING SPLINE FUNCTIONS TO REDUCE THE NUMBER OF DESIGN VARIABLES GENERAL ASPECTS BICUBIC SPLINE SURFACE HERMITE SPLINE SURFACE TENSOR PRODUCT B´EZIER SURFACE OPTIMIZATION RESULTS: RECTANGULAR PLATE ORIGINAL RECTANGULAR PLATE RECTANGULAR PLATE OPTIMIZED WITH COBYLA MINIMIZATION OF MLS (RE?NED FE MESH) MINIMIZATION OF MLS (COARSE FE MESH) MINIMIZATION OF MASS MAXIMIZATION OF THE FUNDAMENTAL FREQUENCY MAXIMIZATION OF THE DI?ERENCE BETWEEN TWO NATURAL FREQUENCIES RECTANGULAR PLATE OPTIMIZED WITH COBYLA USING SPLINES RECTANGULAR PLATE OPTIMIZED WITH PIKAIA: MINIMIZATION OF MASS OPTIMIZATION RESULTS: TWO PLATES JOINED AT 90? ORIGINAL TWO PLATES JOINED AT 90? TWO PLATES JOINED AT 90?OPTIMIZED WITH COBYLA MINIMIZATION OF MLS MINIMIZATION OF MASS WITH FUNDAMENTAL FREQUENCY CONSTRAINT TWO PLATES JOINED AT 90?OPTIMIZED WITH PIKAIA: MAXIMIZATION OF THE DI?ER- ENCE BETWEEN TWO NATURAL FREQUENCIES OPTIMIZATION RESULTS: HALF-CYLINDER ORIGINAL HALF-CYLINDER HALF-CYLINDER OPTIMIZED WITH COBYLA HALF-CYLINDER OPTIMIZED WITH COBYLA USING SPLINES HALF-CYLINDER OPTIMIZED WITH PIKAIA: MINIMIZATION OF MLS 10 OPTIMIZATION RESULTS: GEARBOX 10 1 ORIGINAL GEARBOX 10 2 GEARBOX OPTIMIZED WITH COBYLA: MINIMIZATION OF MLS 11 DISCUSSION 11 1 SUMMARY 11 2 CONCLUSIONS 11 3 FUTURE WORK