Nonlinear Bending of Rectangular Magnetoelectroelastic Thin Plates with Linearly Varying Thickness
-
Feng Wang
and
Chang-ping Chen
Abstract
With employing the von Karman plate theory, and considering the linearly thickness variation in one direction, the bending problem of a rectangular magnetoelectroelastic plates with linear variable thickness is investigated. According to the Maxwell’s equations, when applying the magnetoelectric load on the plate’s surfaces and neglecting the in-plane electric and magnetic fields in thin plates, the electric and magnetic potentials varying along the thickness direction for the magnetoelectroelastic plates are determined. The nonlinear differential equations for magnetoelectroelastic plates with linear variable thickness are established based on the Hamilton’s principle. The Galerkin procedure is taken to translate a set of differential equations into algebraic equations. The numerical examples are presented to discuss the influences of the aspect ratio and span–thickness ratio on the nonlinear load–deflection curves for magnetoelectroelastic plates with linear variable thickness. In addition, the induced electric and magnetic potentials are also presented with the various values of the taper constants.
Funding statement: The project was supported by the National Natural Science Foundation of China (Grant No. 51778551), the Natural Science Foundation of Fujian Province (Grant No. 2012J01009), and the Education Department of Fujian Province (Grant No. JA14050).
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- Numerical Methods for the Derivative Nonlinear Schrödinger Equation
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Articles in the same Issue
- Frontmatter
- A Robust Algorithm for Nonlinear Variable-Order Fractional Control Systems with Delay
- Numerical Methods for the Derivative Nonlinear Schrödinger Equation
- Lax Integrability and Exact Solutions of a Variable-Coefficient and Nonisospectral AKNS Hierarchy
- Modeling of Supersonic/Hypersonic Boundary Layer Transition Using a Single-Point Approach
- A Novel Macromodel based on Krylov Subspace Projection Method for Micromixers with Serpentine Channels
- Approaches to the Numerical Estimates of Grid Convergence of NSE in the Presence of Singularities
- Numerical Solutions of Stochastic Volterra–Fredholm Integral Equations by Hybrid Legendre Block-Pulse Functions
- Positivity and Stability of Standard and Fractional Descriptor Continuous-Time Linear and Nonlinear Systems
- Dynamics of Almost Periodic Solution for a Delayed Facultative Mutualism Model Involving Negative Feedback Terms
- Controllability of Fractional Evolution Inclusions with Noninstantaneous Impulses
- Analysis of a Delayed Predator–Prey System with Harvesting
- Nonlinear Bending of Rectangular Magnetoelectroelastic Thin Plates with Linearly Varying Thickness
- Numerical Method for a Class of Nonlinear Singularly Perturbed Delay Differential Equations Using Parametric Cubic Spline
- Numerical Simulation for Shale Gas Flow in Complex Fracture System of Fractured Horizontal Well
- Real-Time Control of a Rotary Inverted Pendulum using Robust LQR-based ANFIS Controller
- A Study of an Extended Generalized (2+1)-dimensional Jaulent–Miodek Equation
- RBFPUM with QR Factorization for Solving Water Flow Problem in Multilayered Soil
- Classical Magnetism and an Integral Formula Involving Modified Bessel Functions
- Lie Symmetry Analysis of Boundary Layer Stagnation-Point Flow and Heat Transfer of Non-Newtonian Power-Law Fluids Over a Nonlinearly Shrinking/Stretching Sheet with Thermal Radiation
