三次元音響問題における直接微分法に基づく形状感度解析法の定式化

摘要

A set of new boundary integral equations relating the sensitivity coefficients of sound pressure and its normal derivative is presented for three-dimensional acoustic problems based on the direct differentiation method. A linear combination of the derived boundary integral equations is used to avoid divergent, erroneous numerical results around the fictitious eigenfrequencies which are obser­ved for exterior acoustic fields. The boundary integral equations have strongly-singular and hypersingular boundary integrals, and are evaluated as principal values and finite-parts for triang-lular constant element discretization. The present formulation is more efficiently used for the fast multipole boundary element method than the conventional one which is based on the regularization, because multipole expansion formulas and other translation formulas have to be implemented also for the fundamental solution of the Laplace's equation for the conventional formulation. The effectiveness of the method based on the present formulation is demonstrated through a numerical test example for an exterior acoustic field.%自動車車重内の騒音や鉄道・高速道路を走行する車輌から発せられる騒音を低減する方法として，音場の 形状を工夫して散乱波の干渉により，音場内の一定の領域で騒音の低減をはかる方法がある．これは，特定の領域における騒音低減を評価する目的関数を最小化するような音墳形状を表すパラメータ（設計変数）の億を求める最適化問題として定式化することができる．このような設計変数値の計算過程では，目的関数の設計変数に関する変化率，すなわち感度の計算が必要となる場合が多い．