Nonlinear Vibration and Stability Analysis of Functionally Graded Nanobeam Subjected to External Parametric Excitation and Thermal Load

Analysis of vibration stability of simply supported Euler-Bernoulli functionally graded (FG) nanobeam embedded in viscous elastic medium with thermal effect under external parametric excitation is presented in this work. An attempt has been made for the first time is investigating the effect of thermal load on dynamic behavior, amplitude response, instability region and bifurcation points of functionally graded nanobeam. Thermal loads are supposed to be uniform, linear or nonlinear distribution along the thickness direction. Nonlocal continuum theory and the principle of the minimum total potential energy are applied to derive the governing equations. The partial differential equations (PDE) are transported to the ordinary differential equations (ODE) by using the Petrov-Galerkin method and the multiple time scales method are manipulated to solve the motion equation. To study the effect of external parametric excitation and thermal effect, different temperature distributions along the thickness such as uniform, linear, and nonlinear distribution are considered. Moreover, stable and unstable regions and bifurcation points are determined. It is obtained that the thermal load can affect the amplitude response of FG nanobeam. Also, it is observed that the instability of the system is affected by the detuning parameter and the parametric excitation amplitude plays great role in the instability of system. Nanobeams are used in many devices like nanoresonators, nanosensors and nanoswitches. This paper is helpful for designing and manufacturing nanoscale structures specially nanoresonators under different thermal loads.

Effects of Unbalanced Lamination Parameters on the Static Aeroelasticity of a High Aspect Ratio Wing

In this paper, in order to understand the influence of the unbalanced coefficient of composite laminates on the static aeroelasticity of high aspect wings, a series of numerical simulation calculations were carried out, and this work wants to provide some reference for the structural design of aircraft. Considering the influence of geometric nonlinearity, the unidirectional fluid-solid coupling calculation method based on loose coupling is used to control the change of unbalanced coefficient of laminates on the basis of layering angle, layering thickness, and layering region, so as to observe the changes caused to the wings. The relationship between the unbalanced coefficient and the constant thickness layup and the variable thickness layup with 0° and ±45° layup angles was studied, respectively. Then, the layup angle of 90° was added to study the influence of the unbalanced coefficient on the static aeroelasticity of the wing structure with the change of the layup angle and the different choice of layup region. The results show that the deformation is the smallest when the unbalanced coefficient is 0.5, and the deformation trend is evenly distributed along both sides when the unbalanced coefficient is 0.5. When the unbalanced coefficient is changed, adding the 90° layup angle can significantly reduce the overall deformation of the wing and show different sensitivity characteristics to different layup areas. The increase of the unbalanced coefficient makes the chordal displacement gradually change from linear distribution to nonlinear distribution along the spread direction, and the displacement will gradually decrease.

Study on the influence of linear and nonlinear distribution of crosswind on the motion of aircraft wake vortex

Environmental crosswind can greatly affect the development of aircraft wake vortex pair. Previous numerical simulations and experiments have shown that the nonlinear vertical shear of the crosswind velocity can affect the dissipation rate of the aircraft wake vortex, causing each vortex of the vortex pair descent with different velocity magnitude, which will lead to the asymmetrical settlement and tilt of the wake vortex pair. Through numerical simulations, this article finds that uniform crosswind convection and linear vertical shear crosswind convection can also have an effect on the strength of the vortex. This effect is inversely proportional to the cube of the vortex spacing, so it is more intense on small separation vortex pair. In addition, the superposition of crosswind and vortex-induced velocities will lead to the asymmetrical pressure distribution around the vortex pair, which will also cause the tilt of the vortex pair. Furthermore, a new analysis method for wake vortex is proposed, which can be used to predict the vortex trajectory.

Optical Bistability in an Optomechanical System with N-Type Atoms under Nonresonant Conditions

In this paper, the phenomenon of the optical bistability of a cavity field is theoretically investigated in an optomechanical system containing an N-type atomic ensemble. In this hybrid optomechanical system, the atoms are coupled with two controlling light fields besides coupling with the cavity field. Under the nonresonant condition, we analyze the influences of the coupling strength between cavity and atoms, Rabi frequencies of the controlling light field, the detuning between the controlling light field and atoms, and pump field power on the optical bistable behavior of mean intracavity photon number. The nonlinear distribution of the mean intracavity photon number has a potential application in field optical switches and optical bistable devices.

Thermal Buckling of Functionally Graded Sandwich Beams

Thermal buckling of new model of functionally graded (FG) sandwich beams is presented in this study. Material properties and thermal expansion coefficient of FG sheets are assumed to vary continuously along the thickness according to either power-law (P-FGM) or sigmoid function (S-FGM) in terms of the volume fractions of the constituents. Equations of stability are derived based on the generalized higher-order shear deformation beam theory. Thermal loads are supposed to be constant, linear or nonlinear distribution along the thickness direction. An accurate form solution for nonlinear temperature variation through the thickness of S-FGM and P-FGM sandwich beams is presented. Numerical examples are presented to examine the influence of thickness ratio, the inhomogeneity parameter and the thermal loading kinds on the thermal buckling response of various types of FG sandwich beams.

Prediction of Effective Strain Distribution in Two-Pass Drawn Wire

In the multi-pass wire drawing process, the diameter of a wire is decreased by continuously passing it through progressively smaller drawing dies. Although the deformation depends on the process variables, in most wire drawing processes, the wire deformation is concentrated on the surface by its direct contact with the drawing dies, causing a nonlinear distribution of radial direction effective strain from the center to the surface. In this study, a new model for predicting this effective strain in two-pass drawn wire was derived based on the upper bound method, and a finite element analysis and drawing experiment were conducted to validate its effectiveness. The proposed model offers a promising approach to determining and thus controlling the strain in multi-pass drawn wire.

Two-Dimensional Electroosmotic Consolidation Theory of Nonlinear Soil Voltage Distribution Characteristics

Soil voltage is generally assumed to show a linear relationship with distance from the cathode according to the established electroosmotic consolidation equation. However, this assumption is inconsistent with experimental results. To more reasonably reflect the soil consolidation process during electroosmosis treatment, it is necessary to consider the influence of the actual soil voltage distribution trend when establishing the electroosmotic consolidation equation. Electroosmosis results show that soil voltage exhibits nonlinear distribution characteristics against distance from the cathode. The change trend of soil voltage can be well reflected by cubic polynomial fitting. Then, the anodic electrode was taken as the research object, and a two-dimensional horizontal plane model of electroosmosis was established because it represents practical electroosmosis applications more closely than some other models. Based on this established model, the dissipation equation describing the excess pore water pressure and the soil consolidation equation were derived for the electroosmosis treatment process. The derivation process considered both linear and nonlinear soil voltage distributions, wherein the anode was closed and the cathode was open. Finally, the analytical solution was analyzed and validated with model test cases in terms of the excess pore water pressure and average moisture content of the soil. The trend observed in the measured excess pore water pressure was more consistent with that of the theoretical results calculated assuming a nonlinear soil voltage distribution than that obtained using a linear distribution. In addition, the measured values of the average moisture content in the soil were closer to the values calculated under a nonlinear distribution of soil voltage than to those calculated under a linear distribution. These results further show that the established consolidation equation is reasonable when a nonlinear distribution of soil voltage is considered. The proposed consolidation equation can thus improve the application of electroosmotic methods in the future.