Poroelastic structures are widespread in many fields of technology, medicine and biology. Accounting for the presence of a porous skeleton and pore fluid makes it possible to describe the dynamic behavior of the environment more accurately. The presented article deals with the vibrations of inhomogeneous poroelastic media taking into account the initial stress field and the method of reconstruction for such field based on some data on the dynamic behavior of the structure. Initial or residual stresses make considerable contribution to the mechanical capacity of the bodies, and affect on the dynamic behavior. The presence of initial or residual stresses in mechanical structures significantly changes the stress-strain state for such systems and without taking into account this factor, results of simulation may greatly differ from the actual data. There are many methods for determining the initial stress fields, including the X-ray methods, techniques of scratching and drilling, as well as the method of acoustic sensing, that belongs to the nondestructive testing methods and requires a special attention. We considered the problem of reconstruction of the initial stress field for an inhomogeneous poroelastic column, which is based on acoustic sensing method. The equations for the longitudinal oscillations of poroelastic inhomogeneous body in the presence of initial stress field are formulated. The influence of the level of initial stress and Biot modulus on the dynamic behavior of medium is studied. A series of numerical experiments on the reconstruction of various distribution laws for initial stress field are performed.

Рассмотрена задача о восстановлении преднапряжения для неоднородной пороупругой среды на основе метода акустического зондирования. Построены уравнения продольных колебаний неоднородного пороупругого тела при наличии поля предварительных напряжений. Проанализировано влияние уровня предварительных напряжений и модуля Био на динамическое поведение среды. Проведен ряд численных экспериментов по реконструкции различных законов распределения поля предварительных напряжений.