Free Vibration Analysis of Shells of Revolution

Tan, Dongyao

doi:10.1006/jsvi.1997.1406

Cited by 28 publications

(12 citation statements)

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“…For a submesh element (̂,̂+ 1 ), its dynamic stiffness matrix [k i ] (̂) can be obtained by linearly combining ten solutions of (12) and (15). The element-end displacements and force vectors for submesh are denoted as {d} (̂) and {F} (̂) , respectively, the submesh element stiffness matrix…”

Section: Wittrick-williams Algorithmmentioning

confidence: 99%

“…Li et al [10] solved the natural frequencies of conical shells with Hamilton's principle and Rayleigh-Ritz method. In recent decades, general solutions to free vibration of shells of revolution were provided; e.g., Luah and Fan [11] analysed the free vibration of shells of revolution by introducing the spline finite element method; Tan [12] predicted the natural frequencies of general shells of revolution using a substructuring approach.…”

Section: Introductionmentioning

confidence: 99%

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An Exact Dynamic Stiffness Formulation for Predicting Natural Frequencies of Moderately Thick Shells of Revolution

Chen

2018

Mathematical Problems in Engineering

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An exact dynamic stiffness formulation is proposed for calculating the natural frequencies of shells of revolution based on the firstorder Reissner-Mindlin theory. Equations of motion are reduced to be one-dimensional, should the circumferential wave number is specified, and then are rewritten in Hamilton form. Therefore, a shell of revolution with a moderate thickness is analysed as a special skeletal structure with five degrees of freedom at element ends. Dynamic stiffnesses are constructed directly from the one-dimensional governing vibration equations using classic skeletal theory. Number of natural frequencies below a specific value is counted by applying the Wittrick-Williams (W-W) algorithm, and exact eigenvalues can be simply obtained using bisection method. A solution to the number of clamped-end frequencies J 0 in the W-W algorithm is also proposed and proven to be reliable. Numerical examples on a variety of shells with different boundary conditions are investigated, and results are well compared and validated. Influences of a variety of shell parameters on natural frequencies of both cylindrical and spherical shells are discussed in detail, demonstrating that the proposed dynamic stiffness formulation is applicable to analyse natural frequencies of moderately thick shells of revolution with high accuracy.

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Section: Wittrick-williams Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Exact Dynamic Stiffness Formulation for Predicting Natural Frequencies of Moderately Thick Shells of Revolution

Chen

2018

Mathematical Problems in Engineering

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“…In the case of thin shells, it can be judged by references of different years, for example, by [Xi et al 1996;Tan 1998;Wang and Redekop 2005;Grigorenko et al 2006]. Detailed analysis of studies on vibrations of some classes of thick shells of revolution is presented in [Redekop 2006;Kang 2007].…”

Section: Introductionmentioning

confidence: 99%

“…Only publications [Rao et al 1974;Karmishin et al 1975;Grigorenko et al 1986;Bespalova et al 1991;Sivadas 1995;Lam and Hua 1997;1998;Wang et al 1997;Yuan and Liu 2007] directly refer to the object of the given paper. These works mostly consider, based on the Love model, homogeneous across the thickness isotropic Keywords: shells of revolution, inhomogeneity, preliminary stresses, natural frequencies, nonclassic model, numerical-analytical technique.…”

Section: Introductionmentioning

confidence: 99%

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Vibrations of highly inhomogeneous shells of revolution under static loading

Bespalova

Urusova

2008

JOMMS

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An approach to determining natural frequencies of middle-thickness inhomogeneous shells of revolution acted upon by static axisymmetrical loads is proposed. The approach is based on application of the nonclassic shell model that takes into account transverse shears and reduction across the wall thickness. In solving the problem posed, decomposition into two interconnected problems is used. The first problem is related to determination of the initial stress-strain state of shells under static axisymmetrical loads. The second problem is related to determination of natural frequencies of shells relative to this state that appears in the form of parametric terms. To solve the problems, the numerical-analytical technique developed by the authors is used. The efficiency of allowance for reduction across the wall thickness is illustrated on the example of an inhomogeneous middle-thickness cylindrical shell under local loads. Analysis of natural frequencies of the shell having the form of a pneumatic tire is presented depending on the value of internal pressure.

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Fundamental Consideration

Sahoo¹

2016

Design Aids for Stiffened Composite Shells With Cutouts

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Free Vibration Analysis of Shells of Revolution

Cited by 28 publications

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An Exact Dynamic Stiffness Formulation for Predicting Natural Frequencies of Moderately Thick Shells of Revolution

An Exact Dynamic Stiffness Formulation for Predicting Natural Frequencies of Moderately Thick Shells of Revolution

Vibrations of highly inhomogeneous shells of revolution under static loading

Fundamental Consideration

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