Acoustic Resonance of a Two-Dimensional Isotropic Medium Studied Using Airy Stress Function

Ryuichi Tarumi; Shinpei Yamada; Yoji Shibutani

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Acoustic Resonance of a Two-Dimensional Isotropic Medium Studied Using Airy Stress Function

机译：利用艾里应力函数研究二维各向同性介质的声共振

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We have developed a theory that determines a complete set of stress field, σ_(ij), in a freely vibrating two-dimensional isotropic medium within the framework of the calculus of variation. Our formulation is based on the Airy stress function φ and the minimization of the complementary strain energy under the constrain condition ‖φ‖L~2/2 = const. By the Ritz method, the constrained variational problem becomes a linear eigenvalue problem. Numerical analysis yields 36 types of the stress functions φ_i .Unlike the stress fields determined from the conventional resonant ultrasound spectroscopy theory, the stress fields derived from the stress functions φ_i, explicitly satisfy the stress-free natural boundary condition and the equilibrium equation. It is also confirmed that the 36 resonant modes can be classified into four groups according to the parity of the coefficient of the basis function. Furthermore, the stress functions φ_i are orthogonal in the sense of the L2 inner product. These features are similar to those of the conventional resonant ultrasound spectroscopy (RUS) theory.

机译：我们已经开发出一种理论，可以确定在变化演算框架内自由振动的二维各向同性介质中的应力场的完整集合σ_（ij）。我们的公式是基于艾里应力函数φ和约束条件φφL〜2/2 = const时互补应变能的最小化。通过Ritz方法，约束变分问题成为线性特征值问题。数值分析产生了36种应力函数φ_i。与传统共振超声光谱理论确定的应力场不同，从应力函数φ_i得出的应力场明确满足无应力自然边界条件和平衡方程。还证实了，根据基函数的系数的奇偶性，可以将36种共振模式分为四类。此外，应力函数φ_i在L2内积的意义上是正交的。这些特征类似于常规共振超声光谱（RUS）理论的特征。

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《Japanese journal of applied physics》 |2012年第7issue2期|p.07GA03.1-07GA03.4|共4页
作者
Ryuichi Tarumi; Shinpei Yamada; Yoji Shibutani;
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Department of Mechanical Engineering, Osaka University, Suita, Osaka 565-0871, Japan;

Department of Mechanical Engineering, Osaka University, Suita, Osaka 565-0871, Japan;

Department of Mechanical Engineering, Osaka University, Suita, Osaka 565-0871, Japan;

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Acoustic Resonance of a Two-Dimensional Isotropic Medium Studied Using Airy Stress Function

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