Effects of shear stiffness, rotatory and axial inertia, and interface stiffness on free vibrations of a two-layer beam

Lenci, Stefano; Clementi, Francesco

doi:10.1016/j.jsv.2012.07.004

Cited by 35 publications

(9 citation statements)

References 34 publications

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“…Это позволяет использовать в рас-чётах балочные модели, которые строятся на основе классической гипотезы плоских сече-ний или на её уточнённых вариантах [18,32].…”

Section: формулировка модели основные допущенияunclassified

Dynamics of Multilink Rod System With Constraints: A Plane Problem in Finite Element Formulation

2016

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Данилин А.Н. Динамика стержневой системы со связями: плоская задача в конечно-элементной формулировке // Вестник Пермского национального исследовательского политехнического университета. Механика. -2016Механика. - . -№ 4. -С. 338-363. DOI: 10.15593/perm.mech/2016 Danilin A.N. Dynamics of multilink rod system with constraints: a plane problem in finite element formulation. PNRPU Mechanics Bulletin. 2016. No. 4. Рр. 338-363. DOI: 10.15593/perm.mech/2016 В работе моделируется динамическое поведение движущейся конструкции, составленной из гибких стержневых элементов, которые соединяются через шар-ниры. Предполагается, что в шарнирах есть связи -жесткие и нежесткие, управ-ляемые и неуправляемые. Математически они считаются дифференциальными в интегрируемой или неинтегрируемой формах.Модель стержневой системы строится на основе метода конечных элемен-тов, учитывая конечные деформации и нелинейности инерционных сил. Считается, что концы каждого стержневого элемента жестко соединены с твёрдыми телами, размеры которых малы по сравнению с длиной элемента. Каждый конечный эле-мент связывается с локальной системой координат, для которой перемещения, углы поворотов, поступательные и вращательные скорости учитываются строго. Функции формы выбираются в виде квазистатических аппроксимаций локальных перемещений и углов поворотов сечений стержневого элемента. В качестве обоб-щенных координат задачи принимаются абсолютные перемещения и углы поворо-тов краевых сечений конечных элементов модели.Уравнения движения системы составляются на основе принципа Даламбера-Лагранжа. Считается, что на обобщенные координаты системы наложены связи, линейные относительно обобщённых скоростей. Вариация функционала задачи, для которого ищется стационарное значение, преобразуется путём прибавления уравнений связей, умноженных на неопределённые множителя Лагранжа. Вариа-ционная задача для преобразованного функционала решается как свободная. Ус-ловия стационарности вместе с дифференциальными уравнениями связей опре-деляют искомые значения обобщенных координат.В работе предлагается подход, позволяющий избежать громоздких вычисле-ний нелинейных инерционных членов без упрощения физической модели и (или) изменения первоначальной структуры уравнений.Рассмотрен пример развертывания стержневой системы, состоящей из трех гибких стержней, последовательно соединенных через шарниры. Решение нели-нейных уравнений движения получено численным методом с использованием па-раметра длины интегральной кривой решения в качестве аргумента задачи. Такое преобразование доставляет системе разрешающих уравнений наилучшую обу-словленность процесса численного решения. © ПНИПУ Ключевые слова:стержневая система, нелинейная динамика, конечные перемещения и повороты, гибкость, кинематические связи, конечно-элементная формулировка.

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Section: формулировка модели основные допущенияunclassified

Dynamics of Multilink Rod System With Constraints: A Plane Problem in Finite Element Formulation

2016

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“…The parametric excitation in delaminated plates is possible to appear, as well. Similarly to the theory of laminated and composite beams [83][84][85][86][87][88][89][90] the literature is very rich in the different theories to model laminated composite plates and shells. Thin flat plates can be modeled by the classical or Kirchhoff plate theory, 91,92 while for relatively thick plates the first-order shear deformation theory (FSDT or Mindlin), [93][94][95][96][97][98][99][100] second-order shear deformation theory (SSDT), [101][102][103][104][105] general third-order theory (TSDT), [106][107][108] Reddy third-order theory, [109][110][111][112] other higher-order shear deformation theories (HSDT), [113][114][115] layerwise theories, [116][117][118][119][120][121] and the 3D elasticity solutions 122,123 are developed.…”

Section: Department Of Applied Mechanics Budapest University Of Techmentioning

confidence: 99%

Natural vibration-induced parametric excitation in delaminated Kirchhoff plates

Szekrényes

2015

Journal of Composite Materials

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This paper revisits the problem of free vibration of delaminated composite plates with Lévy type boundary conditions. The governing equations are derived for laminated Kirchhoff plates including through-width delamination. The plate is divided into two subplates in the plane of the delamination. The kinematic continuity of the undelaminated part is established by using the system of exact kinematic conditions. The free vibration analysis of orthotropic simply supported Lévy plates reveals that the delaminated parts are subjected to periodic normal and in-plane shear forces. This effect induces parametric excitation leading to the susceptibility of the plates to dynamic delamination buckling during the vibration. An important aspect is that depending on the vibration mode the internal forces have a two-dimensional distribution in the plane of the delamination. To solve the dynamic stability problem the finite element matrices of the delaminated parts are developed. The distribution of the internal forces in the direction of the delamination front was considered. The mode shapes including a half-wave along the width of the plate accompanied by delamination buckling are shown based on the subsequent superimposition of the buckling eigenshapes. The analysis reveals that the vibration phenomenon is amplitude dependent. Also, the phase plane portraits are created for some chosen cases showing some special trajectories. KeywordsDelamination, free vibration, laminated plate theory, dynamic stability, parametric excitation, harmonic balance, finite element method IntroductionDelaminations are typical defects in composite and sandwich structures induced by indentations (e.g. local loading by spherical indentors), 1,2 low-velocity impact and free edge effects (normal and shear stress concentration between layers at free edges), 3-6 finally by fabrication defects. 7,8 The cracks and delaminations reduce significantly the strength and stiffness of composite laminates.9-11 The material defects also influence the dynamic behavior of the structures.12-20 One of the widely known dynamic phenomena is parametric excitation, which takes place in machine tools, 21 [73][74][75][76][77][78] and sandwich beams. 79In Burlayenko and Sadowski, 80 the foam/core debonding in sandwich plates was investigated during free vibration. However, the existence of the parametric excitation was not revealed in any of the former papers.To the best of the author's knowledge, the existence of the parametric excitation in the course of free vibration of delaminated composite beams was first revealed in Szekre´nyes 81 and was solved effectively by the FE and harmonic balance methods in Szekre´nyes.82 It was also shown that the delamination buckling takes place only if the free vibration amplitude exceeds the so-called critical amplitude at a specified point of the beam. The existence of the critical amplitude was also proved experimentally. The parametric excitation in delaminated plates is possible to appear, as well. 9,10,[127][128][129] subseq...

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“…We call such a beam as the Timoshenko beam. Based on the FSDT theory, Lenci and Clementi [19] studied the natural frequency of layered beams sandwiching an elastic interlayer. Murakami [20] presented a laminated Timoshenko theory which considers the interlayer slip in the beam.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Deformations for Two‐Layer Timoshenko Beams Glued by a Viscoelastic Interlayer

Pei

Wang

et al. 2019

Mathematical Problems in Engineering

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An analytical solution of stresses and deformations for two-layer Timoshenko beams glued by a viscoelastic interlayer under uniform transverse load is presented. The standard linear solid model is employed to simulate the viscoelastic characteristics of the interlayer, in which the memory effect of strains is considered. The mechanical behavior of each layer is described by the first-order shear deformation theory (FSDT). By means of the principle of minimum potential energy, a group of equations for displacements and rotation angles are derived out. The final solution is obtained by conducting the Laplace transform and the inversion of Laplace transform to the equation group. Numerical comparison shows that the present solutions and the finite element results are in good agreement. It is shown that the present results are more accurate than those obtained from the Euler-Bernoulli beam theory, especially for thick beams. And the present solutions can accurately describe the variation of stresses and deformations of the beam with the time, compared with those ignoring the memory effect of strains. Finally, the effects of the geometric parameters and material properties of the interlayer on stresses and deformations of the beam are studied in detail.

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Effects of shear stiffness, rotatory and axial inertia, and interface stiffness on free vibrations of a two-layer beam

Cited by 35 publications

References 34 publications

Dynamics of Multilink Rod System With Constraints: A Plane Problem in Finite Element Formulation

Dynamics of Multilink Rod System With Constraints: A Plane Problem in Finite Element Formulation

Natural vibration-induced parametric excitation in delaminated Kirchhoff plates

Analytical Solution of Deformations for Two‐Layer Timoshenko Beams Glued by a Viscoelastic Interlayer

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