A new non-classical Kirchhoff plate model is developed using a modified couple stress theory, a surface elasticity theory and a two-parameter elastic foundation model. A variational formulation based ...on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and the complete boundary conditions and provides a unified treatment of the microstructure, surface energy and foundation effects. The new plate model contains a material length scale parameter to account for the microstructure effect, three surface elastic constants to describe the surface energy effect, and two foundation moduli to represent the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the newly developed plate model includes the models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases and recovers the Bernoulli–Euler beam model incorporating the microstructure, surface energy and foundation effects. To illustrate the new model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection of the simply supported plate with or without the elastic foundation predicted by the current model is smaller than that predicted by the classical model. Also, it is observed that the difference in the deflection predicted by the new and classical plate models is very large when the plate thickness is sufficiently small, but it is diminishing with the increase of the plate thickness. For the free vibration problem, it is found that the natural frequency predicted by the new plate model with or without the elastic foundation is higher than that predicted by the classical plate model, and the difference is significant for very thin plates. These predicted trends of the size effect at the micron scale agree with those observed experimentally. In addition, it is shown both analytically and numerically that the presence of the elastic foundation reduces the plate deflection and increases the plate natural frequency, as expected.
A new model is developed for thermally induced redistributions of free carriers in flexoelectric semiconductor beams using a thermoflexotronic theory. This theory, which accounts for flexotronic, ...strain gradient and temperature effects, is first proposed using the theory of flexoelectric semiconductors, thermoelasticity and strain gradient elasticity. The new beam model is then formulated by applying the thermoflexotronic theory and Bernoulli-Euler kinematic relations, which simultaneously incorporates the flexoelectric, temperature and semiconducting effects and provides all the governing equations and boundary conditions, unlike existing models. To illustrate the new model, the concentration perturbation in a simply supported beam induced by temperature changes in the transverse and axial directions respectively is analytically determined. For the former, the deformed shape and redistribution of free carriers in the beam are analytically obtained and graphically displayed, and the charge accumulation formula capturing the thermoflexotronic effect is analytically derived. For the latter, the axial displacement, electric potential and concentration perturbation of free carriers are analytically determined and graphically illustrated. It reveals that the distribution of the electric potential and redistribution of free carriers can be tailored by controlling the mode and amplitude of the prescribed temperature change.
•A new model for thermally induced redistributions of free carriers in flexoelectric semiconductor beams is developed using the Bernoulli-Euler kinematic relations and a thermoflexotronic theory.•The new beam model simultaneously incorporates the flexoelectric, temperature and semiconducting effects and provides all the governing equations and boundary conditions, unlike existing models.•The concentration perturbation in a simply supported beam induced by temperature changes in the transverse and axial directions respectively is analytically determined.•The distribution of the electric potential and redistribution of free carriers can be tailored by controlling the mode and amplitude of the prescribed temperature change.
A new Bernoulli–Euler beam model is developed using a modified couple stress theory and a surface elasticity theory. A variational formulation based on the principle of minimum total potential energy ...is employed, which leads to the simultaneous determination of the equilibrium equation and complete boundary conditions for a Bernoulli–Euler beam. The new model contains a material length scale parameter accounting for the microstructure effect in the bulk of the beam and three surface elasticity constants describing the mechanical behavior of the beam surface layer. The inclusion of these additional material constants enables the new model to capture the microstructure- and surface energy-dependent size effect. In addition, Poisson’s effect is incorporated in the current model, unlike existing beam models. The new beam model includes the models considering only the microstructure dependence or the surface energy effect as special cases. The current model reduces to the classical Bernoulli–Euler beam model when the microstructure dependence, surface energy, and Poisson’s effect are all suppressed. To demonstrate the new model, a cantilever beam problem is solved by directly applying the general formulas derived. Numerical results reveal that the beam deflection predicted by the new model is smaller than that by the classical beam model. Also, it is found that the difference between the deflections predicted by the two models is very significant when the beam thickness is small but is diminishing with the increase of the beam thickness.
A non-classical third-order shear deformation plate model is developed using a modified couple stress theory and Hamilton’s principle. The equations of motion and boundary conditions are ...simultaneously obtained through a variational formulation. This newly developed plate model contains one material length scale parameter and can capture both the size effect and the quadratic variation of shear strains and shear stresses along the plate thickness direction. It is shown that the new third-order shear deformation plate model recovers the non-classical Reddy-Levinson beam model and Mindlin plate model based on the modified couple stress theory as special cases. Also, the current non-classical plate model reduces to the classical elasticity-based third-order shear deformation plate model when the material length scale parameter is taken to be zero. To illustrate the new model, analytical solutions for the static bending and free vibration problems of a simply supported plate are obtained by directly applying the general forms of the governing equations and boundary conditions of the model. The numerical results show that the deflection and rotations predicted by the new plate model are smaller than those predicted by its classical elasticity-based counterpart, while the natural frequency of the plate predicted by the former is higher than that by the latter. It is further seen that the differences between the two sets of predicted values are significant when the plate thickness is small, but they are diminishing with increasing plate thickness.
A new model for determining band gaps for elastic wave propagation in three-dimensional (3-D) periodic two-phase composites is developed using a modified couple stress theory that accounts for ...microstructure effects. Three types of composites, each containing a different kind of inclusion – spherical, cubic, and cube with square-rod connections, are considered, with the third one representing a co-continuous composite. The plane wave expansion method and the Bloch theorem for periodic media are employed to solve the elastic wave equations in each case, which are converted to an eigenvalue problem. The band gaps are determined from solving the characteristic equation and plotting the resulting eigen-frequencies. The new non-classical model reduces to the classical elasticity-based model when microstructure effects are suppressed. To quantitatively illustrate the newly developed model, a parametric study is conducted for 3-D periodic composites with the three kinds of inclusions. The numerical results reveal that the first band gap values predicted by the current non-classical model are smaller than those predicted by the classical elasticity-based model, and the difference between the two sets of band gap values is large when the unit cell size is very small. Also, it is seen that the volume fraction and inclusion shape have significant effects on the band gap size. These indicate that large band gaps can be attained by tailoring microstructural parameters including the unit cell size, volume fraction and inclusion shape.
Aim: This study was to determine the roles of inflammatory cytokines in paraventricular nucleus (PVN) in modulating sympathetic activity, blood pressure and cardiac sympathetic afferent reflex ...(CSAR).
Methods: Renal sympathetic nerve activity (RSNA) and mean arterial pressure (MAP) were recorded in anaesthetized rats with bilateral sinoaortic denervation and vagotomy. The CSAR was evaluated by the RSNA response to epicardial application of bradykinin (BK). The levels of inflammatory cytokines were measured with ELISA.
Results: The PVN microinjection of pro‐inflammatory cytokines (PIC), tumour necrosis factor (TNF)‐α or interleukin (IL)‐1β, increased the baseline MAP and RSNA, and enhanced the CSAR. Anti‐inflammatory cytokines (AIC), IL‐4 or IL‐13, in the PVN only increased the baseline MAP. In the rats pretreated with TNF‐α or IL‐1β but not in the rats pretreated with IL‐4 or IL‐13, sub‐response dose of angiotensin II caused significant increases in the MAP and RSNA and enhancement in the CSAR. AT1 receptor antagonist losartan in the PVN attenuated the effects of angiotensin II, TNF‐α and IL‐1β, but not the effects of IL‐4 and IL‐13. Stimulation of cardiac sympathetic afferents with epicardial application of BK increased the levels of TNF‐α, IL‐1β but not IL‐4 in the PVN.
Conclusion: TNF‐α or IL‐1β in the PVN increases blood pressure and sympathetic outflow and enhances the CSAR, which is partially dependent on the AT1 receptors, while IL‐4 or IL‐13 in the PVN only increases blood pressure. There is a synergetic effect of Ang II with TNF‐α or IL‐1β on blood pressure, sympathetic activity and CSAR.
This article explores the wormhole geometry in the background of symmetric teleparallel gravity or f(Q)$f(\mathcal {Q})$ gravity, where Q$\mathcal {Q}$ is the non‐metricity term, and definite subject ...for the gravitational interaction. All the energy conditions are investigated for two different generic shape functions. The presence of exotic matter is confirmed due to the violation of the energy conditions. The epicyclic orbits of test particles around wormhole throat for the considered models are discussed. Twin peak Quasi‐periodic oscillations are calculated and presented with the required behavior. We also explore the physical characteristics and stable configuration of thin‐shell developed from the matching of inner obtained solution of wormhole geometry and outer black hole solution in f(Q)$f(\mathcal {Q})$ gravity. The stability of shell is discussed by using the speed of sound parameter for both choices of shape functions, i.e., β1(D)$\beta _1(D)$and β2(D)$\beta _2(D)$. It is found that the position of event horizon does not change for different values of the physical parameter for the choice of β1(D)$\beta _1(D)$ while it changes for β2(D)$\beta _2(D)$. We explore the proper length, shell energy and entropy of the developed structure for different values of physical parameters.
This article explores the wormhole geometry in the background of symmetric teleparallel gravity or f (Q) gravity, where Q is the non‐metricity term, and definite subject for the gravitational interaction. All the energy conditions are investigated for two different generic shape functions. The presence of exotic matter is confirmed due to the violation of the energy conditions. The epicyclic orbits of test particles around wormhole throat for the considered models are discussed. Twin peak Quasi‐periodic oscillations are calculated and presented with the required behavior. The authors also explore the physical characteristics and stable configuration of thin‐shell developed from the matching of inner obtained solution of wormhole geometry and outer black hole solution in f (Q) gravity. The stability of shell is discussed by using the speed of sound parameter for both choices of shape functions, i.e., β1(D) and β2(D)It is found that the position of event horizon does not change for different values of the physical parameter for the choice of β1(D) while it changes for β2(D). The authors explore the proper length, shell energy and entropy of the developed structure for different values of physical parameters.
A new model for thermal buckling of an anisotropic elastic composite beam consisting of a dielectric core and two thin semiconductor surface layers is developed. The field equations and boundary ...conditions for the beam are obtained by using the piezoelectricity, flexoelectricity, strain gradient elasticity and semiconductor theories and the kinematic relations for a Timoshenko beam. The current model includes piezoelectric, flexoelectric and semiconducting effects simultaneously, unlike existing models. A variational formulation based on the principle of minimum potential energy is employed for the dielectric core, where the contribution of the two thin semiconductor surface layers is incorporated through the work done by the free charge density. Two simplified models for piezoelectric and flexoelectric composite beams incorporating the semiconducting effect are obtained as two special cases of the new model for the dielectric composite beam. Thermal buckling of a simply supported composite beam with a piezoelectric or flexoelectric core and two thin semiconductor surface layers is analytically studied by directly applying the two simplified models, leading to the determination of the critical buckling temperature and concentration perturbation of free carriers in the composite beam. Numerical results show that the presence of the piezoelectric or flexoelectric effect results in an increased critical buckling temperature, while the inclusion of the semiconducting effect leads to a reduced value in both cases. In addition, it is seen that the redistributions of free carriers in the piezoelectric composite beam are uniform, whereas those in the flexoelectric composite beam are non-uniform along the beam thickness direction.
A new non-classical Kirchhoff rod model is developed using the modified couple stress theory, which contains one material length scale parameter and can account for microstructure-dependent size ...effects. The governing equations and boundary conditions are determined simultaneously by a variational formulation based on the principle of minimum total potential energy. The newly developed model recovers its classical elasticity-based counterpart as a special case when the microstructure effect is not considered. To illustrate the new non-classical Kirchhoff rod model, two sample problems are analytically solved by directly applying the general formulas derived. One problem is the equilibrium analysis of a helical rod of circular cross section deformed from a straight rod, and the other is the buckling of a straight rod of circular cross section induced by an axial compressive force. In the former, the rod undergoes a twisting-dominated deformation, while in the latter the rod deformation is bending dominated. Two closed-form expressions are obtained for the force and couple needed in deforming the helical rod, and an analytical formula is derived for the critical buckling load required to perturb the axially compressed straight rod, with the microstructure effect incorporated in each case. These formulas reduce to those based on classical elasticity when the microstructure effect is suppressed. For the helical rod problem, the numerical results show that the couple predicted by the current non-classical rod model is significantly larger than that predicted by the classical model when the rod radius is very small, but the difference is diminishing with the increase in the rod radius. For the buckling problem, it is found that the critical buckling load based on the new non-classical Kirchhoff rod model is always higher than that given by the classical elasticity-based model, with the difference being significant for a very thin rod.
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