In this paper, a modified Rayleigh-Lamb equation is derived that takes into account the radial vibrations of a gas bubble coated with a viscoelastic shell and located in an elastic medium. For small oscillations of inclusion, the problem of heat exchange between a gas, a liquid phase, a viscoelastic shell, and an elastic medium is solved. The energy integral is determined. In the case of small disturbances, the dispersion relation is found from the Rayleigh-Lamb equations, energy, and the known wave equation for the bubbly medium. An analytical expression of the equilibrium speed of sound is written out and its dependence on the size of the viscoelastic shell and the disturbance frequency is established. An example of a mixture of polydimethylsiloxane with air bubbles coated with a rubber shell illustrates the influence of the elasticity of the carrier medium and the shell of the bubbles on the dependence of the phase velocity and attenuation coefficient on the perturbation frequency. For a mixture of water with air bubbles coated with a rubber shell, the influence of the dependences of the shear modulus and viscosity of butyl rubber on the frequency of disturbances at different temperature on the dispersion curves is shown. A comparison of the theory with experimental data is given.

在本文中，考虑了涂有粘弹性壳并位于弹性介质中的气泡的径向振动，得出了修正的瑞利-兰姆方程。对于夹杂物的小振动，解决了气体，液相，粘弹性壳和弹性介质之间的热交换问题。确定能量积分。在小扰动的情况下，可以从气泡介质的瑞利-兰姆方程，能量和已知波动方程中找到色散关系。写出了声音平衡速度的解析表达式，并建立了其对粘弹性壳尺寸和干扰频率的依赖关系。聚二甲基硅氧烷与涂有橡胶壳的气泡的混合物的例子说明了载体介质和气泡壳的弹性对相速度和衰减系数对摄动频率的依赖性的影响。对于水与涂有橡胶壳的气泡的混合物，显示了丁基橡胶的剪切模量和粘度对不同温度下扰动频率的依赖性对分散曲线的影响。给出了理论与实验数据的比较。示出了丁基橡胶的剪切模量和粘度的依赖性对分散温度下不同温度下干扰频率的影响。给出了理论与实验数据的比较。示出了丁基橡胶的剪切模量和粘度的依赖性对分散温度下不同温度下干扰频率的影响。给出了理论与实验数据的比较。