Semi-analytical solution for free transverse vibrations of Euler–Bernoulli nanobeams with manifold concentrated masses

In the present study, transverse vibrations of nanobeams with manifold concentrated masses, resting on Winkler elastic foundations, are investigated. The model is based on the theory of nonlocal elasticity in the presence of concentrated masses applied to Euler–Bernoulli beams. A closed-form expression for the transverse vibration modes of Euler–Bernoulli beams is presented. The proposed expressions are provided explicitly as the function of two integrated constants, which are determined by the standard boundary conditions. The utilization of the boundary conditions leads to definite terms of natural frequency equations. The natural frequencies and vibration modes of the concerned nanobeams with different numbers of concentrated masses in different positions under some typical boundary conditions (simply supported, cantilevered, and clamped–clamped) have been analyzed by means of the proposed closed–form expressions in order to show their efficiency. It is worth mentioning that the effect of various nonlocal length parameters and Winkler modulus on natural frequencies and vibration modes are also discussed. Finally, the results are compared with those corresponding to a classical local model.     

Thermal environment effects on wave dispersion behavior of inhomogeneous strain gradient nanobeams based on higher order refined beam theory

In this article, an analytical model for the wave propagation analysis of inhomogeneous functionally graded (FG) nanobeam in thermal environment is developed based on nonlocal strain gradient theory, in which the stress accounts for not only the nonlocal elastic stress field but also the strain gradients stress field. The nanobeam is modeled through a higher order shear deformable refined beam theory which has a trigonometric shear stress function. The temperature field supposed to have a nonlinear distribution across the nanobeam thickness. Temperature-dependent material properties of nanobeams are spatially graded based on Mori–Tanaka model. The governing equations of the temperature-dependent functionally graded (FG) nanobeam are derived using the Hamilton’s principle. Numerical examples show that the characteristics of the wave propagation of FG nanobeam are influenced by various parameters such as nonlocality parameter, length scale parameter, gradient index, and temperature changes.     

Ultrahigh Infrared Photoresponse from Core–Shell Single‐Domain‐VO2/V2O5 Heterostructure in Nanobeam

Infrared (IR) harvesting and detection in red and near‐IR (NIR) part of the solar spectrum have always been a long‐term research area of intense interest. However, limited choices of current photoactive materials have significantly hampered the realization of ultrahigh IR sensitivity under room temperature conditions. The trigger for this requires the exploration of new photo­active materials and the ability to fabricate new photoactive structural design. Herein, a new oxide‐catalogue photoconductive NIR detector with ultrahigh performance built by core/shell nanobeam heterostructures (CSNHs) with the inner single‐domain monoclinic VO₂ (M) core and outer V₂O₅ shell, which is the first example of photoconductive IR detector made from transition metal oxides (TMOs), is presented. Benefited from the well‐defined TMO hetero­junction interface, the ultrahigh responsivity (R_λ) of 2873.7 A W^‐1 and specific detectivity (D*) of 9.23 × 10¹² Jones are achieved at room temperature (at 990 nm; 0.2 mW cm^‐2), recording the best performance compared with those reported IR detectors based on heavy‐metal‐free materials, and even comparable/superior to those traditional ones made from materials including heavy metals. These findings pave a new way to design oxide heterostructures for intriguing applications in optoelectronic and energy harvesting nanodevices.     

Magnetic-saturation zone model for two semipermeable cracks in magneto-electro-elastic medium

Extension of the PS model (Gao et al. [1 H. Gao, T. Y. Zhang, and P. Tong, “Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic,” J. Mech. Phy. Solids, vol. 45, pp. 491–510, 1997.[Crossref], [Web of Science ®] , [Google Scholar]]) in piezoelectric materials and the SEMPS model (Fan and Zhao [2 C. Y. Fan and M. H. Zhao, “Nonlinear fracture of 2-D magnetoelectroelastic media: analytical and numerical solutions,” Int. J. Solids Struct., vol. 48, pp. 2383–2392, 2011.[Crossref], [Web of Science ®] , [Google Scholar]]) in MEE materials, is proposed for two semi-permeable cracks in a MEE medium. It is assumed that the magnetic yielding occurs at the continuation of the cracks due to the prescribed loads. We have model these crack continuations as the zones with cohesive saturation limit magnetic induction. Stroh's formalism and complex variable techniques are used to formulate the problem. Closed form analytical expressions are derived for various fracture parameters. A numerical case study is presented for BaTiO₃ ? CoFe₂O₄ ceramic cracked plate.     

Multiple cracks on the arc-shaped interface in a semi-cylindrical magneto-electro-elastic composite with an orthotropic substrate

The present work investigates the problem of multiple cracks on the arc-shaped interface of a semi-cylindrical magneto-electro-elastic layer bonded onto an orthotropic substrate. Continuously distributed dislocation is used to simulate the anti-plane interfacial cracks. The problem is formulated as a Cauchy singular integral equation by integrating the Green’s function of an interfacial point dislocation. Both the theoretical derivation and numerical computation are verified in special cases. The effects of the interface end, crack space, layer thickness, stiffness ratio and material orthotropy are surveyed, among which the fracture behavior of the interface end deserves special attention in design.     

Free vibration of magneto-electro-elastic nanobeams based on modified couple stress theory in thermal environment

In this paper, the size-dependent free vibration of magneto-electro-elastic (MEE) nanobeams in thermal environment is investigated. Size effects are taken into account using the modified couple stress theory, which is capable of accounting for higher-order electromechanical coupling, and the equations are developed on the basis of Euler–Bernoulli beam model and using von Karman nonlinear strain. The vibration of hinged–hinged nanobeams is investigated by way of example. Effects of various parameters such as temperature, thickness, and length on natural frequencies are demonstrated, and it is indicated that increased length and decreased thickness lead to decreased nanobeam natural frequencies.     

Dynamic fracture behavior of an internal interfacial crack between two dissimilar magneto-electro-elastic plates

In this paper, the anti-plane problem for an interfacial crack between two dissimilar magneto-electro-elastic plates subjected to anti-plane mechanical and in-plane magneto-electrical impact loadings is investigated. Four kinds of crack surface conditions are adopted: magneto-electrically impermeable (Case 1), magnetically impermeable and electrically permeable (Case 2), magnetically permeable and electrically impermeable (Case 3), and magneto-electrically permeable (Case 4). The position of the interfacial crack is arbitrary. The Laplace transform and finite Fourier transform techniques are employed to reduce the mixed boundary-value problem to triple trigonometric series equations in the Laplace transform domain. Then the dislocation density functions and proper replacements of the variables are introduced to reduce the series equations to a standard Cauchy singular integral equation of the first kind. The resulting integral equation together with the corresponding single-valued condition is approximated as a system of linear algebra equations, which can easily be solved. Field intensity factors and energy release rates are determined and discussed. The effects of loading combination parameters on dynamic energy release rate are plotted for Cases 1-3. On the other hand, since the magneto-electrically permeable condition is perhaps more physically reasonable for type III crack, the effect of the crack configuration on the dynamic fracture behavior of the crack tips is studied in detail for Case 4. The results could be useful for the design of multilayered magneto-electro-elastic structures and devices.     

The Boundary Contour Method for Magneto-Electro-Elastic Media with Linear Boundary Elements

This paper presents a development of the boundary contour method (BCM) for magneto-electro-elastic media. Firstly, the divergence-free of the integrand of the magneto- electro-elastic boundary element is proved. Secondly, the boundary contour method formulations are obtained by introducing linear shape functions and Green's functions (Computers & Structures, 82(2004):1599-1607) for magneto-electro-elastic media and using the rigid body motion solution to regularize the BCM and avoid computation of the corner tensor. The BCM is applied to the problem of magneto-electro-elastic media. Finally, numerical solutions for illustrative examples are compared with exact ones and those of the conventional boundary element method (BEM). The numerical results of the BCM coincide very well with the exact solution, and the feasibility and efficiency of the method are verified.     

A beam finite element for magneto-electro-elastic multilayered composite structures

A new finite element based upon an elastic equivalent single-layer model for shear deformable and straight magneto-electro-elastic generally laminated beam is presented. The element has six degrees of freedom represented by the displacement components and the cross-section rotation of its two nodes. The magneto-electric boundary conditions enter the discrete problem as work-equivalent forces and moments while the electro-magnetic state characterization constitutes a post-processing step. The element possesses the superconvergence property for the static problem of beams with uniform cross-section and homogenous material properties along the beam axis direction. Moreover, it is free from the shear locking phenomenon. The developed finite element is validated through comparison with plane-stress results for piezoelectric and magneto-electro-elastic structures. Last, applications for more complex magneto-electro-elastic systems are described.     

The modified couple stress model for bending of normal deformable viscoelastic nanobeams resting on visco-Pasternak foundations

ABSTRACT

The modified couple stress theory (MCST) is utilized to investigate the bending of viscoelastic nanobeams laying on visco-Pasternak elastic foundations based on a new shear and normal deformations beam theory. This model consists of the material length scale coefficient that captures the size impact on small-scale beams. The simply supported beam is made of viscoelastic material, subjected to time harmonic transverse load. The nanobeam is presumed to be laying on double layers of foundations. The first layer is modeled as Kelvin–Voigt viscoelastic model and the second is taken as a shear layer. Based on the proposed beam theory and MCST, the differential motion equations are deduced using Hamilton’s principle. To check the validity of the obtained formulations, the predicted results are compared with those available in the open literature. In addition, the influences of various parameters such as the material length scale parameter, length-to-depth ratio, viscoelastic damping structure, the stiffness and damping coefficients of the viscoelastic substrate, and shear and normal strains on the deflection and stresses are illustrated.