Optimum core design to improve noise attenuation performance and stiffness of sandwich panels used for high-speed railway vehicles

Abstract

In this study, we optimally design the core of a metal sandwich panel used in high-speed railway vehicles to minimize the amount of metal solid in the core and subsequently reduce its weight. The optimum core must satisfy constraints regarding sound transmission class (STC) and compliance. Because the solid-void layout in the core strongly affects the acoustic and static characteristics of sandwich panels, the core layout should be carefully designed when reducing the amount of metal solid. To this end, three topology-optimization problems and one size-optimization problem are formulated and sequentially solved. A single unit cell is periodically repeated in the core. Thus, structural and acoustic topology-optimization problems are first formulated and solved for the unit cell. Based on the optimal topologies obtained for the unit cell, a moderate initial solid-void layout in the unit cell is determined for the size-optimization problem to optimally design core. The effectiveness of the current design approach for the core of the sandwich panel is validated by comparing the STC and compliance values of the optimal core design and a reference design. Nomenclature A N n¼1 finite element assembly operator Bmatrix relating the element strain vector to its nodal displacement vector C m e a nc o m p l i a n c e C ini initial mean compliance c speed of sound in air D constitutive matrix d 1 thickness of thin flat plates at both ends in a sandwich panel d 2 thickness of the bar inside a sandwich panel dis (r,m) distance between the centers of the r th and m th elements E r (χ r ) Young's modulus of the r th element

Partition layout inside a muffler integrated with a thermoelectric generator: Multi-physics analysis and optimal design

“…The functions are called interpolation functions, and their effectiveness in acoustical, thermal, and flow TO problems have been sufficiently validated in previous studies. [12][13][14][15][16]29,30,[32][33][34] The density ð ρ r Þ and bulk modulus ðB r Þ of the r-th finite element in the design domain for the Helmholtz equation are determined by the interpolation functions given as equation ( 20)…”

“…The functions are called interpolation functions, and their effectiveness in acoustical, thermal, and flow TO problems have been sufficiently validated in previous studies. 12–16,29,30,32–34 The density (ρr) and bulk modulus (Br) of the r -th finite element in the design domain for the Helmholtz equation are determined by the interpolation functions given as equation (20)where Tr is the temperature of the r -th element, and the subscripts “air” and “steel” denote the air and steel elements, respectively. The steel elements are constructed as rigid partitions.…”

“…28 On top of the excellent results of the previous studies, two-physics analysis based design results have been reported to reflect a coupling behavior or to increase calculation accuracy for industrial application. For example, based on static and acoustical analyses, Yoon and Lee 29 obtained the optimal topology that simultaneously improves the stiffness and noise attenuation performance of a high-speed train panel, and Yoon et al 30 solved a simple bulkhead design problem by formulating a TO problem for a hybrid structural-acoustic coupling system. Kontoleontos et al 31 formulated and solved viscous flow TO problems including heat transfer.…”