Oscillations of a non-uniform finite hollow cylinder under conditions of complex prestressed state

Yurov, V. O.; Nedin, R.; Vatul’yan, A. O.

doi:10.1016/j.engstruct.2020.111019

Cited by 6 publications

(3 citation statements)

References 29 publications

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“…However, prior to this study, the effects of residual stresses were predominantly confined to the boundary conditions at the fiber-matrix interface and were not integrated into the constitutive relationship governing the incremental stress-strain behavior of the bulk material, be it the fiber or matrix. Several studies have highlighted these inconsistencies [12][13][14]. The integration of conventional linear elasticity and the effects of residual stresses into a modified constitutive relation, rooted in incremental deformation theories [15,16], represents a significant advancement.…”

Section: Introductionmentioning

confidence: 99%

A modified analytical model for the single-fiber pullout problem involving non-classical stress–strain relationships due to residual stresses: Analysis of stress field in the fully bonded region

Pei,

Yang,

Zhou

et al. 2023

Mathematics and Mechanics of Solids

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Upon reevaluating the influence of residual stresses generated by thermal mismatches in fibrous composites during the curing process, we introduce a modified model for the extraction of a single fiber from an elastic matrix. In contrast to previous models, which solely factored residual stress effects into the boundary conditions at the fiber–matrix interface while omitting them from the constitutive relations, our current model acknowledges bulk residual stress as finite values. Consequently, it yields non-conventional constitutive relations to describe the incremental deformation caused by external pulling forces. We have developed a practical semi-analytical series solution for the radial displacement of the matrix and an exact solution for the radial displacement of the fiber. To validate our modified model, we simplify it to a scenario where the influence of residual stress on the stress–strain relationship is excluded and compare it with results from existing literature. This comparison underscores the soundness of our modified model. We present a phase diagram to illustrate how the impact of residual stress on stress field prediction varies based on the ratio of the fiber modulus to the matrix modulus. This phase diagram serves as a valuable tool for evaluating whether it is advisable to transition from the previous mechanical model, which disregards the influence of residual stress on the stress–strain relationship, to the new model, which takes this influence into account within the stress–strain relationship.

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Section: Introductionmentioning

confidence: 99%

A modified analytical model for the single-fiber pullout problem involving non-classical stress–strain relationships due to residual stresses: Analysis of stress field in the fully bonded region

Pei,

Yang,

Zhou

et al. 2023

Mathematics and Mechanics of Solids

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show abstract

“…Для решения обратной задачи предложен специальный итерационный подход, основанный на технике регуляризации; проведены вычислительные эксперименты по восстановлению предварительного состояния. В [23] исследована задача для конечного цилиндра в условиях сложного начального напряженного состояния, описываемого четырьмя ненулевыми компонентами тензора ПН. На основе метода возмущений выведены формулы, позволяющие приближенно найти изменения резонансных частот, вызванные наличием неоднородного поля ПН, проанализировано влияние уровней ПН на изменение собственных частот.…”

Section: Introductionunclassified

Modelling and Analysis of Initial Stress State in a Thin-Wall Cylinder With Variable Characteristics

Vatul’yan

Nedin

Yurov

2023

PSP

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A linearized model of prestressed elastic body vibrations is described in terms of the nonsymmetric Piola stress tensor, and a weak statement of the original problem is given. With the help of the Lagrange variational principle, we construct a statement of the problem of steady axisymmetric oscillations of a thin-walled (shell-like) cylinder with variable material properties in the presence of an inhomogeneous prestress field. The motion equations, essential and natural boundary conditions are formulated. Integral characteristics are introduced that average the change in prestresses and material properties over the shell thickness. On the basis of the model presented, the problem on steady-state vibrations of a functionally graded prestressed cylindrical shell is numerically investigated via the shooting method; the influence of the laws of change in material modules and prestress components on dynamic characteristics (e.g., amplitude-frequency characteristics, natural vibration frequencies) is analyzed, a comparative analysis of the solutions is carried out depending on the thin-walled parameter. For the considered cylindrical shell with axial inhomogeneity, based on the acoustic sounding data, we study the inverse problem of restoring two laws of prestress inhomogeneity characterizing the nonuniform initial stress-strain state of tension or inflation. As additional information, we consider the measurement data of the displacement components on the cylinder's surface, given in a set of points at a certain frequency of steady-state oscillations; in such a case, the material characteristics are considered to be known and may depend on the axial coordinate, which makes it possible to set an arbitrary functional gradient along the axis of the cylinder. The mode of probing loading is determined by specifying the traction type and oscillation frequency. Explicit formulas for the desired laws of prestress inhomogeneity are obtained, and computational experiments are carried out to restore them. A high accuracy of reconstruction is revealed far from the ends of the cylinder when probing at a frequency in the vicinity of the first resonance.

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“…Распространение крутильных волн в цилиндре описывалось при этом с использованием трехмерной линеаризованной теории деформирования тел при наличии ПН. В работе [12] исследуется прямая задача для конечного цилиндра в условиях сложного начального напряженного состояния, описываемого четырьмя компонентами ПН. На основе метода возмущений выведены формулы, позволяющие приближенно найти изменения резонансных частот, вызванные наличием заданного неоднородного поля ПН, проанализировано влияние уровней ПН на изменение собственных частот цилиндра.…”

Section: Introductionunclassified

On the Reconstruction of Prestress Fields in a Hollow Cylinder

Nedin

Yurov

2023

PNRPU Mechanics Bulletin

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The present research is devoted to the development of the theoretical foundations of nondestructive acoustic method for identifying inhomogeneous prestress fields in a hollow cylinder, depending on the probing loading type. A linearized model of steady oscillations of an elastic body in the presence of an inhomogeneous prestress field of arbitrary nature is considered in the standard and weak formulations. On the basis of this model, we formulate a problem for a cantilever-clamped prestressed hollow cylinder that performs steady axisymmetric vibrations under three types of probing loading. A corresponding weak formulation of the problem in the cylindrical coordinate system is presented, in which six independent components of the prestress tensor are taken into account. At that, a case of prestress fields obtained by applying some initial mechanical external static load is considered. In the presence and absence of prestresses of various types, amplitude-frequency dependences are analyzed, and resonant and natural frequencies are found in a wide frequency range. Numerical calculations were carried out using the FEM on a non-uniform grid; mesh refinement is carried out in the vicinity of the boundary points, where the type of boundary conditions changes. Based on the numerical solution of an auxiliary set of direct problems, seven types of prestress fields are constructed, differing in the types of initial loading, most often encountered in practice. To assess the possibility of implementing the procedure for reconstructing prestresses of each of the considered types, a sensitivity analysis was additionally performed, which showed that for some prestress types there are frequencies and types of probing loading for which the presence of prestress is practically not manifested. The sensitivity analysis performed made it possible to implement the optimal method of probing loading when solving the inverse coefficient problem. The statement of the new inverse problem on the restoration of arbitrary inhomogeneous prestress fields in the considered finite hollow cylinder is formulated. When restoring the prestress of a given structure, the inverse problem is reduced to finding a set of parameters from an ill-conditioned algebraic system, which was studied with the help of the A.N. Tikhonov regularization method. Additional data for solving the inverse problem was obtained on the basis of probing both via a single load and via combined probing modes. It has been found that it is most effective to use a combined loading mode and use a sufficiently wide frequency range when selecting sounding frequencies. The results of computational experiments on the reconstruction of six components of the prestress tensor are presented and analyzed, and recommendations are proposed for choosing the optimal modes of acoustic sounding.

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Oscillations of a non-uniform finite hollow cylinder under conditions of complex prestressed state

Cited by 6 publications

References 29 publications

A modified analytical model for the single-fiber pullout problem involving non-classical stress–strain relationships due to residual stresses: Analysis of stress field in the fully bonded region

A modified analytical model for the single-fiber pullout problem involving non-classical stress–strain relationships due to residual stresses: Analysis of stress field in the fully bonded region

Modelling and Analysis of Initial Stress State in a Thin-Wall Cylinder With Variable Characteristics

On the Reconstruction of Prestress Fields in a Hollow Cylinder

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