Static and vibration analysis of orthotropic toroidal shells of variable thickness by differential quadrature

Jiang, Wen-An; Redekop, D.

doi:10.1016/s0263-8231(02)00116-7

Cited by 31 publications

(17 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The values of natural frequencies calculated according to expression (21) for different n and m are in sufficiently good agreement with the numerical and experimental results given in the literature. This is indicative of the correctness of applying hypotheses (9) and (10) to the analysis of the vibration frequencies of a cylindrical shell. We will also use them in the analysis of toroidal shells.…”

mentioning

confidence: 69%

“…(9) has made it possible to express all the functions in (14) in terms of only one unknown quantity -the tangential displacement v. Using a cylindrical shell as an example, we will show that the use of hypotheses of (9) and (10) in the analysis of natural frequencies is justified.…”

Section: Introductionmentioning

confidence: 89%

“…Moreover, it is very difficult to find the correlation between the vibration modes of cylindrical and toroidal shells of the same length that are fastened in a similar way, even though the curvature parameter α of the latter tends to zero [9]. Therefore, despite a great number of the solution methods, the results obtained with their aid [7][8][9][10][11][12] are of a special character, and the solution procedure as such consists in the application of numerical methods, even though the problem statement is presented in the analytical form. In such solutions, the integral properties of the beam sections are not extracted.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Calculation of natural and forced vibrations of a piping system. Part 2. Dynamic stiffness of a pipe bend

Оrynyak

Radchenko

2007

Strength Mater

View full text Add to dashboard Cite

The notion of the dynamic flexibility factor of a pipe bend to be used in problems on the calculation of harmonic vibrations of pipelines is formulated. Based on the Vlasov semi-momentless theory, simplifying hypotheses are introduced that make it possible to reduce the problem statement to the solution of the quartic differential equation. Using the results of the dynamic analysis for toroidal shells, the procedure for taking into account the increased flexibility of pipe bends under dynamic loading has been developed. The expression for the flexibility factor is derived as a function of both the geometrical parameters of the bend and the vibration frequency. The efficiency of the derived expression for the flexibility factor is illustrated by a great number of examples.

show abstract

mentioning

confidence: 69%

Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Calculation of natural and forced vibrations of a piping system. Part 2. Dynamic stiffness of a pipe bend

Оrynyak

Radchenko

2007

Strength Mater

View full text Add to dashboard Cite

show abstract

“…The dynamic stiffness method was employed by Efraim and Eisenberger [88] to compute the natural frequencies of thick spherical shell panels with variable thickness for various boundary restraints, taking into account both the effects of transverse shear stresses and rotary inertia. Finally, Jiang and Redekop [89] studied the free vibrations of orthotropic toroidal shells described by the Sanders-Budiansky equations by means of a semi-analytical differential quadrature method. In this circumstance, the variable thickness profile is defined by a sinusoidal variation and the solutions are obtained for different geometric configurations.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

et al. 2017

View full text Add to dashboard Cite

Abstract:The main aim of the present paper is to solve numerically the free vibration problem of sandwich shell structures with variable thickness and made of Functionally Graded Materials (FGMs). Several Higher-order Shear Deformation Theories (HSDTs), defined by a unified formulation, are employed in the study. The FGM structures are characterized by variable mechanical properties due to the through-the-thickness variation of the volume fraction distribution of the two constituents and the arbitrary thickness profile. A four-parameter power law expression is introduced to describe the FGMs, whereas general relations are used to define the thickness variation, which can affect both the principal coordinates of the shell reference domain. A local scheme of the Generalized Differential Quadrature (GDQ) method is employed as numerical tool. The natural frequencies are obtained varying the exponent of the volume fraction distributions using higher-order theories based on a unified formulation. The structural models considered are two-dimensional and require less degrees of freedom when compared to the corresponding three-dimensional finite element (FE) models, which require a huge number of elements to describe the same geometries accurately. A comparison of the present results with the FE solutions is carried out for the isotropic cases only, whereas the numerical results available in the literature are used to prove the validity as well as accuracy of the current approach in dealing with FGM structures characterized by a variable thickness profile.

show abstract

“…Jiang and Redekop [11] studied the free vibration characteristics of linear elastic orthotropic toroidal VT shells based on the Sanders-Budiansky shell equations, and Kang and Leissa [12] also discussed the free vibration on VT paraboloids shells by using a three-dimensional method. Recently, based on the polynomial fitted thickness, VT plates' various combinations of boundary conditions were investigated by Shufrin and Eisenberger [13], where two shear deformation plate theories were applied to provide accurate results in solving natural frequencies.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Similitude Design Method of the Distorted Model on Variable Thickness Cantilever Plates

et al. 2016

View full text Add to dashboard Cite

Abstract:In the present study, a new method of predicting the dynamic behavior of a variable thickness (VT) cantilever plate by using a thin plate scaled model is proposed. The thin plate model, defined as the model thin (MT) plate, is designed by using the newly proposed similitude design method. The method is derived based on the transfer matrix of both the stepped thickness (ST) plate that is simplified by the VT plate and the thin plate. The thickness of the MT plate is calculated by introducing the equivalent thickness corresponding to each VT plate's vibration modals, such that a series of accurate distorted scaling laws are provided to predict each corresponding property. Moreover, an algorithm of designing the MT plate is proposed and a design process is summarized in steps. Finally, an example, where the prototype VT plate is made of 42 CrMo and the MT plate is made of NO. 45 steel, is discussed to validate the proposed design method, showing that the MT plate, which is designed by using the proposed method, can accurately predict the dynamic properties of the prototype VT plate, and showing its significance in engineering practice.

show abstract

Static and vibration analysis of orthotropic toroidal shells of variable thickness by differential quadrature

Cited by 31 publications

References 12 publications

Calculation of natural and forced vibrations of a piping system. Part 2. Dynamic stiffness of a pipe bend

Calculation of natural and forced vibrations of a piping system. Part 2. Dynamic stiffness of a pipe bend

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

Dynamic Similitude Design Method of the Distorted Model on Variable Thickness Cantilever Plates

Contact Info

Product

Resources

About