A direct method for solving the inverse problem of determining shape cross section a rod is proposed. The based on Neumann series Bessel functions representations solutions Sturm-Liouville equations. first coefficient representation sufficient recovery unknown function. system linear algebraic equations finding this obtained. proposed leads to an efficient numerical algorithm.

Abstract In present paper the inverse problem on identification of three non‐homogeneous residual stress components in rectangular plate steady‐state vibration regime is considered. The equation building iterative process solving formulated. An approach to reconstruction stresses described basis introduction Airy prestress function. technique leading a system linear algebraic equations at each iteration proposed. Results conducting series computational experiments are depicted and discussed.

In this study, modelling and identification of prestress state in functionally graded plate within the framework Timoshenko theory are discussed. With help variational principles, statements boundary problems for stationary vibration inhomogeneous prestressed plates have been derived taking into account various factors state. The comparative analysis classical nonclassical models has conducted. effect on solution characteristics estimated. New approaches to solving inverse a reconstruction...

Based on the general linear elasticity relations, an axisymmetric problem steady‐state oscillations of a functionally graded hollow cylinder is formulated. The Lamé parameters are considered variable in radial coordinate. Oscillations caused by distributed load applied to outer part boundary. Using separation method, direct determining and longitudinal components displacement field investigated. influence laws variation for acoustic characteristics analysed. inverse coefficient...

Abstract This research is devoted to the development of theoretical foundations for identification an essentially inhomogeneous prestressed state by analyzing gain‐frequency characteristic boundary points body. The proposed scheme reconstruction prestresses constructed on iterative processes. It includes finite element solution direct problem and regularizing procedure solve Fredholm integral equation first kind in inverse problem. In series one‐dimensional model examples it was shown that...

We propose a scheme of efficient solving an inverse coefficient problem on reconstruction unknown laws variation mechanical properties inhomogeneous isotropic cylindrical region. The is performed step‐by‐step by means two problems torsional and radial vibrations the considered region that provides formulation searching functions. build iterative processes stated; in frames each process, we derive systems Fredholm integral equations 1st 2nd kind order to find corrections functions relative...

Analysis of inhomogeneous residual stress (RS) fields in bodies is one the major problems mechanics deformable solid bodies. In present research new techniques identification RS are developed on basis surface displacement measurement a set points under vibrating sounding load. Corresponding nonlinear ill-posed inverse (IP) formulated and solved numerically by means iterative regularization. Based computational experiments, most advantageous load types frequency ranges providing best...

Аннотация.Представлен новый подход к решению задачи об идентификации переменных характеристик неоднородного упругого изотропного тела.Приведены наиболее употребительные постановки задач определении механических (параметры Ламе и плотность -функции координат).Обратная задача свойств в силу своей существенной нелинейности обычно решается итерационным образом, причем каждая итерация требует решения прямой для некоторого начального приближения системы интегральных уравнений Фредгольма первого...

The problem on radial oscillations of an elastic cylinder with inhomogeneous residual stress (RS) is considered. Two acoustic techniques RS reconstructing are suggested. Within the framework first method, a set displacement values assumed to be known, while frequency fixed. second value at outer radius known for frequencies. examples numerical identification experiments presented.