A time spectral method for solving the nonlinear dynamic equations of a rectangular elastic plate

Muradova, Aliki D.

doi:10.1007/s10665-014-9752-z

Cited by 3 publications

(6 citation statements)

References 17 publications

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“…Spatially-discretized system. We consider an approximate analytical solution of (1), (2) in the form of partial sums of double Fourier series with the timedependent coefficients, ( [10])…”

Section: Governing Equationsmentioning

confidence: 99%

“…The operators H, B, P and F take different forms depending on the boundary conditions. The expressions for them and for A 1,2 and A 2,N can be found in [10]. Substituting ( 13) into ( 12) we obtain…”

Section: Governing Equationsmentioning

confidence: 99%

“…Initial and boundary conditions are set up for the system. The equations are spatially-discretized by a time spectral method ( [10]). The obtained system of nonlinear ordinary differential equations (ODEs) is solved by the implicit iterative Newmark-β method [12].…”

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confidence: 99%

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Adaptive Neuro-Fuzzy vibration control of a smart plate

Muradova¹,

Tairidis²,

Stavroulakis³

2017

Numerical Algebra, Control &Amp; Optimization

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In the present paper, the vibration supression of a smart plate with the use of ANFIS (Adaptive Neuro-Fuzzy Inference System) is investigated. The whole system consists of a nonlinear mechanical model, which is an extension of the von Kármán plate model with control. The structure is subjected to external disturbances and generalized control forces. Initial and boundary conditions are set up. The initial boundary value problem is spatiallydiscretized by a time spectral method. The obtained discretized model is a system of nonlinear ordinary differential equations (ODEs) with respect to time. A neuro-fuzzy inference system is built and tested in order to create a nonlinear controller for the vibration supression of the plate. More specifically, a Sugeno-type fuzzy inference system is employed and trained through ANFIS. The inputs of the controller are the displacement and the velocity and the output is the control force. An effective optimization procedure is proposed and numerical results are presented.

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“…Spatially-discretized system. We consider an approximate analytical solution of (1), (2) in the form of partial sums of double Fourier series with the timedependent coefficients, ( [10])…”

Section: Governing Equationsmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive Neuro-Fuzzy vibration control of a smart plate

Muradova¹,

Tairidis²,

Stavroulakis³

2017

Numerical Algebra, Control &Amp; Optimization

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“…The operators H, B, P and F take different forms depending on the boundary conditions. The expressions for them and for A 1,2 and A 2,N can be found in [25] and [26]. The convergence of the method is investigated in [26].…”

Section: Spatial Discretization Of (1) (2)mentioning

confidence: 99%

Hybrid control of vibrations of a smart von Kármán plate

Muradova

Stavroulakis

2015

Acta Mech

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The suppression of large vibrations of a smart thin elastic rectangular von Kármán's plate is considered. The plate is subjected to external disturbances and generalized control forces produced by electromechanical feedback. The considered nonlinear initial-boundary value problem is spatially discretized by means of the time spectral method. The implicit Newmark-β iterative method is employed for the time integration of the obtained system of nonlinear equations of motion. Nonlinear controllers are designed, based on a fuzzy inference system. Two numerical algorithms involving a general control of displacement/velocity and a direct control of the Fourier coefficients are proposed. The techniques have been implemented within MATLAB environment with the use of the fuzzy logic toolbox. Numerical examples are presented.

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“…The classical linear and nonlinear plate equations are the main keys for creating various plate models, including delamination of composite plates (Vasiliev and Morozov [27], Stavroulakis and Panagiotopoulos [28], Storakers and Andersson [29], Xue et al [30], and Haghani et al [31]), contact problems (Ohtake et al [32,33], Borisovich et al [34], and Malekzadeh and Setoodeh [35], Muradova and Stavroulakis [36][37][38][39], Muradova et al [40], Fichera [41]), analysis of buckled plates (Ciarlet and Rabier [3], Caloz and Rappaz [42], Matkowsky; Putnick [43], Chien et al [44], Chien et al [45], Muradova [46][47][48], Dossou and Pierre [49]), etc.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review

Muradova

Stavroulakis

2020

Mathematics

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A review of mathematical models for elastic plates with buckling and contact phenomena is provided. The state of the art in this domain is presented. Buckling effects are discussed on an example of a system of nonlinear partial differential equations, describing large deflections of the plate. Unilateral contact problems with buckling, including models for plates, resting on elastic foundations, and contact models for delaminated composite plates, are formulated. Dynamic nonlinear equations for elastic plates, which possess buckling and contact effects are also presented. Most commonly used boundary and initial conditions are set up. The advantages and disadvantages of analytical, semi-analytical, and numerical techniques for the buckling and contact problems are discussed. The corresponding references are given.

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A time spectral method for solving the nonlinear dynamic equations of a rectangular elastic plate

Cited by 3 publications

References 17 publications

Adaptive Neuro-Fuzzy vibration control of a smart plate

Adaptive Neuro-Fuzzy vibration control of a smart plate

Hybrid control of vibrations of a smart von Kármán plate

Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review

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