A non-linear dynamic lumped-parameter model of a rectangular plate

Bayles, D.J.; Lowery, R. L.; Boyd, D. E.

doi:10.1016/0022-460x(72)90817-6

Cited by 14 publications

(7 citation statements)

References 4 publications

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“…Together with equations ( 1) and (2), it is able to express the conservation of linear momentum in two dimensions. Further, the three Föppl-von Karman equations [1,21,26] can be reduced to two, by introducing Airy's stress function F(x, y, t), as defined by…”

Section: Problem Definitionmentioning

confidence: 99%

“…Within the multitude of existing SDOF formulations, a critical examination highlights that most of them are developed on the basis of a sinusoidal load function (see, for example, [25][26][27]33]). Minimum variations can be found in the reference Cartesian system.…”

Section: Blast Load Descriptionmentioning

confidence: 99%

“…Minimum variations can be found in the reference Cartesian system. As far as the reference x, y axes are located at the central point of the midplane of the plate in Figure 2(a), for example, the outof-plane deflections, w, are commonly expressed as [25][26][27]33] w(x, y, t) � w 0 (t) Conversely, when the external load is described considering reference coordinate system from Bayles et al [26], the resulting displacement of the plate is given by (i.e., [1,33])…”

Section: Blast Load Descriptionmentioning

confidence: 99%

“…In the past, a number of researchers investigated the structural response of plates using various SDOF formulations. Several studies have been presented for thin plates under large amplitude vibrations (see [1,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]). Different solving techniques have been generally adopted, and the response of thin elastic plates has been mostly investigated under a specific set of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Li and Jones investigated the dynamic response of clamped circular plates subjected to blast loading, using the Johansen yield criterion which includes the effect of bending moments along with transverse shear [35]. Based on literature review [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], it is important to mention that most of the available SDOF models for thin elastic plates are based on bending theory only, wherein membrane effects were considered through a bending resistance function and therefore indirectly accounted in the form of an equivalent bending stiffness only. Earlier researchers, in some other cases, employed separately the membrane effect (as a nonlinear term of the equation of motion) and explored the SDOF response of thin elastic plates under blast loading [33].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Enhanced Single‐Degree‐of‐Freedom Analysis of Thin Elastic Plates Subjected to Blast Loading Using an Energy‐Based Approach

Goel

Thimmesh

Shirbhate

et al. 2020

Advances in Civil Engineering

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Single-degree-of-freedom (SDOF) models are known to represent a valid tool in support of design. Key assumptions of these models, on the other hand, can strongly affect the expected predictions, hence resulting in possible overconservative or misleading estimates for the response of real structural systems under extreme actions. Among others, the description of the input loads can be responsible for major design issues, thus requiring the use of more refined approaches. In this paper, a SDOF model is developed for thin elastic plates under large displacements. Based on the energy approach, careful attention is given for the derivation of the governing linear and nonlinear parameters, under different boundary conditions of technical interest. In doing so, the efforts are dedicated to the description of the incoming blast waves. In place of simplified sinusoidal pressures, the input impulsive loads are described with the support of infinite trigonometric series that are more accurate. The so-developed SDOF model is therefore validated, based on selected literature results, by analyzing the large displacement response of thin elastic plates, under several boundary conditions and real blast pressures. Major advantage for the validation of the proposed SDOF model is obtained from experimental finite element (FE) and finite difference (FD) models of literature, giving evidence of a rather good correlation and confirming the validity of the presented formulation.

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Section: Problem Definitionmentioning

confidence: 99%

Section: Blast Load Descriptionmentioning

confidence: 99%

Section: Blast Load Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Enhanced Single‐Degree‐of‐Freedom Analysis of Thin Elastic Plates Subjected to Blast Loading Using an Energy‐Based Approach

Goel

Thimmesh

Shirbhate

et al. 2020

Advances in Civil Engineering

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Transient analysis of geometrically linear and non‐linear structures by a combined finite‐element‐Riccati‐transfer substructure method

Zhu¹,

Xue²

1993

Numerical Meth Engineering

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The combined finite-element-Riccati-transfer substructure method is applied to the transient analysis of the structures under various excitations with small and large displacements, respectively. The advantages include reductions in the order of standard transfer equation systems, in the computational efforts, and in the propagation of round-off errors produced in recursive multiplications of the transfer matrices. Meanwhile, a methodology for analysing transfer substructures is, in combination with exact dynamic condensation and generalized Riccati transformation, proposed to develop the finite element and transfer matrix (FETM) techniques. The Newmark method and Wilson-O method are used for time integrations with respect to linear and non-linear problems. The modified Newton -Raphson method is employed for equilibrium ileration in each time step. Numerical examples are presented to demonstrate the high efficiency and accuracy of the proposed method for the transient responses of plates. The results from thesc examples agree well with those obtaincd by other methods.

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Large amplitude natural frequencies of rectangular plates with mixed boundary conditions

Ramachandran

1976

Journal of Sound and Vibration

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A non-linear dynamic lumped-parameter model of a rectangular plate

Cited by 14 publications

References 4 publications

Enhanced Single‐Degree‐of‐Freedom Analysis of Thin Elastic Plates Subjected to Blast Loading Using an Energy‐Based Approach

Enhanced Single‐Degree‐of‐Freedom Analysis of Thin Elastic Plates Subjected to Blast Loading Using an Energy‐Based Approach

Transient analysis of geometrically linear and non‐linear structures by a combined finite‐element‐Riccati‐transfer substructure method

Large amplitude natural frequencies of rectangular plates with mixed boundary conditions

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