Peridynamic governing equations of fluid mechanics for barotropic flow are developed. As a special case of such a flow, linearized acoustics is also considered. The peridynamic governing equation of acoustics is also developed and discussed in detail. In order to obtain these new peridynamic governing equations, integral operators called “peridynamic D operators” are developed systematically, which are obtained by directly requiring the peridynamic D operators to converge to corresponding classical differential operators as the generalized material horizon approaches 0. Even though peridynamic D operators are applied only to fluid mechanics, acoustics, and heat conduction in an anisotropic inhomogeneous material in the present paper, it is clear that these peridynamic D operators can be used in any other field of mathematical physics to obtain a peridynamic (nonlocal) version of the governing equations. As an application of the newly obtained peridynamic governing equations, a time-dependent 3D (three-dimensional) peridynamic acoustics equation with a sound source is analytically solved for two different initial pressure disturbance profiles, and the results are discussed. These are believed to be the first exact analytical solutions for peridynamic acoustics.

建立了正压流体力学的蠕变控制方程。作为这种流动的特例，还考虑了线性声学。还开发并详细讨论了声学的环绕动力学控制方程。为了获得这些新的周动力控制方程，系统地开发了称为“周动力D算子”的积分算子，该积分算子是通过在广义材料层接近0时直接要求周动力D算子收敛到相应的经典微分算子而获得的。本文中D算子仅适用于各向异性非均质材料中的流体力学，声学和热传导，显然，这些周动力D算子可用于数学物理学的任何其他领域，以获得控制方程的周动力（非局部）形式。作为新获得的绕动控制方程的一种应用，针对两个不同的初始压力扰动曲线，解析求解了带有声源的时变3D（三维）绕动声学方程，并对结果进行了讨论。据信，这些是针对环绕动力声学的首个精确分析解决方案。并讨论结果。据信，这些是针对环绕动力声学的首个精确分析解决方案。并讨论了结果。据信，这些是针对环绕动力声学的首个精确分析解决方案。