Analytical and mathematical simulation for nonlinear stability of scale-dependent magneto-electro-elastic system

Buckling and free vibration analysis of high speed rotating carbon nanotube reinforced cylindrical piezoelectric shell

Geometrically nonlinear buckling of functionally graded magneto-electro-elastic (FG-MEE) nanoshells with the use of classical shell theory and nonlocal strain gradient theory (NSGT) has been analyzed in present research. Mathematical formulation based on NSGT gives two scale coefficients for simultaneous description of structural stiffness reduction and increment. Functional gradation of material properties is described based on power-law formulation. The nanoshell is under a multi-physical field related to applied voltage, magnetic potential, and mechanical load. Exerting a strong electric voltage, magnetic potential or mechanical load may lead to buckling of nanoshell. Taking into account geometric nonlinearity effects after buckling, the behavior of nanoshell in post-buckling regime can be analyzed. Nonlinear governing equations are reduced to ordinary equations utilizing Galerkin's approach and post-buckling curves are obtained based on an analytical procedure. It will be shown that post-buckling curves are dependent on nonlocal/strain gradient parameters, electric voltage magnitude and sign, magnetic potential magnitude and sign and material gradation exponent.

Nonlinear dynamic modeling of geometrically imperfect magneto-electro-elastic nanobeam made of functionally graded material

Radial vibration analysis of pseudoelastic shape memory alloy thin cylindrical shells by the differential quadrature method

A three-dimensional layerwise-differential quadrature free vibration analysis of laminated cylindrical shells

The conventional finite element method (FEM) cannot investigate the size effect on thermal residual stresses induced by the sintering process in micro multilayer ceramic capacitors (MLCCs). In this paper, a FE two-dimensional single layer model is developed for investigation of the effect of the micro scale on prediction of the residual thermal stresses in MLCCs. In this FE single layer model, the strain gradient effect is considered. It is found that with decreasing single layer thickness, the shear stress increases significantly in the ceramic layer near the electrode tip, which might cause cracking of the ceramic layer near the electrode tip. The numerical results also show that the predictions of the thermal residual stresses in MLCCs are strongly dependent on the micro scale. The residual thermal stresses induced by the sintering process exhibit strong size effects and, therefore, the strain gradient effect should be taken into account in the design and evaluation of MLCC devices.

The theories of nonlocal, refined plate, and surface effects are used in this study to investigate the free vibration of magnetoelectroelastic (MEE) nanoplates resting on elastic foundations. For this purpose, the MEE nanoplate is subjected not only to external magnetic and electric potentials but also to thermal and shear in-plane loads. The refined plate theory is used and the Maxwell equations and magnetoelectric boundary conditions employed to determine the variations in the electric and magnetic potentials along the direction of the nanoplate thickness. This is followed by deriving the governing equations based on the Hamilton’s principle, which are then solved via the generalized differential quadrature method. In a later stage of the study, the effects of electric and magnetic potentials, nonlocal parameter, thermal and shear in-plane loading, Winkler and shear moduli, different boundary conditions, and aspect ratio are explored in a parametric study on the surface effects of vibration characteristics of MEE nanoplates. It is found that the effect of surface parameters enhanced with increases in nonlocal parameter, electric potential, in-plane shear load, and temperature change. However, this effect is observed to decrease when the magnetic potential, dimensionless Winkler and shear moduli, and nanoplate thickness are augmented.

Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory

Nonlinear transient response of magneto-electro-elastic cylindrical shells with initial geometric imperfection

At present, dynamic investigations of rotating magneto-electro-elastic (MEE) cylindrical shells subjected to low-velocity-impact loading remain unexplored. Given their unique magnetoelectric coupling capabilities, which enable rapid energy conversion across magnetic, electrical, and mechanical fields, this study develops displacement-based formulations for geometrically imperfect MEE cylindrical shells using Love’s thin-shell theory. The constitutive relations governing multi-coupled electric, magnetic, and thermal fields are derived from Maxwell’s equations and thermodynamic principles. Nonlinear governing equations are formulated via the Euler-Lagrange principle, with subsequent solutions for vibration-induced central deflection obtained using the Runge-Kutta method. Comparative studies with benchmark cases and convergence assessments validate the proposed methodology. Finally, parametric analyses elucidate the quantitative characterization of initial imperfections, electric potential, magnetic potential, thermal conditions, and impact velocity.

Dynamic analysis of composite cylindrical shells using differential quadrature method (DQM)

Three-dimensional vibration analysis of arbitrary angle-ply laminated cylindrical shells using differential quadrature method

Static analysis of functionally graded cylindrical shell with piezoelectric layers using differential quadrature method

In this paper, three-dimensional static and free vibration analysis of functionally graded graphene platelets-reinforced composite (FG-GPLRC) truncated conical shells, cylindrical shells and annular plates with various boundary conditions is carried out within the framework of elasticity theory. The main contribution of the present work is that formulation for free vibration and bending behavior of the FG-GPLRC truncated conical shell based on theory of elasticity has not yet been reported. Additionally, formulation and solution for cylindrical shell and annular plate are derived by changing the semi vertex angle in formulation and solution of FG-GPLRC truncated conical shell. A semi-analytical solution is proposed base on employing differential quadrature method (DQM) together with state-space technique. Validity of current approach is assessed by comparing its numerical results with those available in the literature. An especial attention is drawn to the role of GPLs weight fraction, patterns of GPLs distribution through the thickness direction, geometrical parameters such as semi-vertex angle, length to mid-radius ratio on natural frequencies and bending characteristics. Numerical results reveal that desirable static and free vibration response (such as lower radial deflection and higher natural frequencies) can be achieved by locating more square shaped GPLs near inner and outer surfaces.

Based upon differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), mechanical-hygro-thermal vibrational analyzes of shear deformable porous functionally graded (FG) nanoplate on visco-elastic medium has been performed. The presented formulation incorporates two scale factors for examining vibrational behaviors of nano-dimension plates more accurately. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. It is supposed that the nano-size plate is exposed to hygro-thermal and variable compressive mechanical loadings. The governing equations achieved by Hamilton\'s principle are solved implementing DQM. Presented results indicate the prominence of moisture/temperature variation, damping factor, material gradient index, nonlocal coefficient, strain gradient coefficient and porosities on vibrational frequencies of FG nano-size plate.