Optimization of Boundary Supports for Sound Radiation Reduction of Vibrating Structures

Abstract

The purpose of this research is to design optimal boundary supports for minimum structural sound radiation. The influence of the boundary conditions on the structural dynamics of a cantilever beam is first examined to motivate the research. The boundary supports constraining both the in- and out-of-plane degrees of freedom of the plate are considered as the design parameters. The fixed and free boundary degrees of freedom are represented by a continuous function with the help of homogenization. Analytical expressions of sensitivity functions are employed in the optimization, leading to more efficient and accurate numerical solutions. The sensitivity expressions are based on the linear equation system obtained with the finite element method. Numerical examples of single frequency and broadband optimizations are presented. The sensitivity of the optimal design parameters with respect to small random perturbations is also studied. The examples demonstrate that an encouraging reduction of sound radiation as measured by the mean square normal velocity can be achieved with the optimal boundary conditions as compared with the base line structure.

Structural-Acoustic Optimization of Composite Sandwich Structures: A Review

“…Methods in topology optimization of static problems are well developed and extended to dynamic problems including structural-acoustic optimizations (Pedersen and Pederson, 2005;Denli and Sun, 2007b). Among these methods, there are heuristic approaches called material homogenization methods employed with optimality criteria or the method of moving asymptotes algorithms.…”

“…Optimization studies of boundary supports for compliant mechanism design have also attracted the attention of researchers (Bendsoe and Sigmund, 2003). Recently, boundary conditions have been optimized to minimize sound radiation from vibrating structures (Denli and Sun, 2007b).…”

Minimizing the radiated sound power from vibrating plates by using in-plane functionally graded materials

“…Some of the most important sound radiation elements include vibrating plate structures. Sound radiation minimization is typically performed via passive methods by adding auxiliary elements to the original structure like masses [1][2][3], adding stiffeners [4][5][6][7], local thickness distribution [8][9][10][11], modifying boundary supports [12][13][14][15], shape modification [16][17][18][19], and/or using material tailoring [20].…”

Identification of Acoustic Characteristics of Honeycomb Sandwich Composite Panels Using Hybrid Analytical/Finite Element Method1

“…For the purpose of improving the acoustic performance of sandwich composite structures, Denli and Sun investigated optimal designs of a sandwich composite beam [28], sandwich beams with cellular cores [29], and sandwich cylindrical shells [30]. In addition, they studied the optimal boundary support conditions for improving the acoustic performance [31] and summarized previous research activities on sandwich composite panel modeling and optimization methods in Ref. [32].…”