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Free and forced bending vibrations of a thin plate in a perfect compressible fluid with energy dissipation taken into account
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-01-29 , DOI: 10.1002/zamm.201900102 V. N. Paimushin 1, 2 , D. V. Tarlakovskii 3, 4 , V. A. Firsov 1 , R. K. Gazizullin 1
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-01-29 , DOI: 10.1002/zamm.201900102 V. N. Paimushin 1, 2 , D. V. Tarlakovskii 3, 4 , V. A. Firsov 1 , R. K. Gazizullin 1
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A refined statement of stationary dynamic acoustoelasticity problems of thin isotropic plates surrounded from both sides by acoustic media assumed to be perfect compressible fluids has been studed. The problem statement takes into account the energy dissipation in the material of the plate and fluid on the basis of the Kelvin‐Voigt hysteresis model. The refinement of the fluid behavior is based on the assumption that the pressure increment is proportional not only to volumetric strain, but also to the rate of its volumetric strain. This assumption allows us to obtain the generalized Helmholtz wave equation by introducing Skudrzyk's complex sound velocity into consideration to take account of the energy dissipation. The motion equations of the plate are based on the classical Kirchhoff‐Love model and are obtained in two versions. In the first version unsimplified three‐dimensional wave equations are used to determine the aerohydrodynamic load acting on a plate. The second version is based on simplifying the equations of fluid motion by the introduction of the well‐known hypothesis of plane reflection and emission of sound waves. On the basis of the derived equations, exact analytical solutions of two types of problems are obtained. The first type is related to the problem of free vibrations of a rectangular plate hinged around the contour when complex eigenfrequencies were defined. The second type is related to the problem of forced vibrations of the plate under the action of a flat mono‐harmonic incident sound wave when sound transmission loss, the stress‐strain state parameters of the plate as well as the laws of change in sound pressure in a fluid were determined. It is shown that correct and more meaningful solutions of acoustoelasticity problems of the considered class are possible only in case of describing the behavior of a fluid with unsimplified three‐dimensional wave equations with consideration of the energy dissipation.
中文翻译：
考虑到能量耗散，在理想的可压缩流体中薄板的自由弯曲和强制弯曲振动
已经研究了细小的各向同性板的稳态动态声弹性问题的精细表述，该板由两侧均被假定为完美可压缩流体的声学介质包围。该问题陈述在开尔文-沃格特磁滞模型的基础上考虑了板和流体材料的能量耗散。流体行为的细化基于这样的假设：压力增量不仅与体积应变成正比，而且还与其体积应变率成正比。该假设使我们能够通过引入Skudrzyk的复声速来考虑能量耗散，从而获得广义的亥姆霍兹波方程。板的运动方程基于经典的Kirchhoff-Love模型，并有两个版本。在第一个版本中，未简化的三维波动方程用于确定作用在板上的空气动力载荷。第二种形式是通过引入众所周知的平面反射和声波发射假设来简化流体运动方程。根据导出的方程，可以获得两种类型问题的精确解析解。第一种类型与在定义复杂特征频率时围绕轮廓铰接的矩形板的自由振动问题有关。第二种类型与在传声损耗，平坦的单谐波入射声波作用下板的强迫振动，板的应力-应变状态参数以及声压的变化规律有关。确定了液体中。
更新日期：2020-01-29
中文翻译：
考虑到能量耗散，在理想的可压缩流体中薄板的自由弯曲和强制弯曲振动
已经研究了细小的各向同性板的稳态动态声弹性问题的精细表述，该板由两侧均被假定为完美可压缩流体的声学介质包围。该问题陈述在开尔文-沃格特磁滞模型的基础上考虑了板和流体材料的能量耗散。流体行为的细化基于这样的假设：压力增量不仅与体积应变成正比，而且还与其体积应变率成正比。该假设使我们能够通过引入Skudrzyk的复声速来考虑能量耗散，从而获得广义的亥姆霍兹波方程。板的运动方程基于经典的Kirchhoff-Love模型，并有两个版本。在第一个版本中，未简化的三维波动方程用于确定作用在板上的空气动力载荷。第二种形式是通过引入众所周知的平面反射和声波发射假设来简化流体运动方程。根据导出的方程，可以获得两种类型问题的精确解析解。第一种类型与在定义复杂特征频率时围绕轮廓铰接的矩形板的自由振动问题有关。第二种类型与在传声损耗，平坦的单谐波入射声波作用下板的强迫振动，板的应力-应变状态参数以及声压的变化规律有关。确定了液体中。
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