Computational evaluation of electro-magnetic circuits’ effect on the coupled response of multifunctional magneto-electro-elastic composites plates exposed to hygrothermal fields

2020 ◽  
pp. 095440622095448 ◽  
Author(s):  
M Vinyas ◽  
D Harursampath
Keyword(s):  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Fe Model ◽  
Energy Principle ◽  
Magnetic Circuits ◽  
Computational Evaluation ◽  
Electro Magnetic ◽  
Elastic Composites ◽  
Static Behaviour

This work presents a higher order finite element (FE) model to gauge the static behaviour of hygrothermo-magneto-electro-elastic (HTMEE) plates with different electro-magnetic circuits. The FE model is composed of eight-noded isoparametric elements. The displacement equations are presumed to obey the higher order shear deformation theory (HSDT) and the governing equations of motion are obtained with the support of the virtual energy principle. The correctness of the FE model is verified against previously published results. The influence of electro-magnetic boundary conditions associated with hygrothermal loads, stacking sequences, empirical constants and different loading profiles have been studied in detail. The results of this article are the first of its kind in literature. Hence, it is believed to set benchmark for future investigations on multifunctional structures.

Effect of carbon nanotube-reinforced magneto-electro-elastic facings on the pyrocoupled nonlinear deflection of viscoelastic sandwich skew plates in thermal environment

2021 ◽  
pp. 146442072110440
Author(s):  
Vinyas Mahesh
Keyword(s):  
Carbon Nanotube ◽  
Complex Modulus ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Energy Principle ◽  
Design Engineers ◽  
Total Potential ◽  
Viscoelastic Core

This work presents a finite-element-based numerical formulation to evaluate the nonlinear deflections of magneto-electro-elastic sandwich skew plates with a viscoelastic core and functionally graded carbon nanotube-reinforced magneto-electro-elastic face sheets. Meanwhile, the proposed formulation accommodates the geometrical skewness as well. The magneto-electro-elastic sandwich skew plate is operated in the thermal environment and subjected to various multiphysics loads, including electric and magnetic loads. The viscoelastic core is modelled via the complex modulus approach. Two different forms of viscoelastic cores, such as Dyad 606 and EC 2216, are considered in this study. Also, different thickness configurations of core and facing arrangements are taken into account. The plate kinematics is presumed through higher-order shear deformation theory, and von Karman's nonlinear strain displacement relations are incorporated. The global equations of motion are arrived at through the total potential energy principle and solved via the direct iterative method. Special attention is paid to assessing the influence of pyroeffects, coupling fields and electromagnetic boundary conditions on the nonlinear deflections of magneto-electro-elastic sandwich plates working in the thermal environment and subjected to electromagnetic loads, which is the first of its kind. Also, parametric studies dealing with the skew angles, carbon nanotube distributions and volume fractions, thickness ratio, and aspect ratio have been discussed. The results of this work are believed to be unique and serve as a guide for the design engineers towards developing sophisticated smart structures for various engineering applications.

Vibration control of magnetostrictive plate under multi- physical loads via trigonometric higher order shear deformation theory

2015 ◽  
Vol 23 (19) ◽  
pp. 3057-3070 ◽  
Author(s):  
Ali Ghorbanpour Arani ◽  
Z Khoddami Maraghi ◽  
H Khani Arani
Keyword(s):  
Elastic Medium ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Feedback Gain ◽  
First Time ◽  
Free Vibration Response

For the first time in this research, a feedback control system is used to study the free vibration response of rectangular plate made of magnetostrictive material. In this regard, magnetostrictive plate (MsP) is analyzed by trigonometric higher order shear deformation theory that involved six unknown displacement functions and does not require shear correction factor. The MsP is supported by elastic medium as Pasternak foundation which considers both normal and shears modules. Also the MsP undergoes in-plane forces in x and y directions. Considering simply supported boundary condition, six equations of motion are derived using Hamilton’s principle and solved by differential quadrature method. Results indicate the effect of aspect ratio, thickness ratio, elastic medium, compression and tension loads on vibration behavior of MsP. Also, findings show the controller effect of velocity feedback gain to minimize the frequency as far as other parameters become ineffective. These findings can be used to active noise and vibration cancellation systems in many structures.

Well-posed two-phase nonlocal integral models for free vibration of nanobeams in context with higher-order refined shear deformation theory

2021 ◽  
pp. 107754632110399
Author(s):  
Pei Zhang ◽  
Hai Qing
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Well Posedness ◽  
Governing Equations ◽  
Two Phase

In this article, the well-posedness of several common nonlocal models for higher-order refined shear deformation beams is studied. Unlike the case of classic beams models, both strain-driven and stress-driven purely nonlocal theories lead to an ill-posed issue (i.e., there are excessive mandatory boundary conditions) when considering higher-order shear deformation assumption. As an effective remedy, the well-posedness of strain-driven and stress-driven two-phase nonlocal (StrainDTPN and StressDTPN) models is pertinently evidenced by studying the free vibration problem of nanobeams. The governing equations of motion and standard boundary conditions are derived from Hamilton’s principle. The integral constitutive relation is transformed equivalently to a differential form equipped with two constitutive boundary conditions. Using the generalized differential quadrature method (GDQM), the governing equations in terms of displacements are solved numerically. Numerical results show that both the StrainDTPN and StressDTPN models can predict consistent size-effects of beams with different boundary conditions.

Nonlinear Vibrations of Pressurized Functionally Graded Plates Using Higher-Order Thickness Stretching Theory

2014 ◽  
Author(s):  
F. Alijani ◽  
M. Amabili
Keyword(s):  
Nonlinear Vibrations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Numerical Continuation ◽  
Normal Strain ◽  
Rectangular Plates ◽  
Functionally Graded Plates

Nonlinear vibrations of moderately thick functionally graded (FG) rectangular plates are investigated by considering a higher-order shear deformation theory that takes into account the thickness deformation effect. The geometrically nonlinear strain-displacement relationships are derived retaining full non-linear terms in the in-plane and transverse displacements and the three-dimensional constitutive equations are used by removing the assumption of zero transverse normal strain. The plate is assumed to have immovable boundary conditions at the edges. The equations of motion are obtained by using multi-modal energy approach. A code based on pseudo arc-length continuation and collocation scheme is utilized for numerical continuation and bifurcation analysis. Results show that higher-order thickness deformation theories yield a significant accuracy improvement for nonlinear vibrations of highly pressurized functionally graded plates.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

A New Nonlinear Higher-Order Shear Deformation Theory for Nonlinear Vibrations of Laminated Shells

2010 ◽  
Author(s):  
M. Amabili ◽  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Curvilinear Coordinates ◽  
Geometrically Nonlinear ◽  
Geometric Imperfections ◽  
Laminated Shells

A consistent higher-order shear deformation nonlinear theory is developed for shells of generic shape; taking geometric imperfections into account. The geometrically nonlinear strain-displacement relationships are derived retaining full nonlinear terms in the in-plane displacements; they are presented in curvilinear coordinates in a formulation ready to be implemented. Then, large-amplitude forced vibrations of a simply supported, laminated circular cylindrical shell are studied (i) by using the developed theory, and (ii) keeping only nonlinear terms of the von Ka´rma´n type. Results show that inaccurate results are obtained by keeping only nonlinear terms of the von Ka´rma´n type for vibration amplitudes of about two times the shell thickness for the studied case.

Approximate vibration analysis of laminated curved panel using higher-order shear deformation theory

2004 ◽  
Vol 20 (3) ◽  
pp. 238-246
Author(s):  
Shi Jianwei ◽  
Nakatani Akihiro ◽  
Kitagawa Hiroshi
Keyword(s):  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Curved Panel

TSDT theory for free vibration of functionally graded plates with various material properties

2021 ◽  
Vol 8 (4) ◽  
pp. 691-704
Author(s):  
M. Janane Allah ◽  
◽  
Y. Belaasilia ◽  
A. Timesli ◽  
A. El Haouzi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Implicit Algorithm ◽  
Proposed Model ◽  
Graded Material ◽  
Composite Modeling

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

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