On one approach to studying free vibrations of cylindrical shells of variable thickness in the circumferential direction within a refined statement

Grigorenko, А. Ya.; Efimova, T. L.; Sokolova, L. V.

doi:10.1007/s10958-010-0156-y

Cited by 6 publications

(2 citation statements)

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“…To study the effect of cracks on the natural Mesh refinement for vibration disturbance frequencies and mode shapes of cracked beams, Li (2001) proposed an exact approach for free vibration analysis of a non-uniform beam with an arbitrary number of cracks and concentrated masses. To study the influence of a change in shell thickness on the distribution of its natural frequencies, Grigorenko et al (2010) introduced the spline collocation method for finding the frequencies of free vibrations of circular closed cylindrical shells of variable thickness in the circumferential direction. Grigorenko et al (2011) used a holographic interferometry technique to determine the frequencies of the free vibrations of isotropic circular cylindrical shells.…”

Section: Introductionmentioning

confidence: 99%

“…To study the effect of cracks on the natural frequencies and mode shapes of cracked beams, Li (2001) proposed an exact approach for free vibration analysis of a non-uniform beam with an arbitrary number of cracks and concentrated masses. To study the influence of a change in shell thickness on the distribution of its natural frequencies, Grigorenko et al. (2010) introduced the spline collocation method for finding the frequencies of free vibrations of circular closed cylindrical shells of variable thickness in the circumferential direction.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive mesh refinement for finite element analysis of the free vibration disturbance of cylindrical shells due to circumferential micro-crack damage

Wang

Kennedy

et al. 2022

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PurposeModerately thick circular cylindrical shells are widely used as supporting structures or storage cavities in structural engineering, rock engineering, and aerospace engineering. In practical engineering, shells often work with micro-cracks or defects. The existence of micro-crack damage may result in the disturbance of dynamic behaviours and even induce accidental dynamic disasters. The free vibration frequency and mode are important parameters for the dynamic performance and damage identification analysis. In particular, stiffness weakening of the local damage region leads to significant changes in the vibration mode, which makes it difficult for the mesh generated in the conventional finite element method to capture a high-precision solution of the local oscillation.Design/methodology/approachIn response to the above problems, this study developed an adaptive finite element method and a crack damage characterisation method for moderately thick circular cylindrical shells. By introducing the inverse power iteration method, error estimation, and mesh subdivision refinement technique for the analysis of finite element eigenvalue problems, an adaptive computation scheme was constructed for the free vibration problem of moderately thick circular cylindrical shells with circumferential crack damage.FindingsBased on typical numerical examples, the established adaptive finite element solution for the free vibration of moderately thick circular cylindrical shells demonstrated its suitability for solving the high-precision free vibration frequency and mode of cylindrical shell structures. The any order frequency and mode shape of cracked cylindrical shells under the conditions of different ring wave numbers, crack locations, crack depths, and multiple cracks were successfully solved. The influences of the location, depth, and number of cracks on the disturbance of dynamic behaviours were analysed.Originality/valueThis study can be used as a reference for the adaptive finite element solution of free vibration of moderately thick circular cylindrical shells with cracks and lays the foundation for further development of a high-performance computation method suitable for the dynamic disturbance and damage identification analysis of general cracked structures.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive mesh refinement for finite element analysis of the free vibration disturbance of cylindrical shells due to circumferential micro-crack damage

Wang

Kennedy

et al. 2022

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Solutions of Dynamic Problems Based on the Refined Model

Grigorenko

Müller

Grigorenko

et al. 2016

Recent Developments in Anisotropic Heterogeneous Shell Theory

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Static and Dynamic Problems for Anisotropic Inhomogeneous Shells with Variable Parameters and Their Numerical Solution (Review)

Grigorenko¹,

Grigorenko

2013

Int Appl Mech

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Studies on the static and dynamic deformation of isotropic and anisotropic elastic shell-like bodies of complex shape performed using classical and refined problem statements are reviewed. To solve two-dimensional boundary-value problems and eigenvalue problems, use is made of a nontraditional discrete-continuum approach based on the spline-approximation of the unknown functions of partial differential equations with variable coefficients. This enables reducing the original problem to a system of one-dimensional problems solved with the discrete-orthogonalization method. An analysis is made of numerical results on the distribution of stress and displacement fields and dynamic characteristics depending on the loading and boundary conditions, geometrical and mechanical parameters of elastic bodies. Emphasis is placed on the accuracy of the results Keywords: shell structures, static and dynamic problems, variable parameters, models, discrete-continuum methods Introduction.Many members of modern engineering structures have the form of intricately shaped shells fixed in various ways and subjected to various distributed and local loads. Shell elements are widely used to meet the requirements imposed by the severe operating conditions of machines, aircraft, transportation vehicles, industrial and civil facilities. The complication of the configuration of shell elements necessitates developing a theory and methods for solving static and dynamic problems for shells made of anisotropic inhomogeneous materials.A typical feature in the development of the theory of plates and shells is the relationship between the setting up of a mathematical model describing a given class of problems and the development of a method for solving them. For example, Kirchhoff's theory of thin plates [101] and the Kirchhoff-Love theory of thin shells [97] tend not only to provide a realistic description of the deformation of plates and shells, but also to make such models so simple as to solve a number of problems with available computational capability. An example of such relationship is the Donnell-Mushtari-Vlasov theory of shells [5,28,36]. Its basic equations were simplified so as to find solutions to some classes of problems over wide ranges of their characteristics, which is demonstrated by the names given to this theory: technical theory of shells, theory of shallow shells, theory of shells with highly variable stress state [2,8,9,16,20,23,24,29,37]. This relationship is even stronger nowadays when computers are widely used to solve problems in the theory of shells and mathematical models for certain classes of shells are set up so as to provide for all aspects and possibilities associated with the solution of problems [63].The solution of two-dimensional boundary-value problems of the statics and dynamics of plates, shells, and solids described by partial differential equations with variable coefficients involves severe computational difficulties. To solve them, use is sometimes made of approaches based on separation of variables and redu...

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On one approach to studying free vibrations of cylindrical shells of variable thickness in the circumferential direction within a refined statement

Cited by 6 publications

References 1 publication

Adaptive mesh refinement for finite element analysis of the free vibration disturbance of cylindrical shells due to circumferential micro-crack damage

Adaptive mesh refinement for finite element analysis of the free vibration disturbance of cylindrical shells due to circumferential micro-crack damage

Solutions of Dynamic Problems Based on the Refined Model

Static and Dynamic Problems for Anisotropic Inhomogeneous Shells with Variable Parameters and Their Numerical Solution (Review)

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