Dynamic response of circular and annular circular plates using spectral element method

Shirmohammadi, Fatemeh; Bahrami, Saeed

doi:10.1016/j.apm.2017.08.014

Cited by 32 publications

(7 citation statements)

References 25 publications

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“…Aiming at the vibration problem of plate structures, scholars have conducted many researches. The calculation for displacement of annular plate with different thicknesses and different internal-external diameter ratios under impact load was carried out by Shirmohammadi et al [1] to investigate the vibration through spectral element method. Ma et al [2,3] presented the nonlinear oscillation of stiffened plate with four-sided clamped and four-sided simply supported boundary conditions, and relationship between nonlinear natural frequency and amplitude was given by ANSYS analysis.…”

Section: Introductionmentioning

confidence: 99%

Magnetoelastic nonlinear free vibration of an annular plate under a nonuniform magnetic field of the long straight current‐carrying wire

Hao

2022

Z Angew Math Mech

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In this article, the magnetoelastic nonlinear free vibration of a thin conductive annular plate under the nonuniform toroidal magnetic field is investigated, where the magnetic field is generated by a long straight current-carrying wire.Based on electromagnetic theory, expressions of the nonuniform magnetic field, electromagnetic forces are deduced. The nonlinear free vibration equation of plate is derived by using the Hamilton principle. Considering different boundary conditions, the axisymmetric vibration differential equation is achieved by the Galerkin method. The method of multiple scales is employed to obtain the second-order approximate analytical solutions and natural frequency. In numerical calculation, the characteristics of nonlinear natural vibration and singular points varying with different parameters, for example, current intensity and plate size, are presented, respectively. The results indicate that, with the increase of current, natural frequency increases and then stabilizes in the inner-clamped and out-free (C-F) boundary, but decreases and stabilizes in the cases of the inner-clamped and out-clamped (C-C) boundary or inner-simply and out-simply (S-S) boundary. Moreover, when wire current is off, natural frequency maintains a constant, where the equilibrium solution of the system is a center. In addition, for all boundary conditions, natural frequency increases significantly with increase of internal radius and thickness, but decreases with the increase of outer radius.

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Section: Introductionmentioning

confidence: 99%

Magnetoelastic nonlinear free vibration of an annular plate under a nonuniform magnetic field of the long straight current‐carrying wire

Hao

2022

Z Angew Math Mech

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“…Civalek and Acar (2007) used the DSC method to investigate the bending results for the Mindlin plates on elastic foundations; the effects of boundary conditions, foundation parameters, and shear deformation on the plate were also investigated. Shirmohammadi and Bahrami (2018) used the spectral element method to investigate the vibration under impact load for the circular and annular circular plates; the effects of various thicknesses and internal-to-external radius ratios on the circular plates were also investigated. Demir and Civalek (2017) used the nonlocal FEM via Hermitian cubic shape functions to investigate the thermal vibration of nanobeams embedded in an elastic matrix; the effects of Pasternak foundation parameter and thermal environments on the vibration frequency were investigated.…”

Section: Introductionmentioning

confidence: 99%

Vibration frequency of thick functionally graded material cylindrical shells with fully homogeneous equation and third-order shear deformation theory under thermal environment

Hong

2020

Journal of Vibration and Control

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The effects of third-order shear deformation theory and varied shear correction coefficient on the vibration frequency of thick functionally graded material cylindrical shells with fully homogeneous equation under thermal environment are investigated. The nonlinear coefficient term of displacement field of third-order shear deformation theory is included to derive the fully homogeneous equation under free vibration of functionally graded material cylindrical shells. The determinant of the coefficient matrix in dynamic equilibrium differential equations under free vibration can be represented into the fully fifth-order polynomial equation, thus the natural frequency can be found. Two parametric effects of environment temperature and functionally graded material power law index on the natural frequency of functionally graded material thick cylindrical shells with and without the nonlinear coefficient term of displacement fields are computed and investigated.

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“…Eksenel dönel plaklarla ilgili önceki çalışmalar on yıllardır yapılagelmektedir. Konuyla ilgili çalışmalara; kabukların analiz ve tasarımı [1], ince kabuk teorisi [2], dinamik kabuk problemleri için sonlu eleman yaklaşımı [3], dinamik analizler için doğrudan integrasyon yöntemlerinin karşılaştırılması [4], elastik kabukların zorlanmış titreşimi [5], rijitlik matrislerinin elde edilmesi ve uygulanması [6], ortotropik ve viskoelastik pakların Laplace uzayında dinamik analizi [7], silindirik kabukların statik ve dinamik analizleri [8], spektral eleman metodu kullanılarak dairesel ve halka şeklinde plakların dinamik analizi [9], dairesel ve halka şeklindeki ince plakların serbest titreşimi için Hamilton yaklaşımı [10] ve dikdörtgen plakların serbest ve zorlanmış titreşimi için sonlu farklar yöntemi uygulamaları [11] örnek olarak gösterilebilir.…”

Section: Introductionunclassified

Dai̇resel Plaklarin Sonlu Elemanlar Yöntemi̇ İle Laplace Uzayinda Di̇nami̇k Anali̇zi̇

Noori¹,

Temel²

2019

Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi

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ÖZBu çalışmada, eksenel dönel simetrik dairesel plak problemlerin iki farklı dinamik yükleme altındaki davranışları teorik olarak araştırılmıştır. Eksenel dönel simetrik dairesel plak cisimlerin sönümlü titreşimleri, iki boyutlu düzlemsel eleman modeli kullanılarak, sonlu elemanlar ve Laplace dönüşüm metotlarının birlikte kullanılması ile elde edilmiştir. Plak malzemesi izotrop, lineer elastik veya viskoelastik kabul edilmiştir. Viskoelastik malzeme durumunda Kelvin sönüm modeli kullanılmıştır. Kelvin modelinde elastik sabitler, elastik-viskoelastik analojisi yardımı ile Laplace uzayında kompleks karşıtları ile yer değiştirmektedir. Sistemi idare eden hareket denklemi öncelikle zaman uzayında elde edilmiştir. Ardından sistem hareket denklemine Laplace dönüşümü uygulanarak elde edilen lineer cebrik denklem takımı, sayısal olarak çözülmüştür. Dönüşmüş uzayda elde edilen çözümlerden zaman uzayına geçmek için etkin bir sayısal ters Laplace dönüşüm metodu kullanılmıştır. Bu işlem kullanılarak sonlu elemanlar yöntemine dayalı bir bilgisayar programı hazırlanmıştır. Hazırlanan bilgisayar programının sonuçları, ANSYS sonlu eleman paket programı kullanılarak hesaplanan sonuçlar ile karşılaştırılıp, bu yöntemin doğruluğu ve üstünlüğü gösterilmiştir. ABSTRACTIn this study, dynamic analysis of axisymmetric circular plates subjected to two type of dynamic loads are theoretically investigated. The solutions of damped response of the considered structure have been obtained by the Laplace transform method and finite element method using the two dimensional plane elements. Materials of the plate are assumed to be isotropic, linear elastic and/or viscoelastic. In the viscoelastic material case, the Kelvin model is employed. According to the correspondence principle the material constants are replaced with their complex counterparts in the Laplace domain. The governing equations of motion of the problem are first obtained in the time domain. Laplace transform is then applied and the set of simultaneous linear algebraic equations are solved numerically in the transferred domain. The solutions obtained are transformed to the time domain using an

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Dynamic response of circular and annular circular plates using spectral element method

Cited by 32 publications

References 25 publications

Magnetoelastic nonlinear free vibration of an annular plate under a nonuniform magnetic field of the long straight current‐carrying wire

Magnetoelastic nonlinear free vibration of an annular plate under a nonuniform magnetic field of the long straight current‐carrying wire

Vibration frequency of thick functionally graded material cylindrical shells with fully homogeneous equation and third-order shear deformation theory under thermal environment

Dai̇resel Plaklarin Sonlu Elemanlar Yöntemi̇ İle Laplace Uzayinda Di̇nami̇k Anali̇zi̇

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