Vibration analysis of singly curved rectangular plates

Petyt, M.; Nath, J.M. Deb

doi:10.1016/s0022-460x(70)80053-0

Cited by 17 publications

(3 citation statements)

References 6 publications

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“…The energy contributions due to these springs are added to equation (19) to form the total potential energy for the entire system. The energy contribution ub due to these springs is given by (22) In the treatment of boundary conditions, for a free boundary condition the coefficient of the springs is assumed to be zero. If it is assumed to be infinite, this will produce a fixed edge condition.…”

Section: Formulation By Spline Strip Methodsmentioning

confidence: 99%

Application of spline strip method to analyse vibration of open cylindrical shells

Mizusawa

1988

Numerical Meth Engineering

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SUMMARYThis paper deals with the vibration ofopen cylindrical shells by the spline strip method based on Novozhilov's shell theory. Convergence of the solutions is investigated in a few examples and is found to be satisfactory. The accuracy of the results is compared with those calculated by other numerical methods and found to be in good agreement.The effect of inlcuded angles and inplane constraints on vibrating characteristics of simply supported cylindrical shells is shown.

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Section: Formulation By Spline Strip Methodsmentioning

confidence: 99%

Application of spline strip method to analyse vibration of open cylindrical shells

Mizusawa

1988

Numerical Meth Engineering

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“…Petyt and Nath performed the free vibration characteristics of singly curved rectangular plates. The Kantorovich method is employed to diminish the partial * Corresponding author/Yazışılan Yazar differential equations of motion [3]. A new finite difference approach is presented by Bhattacharya for the solution of static and dynamic deflections of plates.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of a pre-stressed curved thin plate

GONENLI¹,

OZTURK²,

DAS³

2022

Pamukkale J Eng Sci

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In this study, the free vibration analysis of cantilever isotropic thin plate, which is a large deflected, is investigated. The large deflection is obtained by applying an external distributed vertical load on the cantilever plate then fixing from the other end as the deflection is large. The non -linear deflection curve of the largely deflected flexible plate is obtained from the large deflection equation of the beams. The curved thin plate is modeled by using the finite element method considering a four-node quadrilateral flat shell element. The effects of the load parameter on the natural frequency parameters and mode shapes are investigated. The results are given in tables and graphics. In addition, the natural frequency parameters obtained from the present model are compared with those of ANSYS software to verify the reliability and validity of the present model. The load parameter that forms the curved thin plate changes mode shapes of the plate structure.Bu çalışmada, büyük çökmeli izotropik ince plakanın serbest titreşim analizi incelenmiştir. Büyük çökme, tek tarafı sabitlenmiş plakaya harici bir dağıtılmış dikey yük uygulanarak ve ardından diğer uçtan sabitlenerek elde edilir. Bükülmüş esnek levhanın doğrusal olmayan çökme eğrisi, kirişlerin büyük çökme denkleminden elde edilir. Eğri ince levha, dört düğümlü dörtgen yassı kabuk eleman dikkate alınarak sonlu elemanlar yöntemi kullanılarak modellenmiştir. Yük parametresinin doğal frekans parametreleri ve mod şekilleri üzerindeki etkileri incelenmiştir. Sonuçlar, tablolar ve grafikler halinde verilmiştir. Ek olarak, mevcut modelden elde edilen doğal frekans parametreleri, mevcut modelin güvenilirliğini ve geçerliliğini doğrulamak için ANSYS yazılımı ile karşılaştırılır. Eğri ince levhayı oluşturan yük parametresi, levha yapısının mod şekillerini değiştirir.

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“…Nath [9] determined the natural frequencies of a fully clamped cylindrical shell. Kantorovich's method for reducing the partial differential equations to a set of ordinary differential equations was applied by Petyt and Nath [10] to study the free vibration characteristics of a singly curved rectangular plate. Petyt [11] also collected four theoretical methods for the vibration analysis of a singly curved rectangular plate and compared numerical results with the experimental results [9].…”

Section: Introductionmentioning

confidence: 99%

Curvature Effects on the Vibration Characteristics of Doubly Curved Shallow Shells with General Elastic Edge Restraints

Shi

Yang

Jiang

et al. 2015

Shock and Vibration

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Effects of curvature upon the vibration characteristics of doubly curved shallow shells are assessed in this paper. Boundary conditions of the shell are generally specified in terms of distributed elastic restraints along the edges. The classical homogeneous boundary supports can be easily simulated by setting the stiffnesses of restraining springs to either zero or infinite. Vibration problems of the shell are solved by a modified Fourier series method that each of the displacements is invariably expressed as a simple trigonometric series which converges uniformly and acceleratedly over the solution domain. All the unknown expansion coefficients are treated equally as a set of independent generalized coordinates and solved using the Rayleigh-Ritz technique. The current method provides a unified solution to the vibration problems of curved shallow shells involving different geometric properties and boundary conditions with no need of modifying the formulations and solution procedures. Extensive tabular and graphical results are presented to show the curvature effects on the natural frequencies of the shell with various boundary conditions.

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Vibration analysis of singly curved rectangular plates

Cited by 17 publications

References 6 publications

Application of spline strip method to analyse vibration of open cylindrical shells

Application of spline strip method to analyse vibration of open cylindrical shells

Vibration analysis of a pre-stressed curved thin plate

Curvature Effects on the Vibration Characteristics of Doubly Curved Shallow Shells with General Elastic Edge Restraints

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