A new continuum model is developed to study the influence of surface stress on the behaviors of piezoelectric nanobeams. Different from existing piezoelectric surface models which only consider the surface properties,...A new continuum model is developed to study the influence of surface stress on the behaviors of piezoelectric nanobeams. Different from existing piezoelectric surface models which only consider the surface properties, the proposed model takes surfaceinduced initial fields into consideration. Due to the fact that the surface-induced initial fields are totally different under various boundary conditions, two kinds of beams, the doubly-clamped beam and the cantilever beam, are analyzed. Furthermore, boundary conditions can affect not only the initial state of the piezoelectric nanobeam but also the forms of the governing equations. Based on the Euler-Bernoulli beam theory, the nonlin- ear Green-Lagrangian strain-displacement relationship is applied. In addition, the surface area change is also considered in the proposed model. The governing equations of the doubly-clamped and cantilever beams are derived by the energy variation principle. Com- pared with existing Young-Laplace models, the proposed model for the doubly-clamped beam is similar to the Young-Laplace models. However~ the governing equation of the cantilever beam derived by the proposed model is very different from that derived by the Young-Laplace models. The behaviors of piezoelectric nanobeams predicted by these two models Mso have significant discrepancies, which is owing to the surface-induced initial fields in the bulk beam.展开更多
In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magnetomelectro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, a...In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magnetomelectro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.展开更多
Based on the theory of elastic mechanics, a dynamical model of an encapsulated gas microbubble under ultrasound is presented.The dynamical motion of the microbubble is divided into three states: buckled, elastic, and ...Based on the theory of elastic mechanics, a dynamical model of an encapsulated gas microbubble under ultrasound is presented.The dynamical motion of the microbubble is divided into three states: buckled, elastic, and ruptured. The model describes the compression-only behavior appropriately and derives the transient variation of the resonance frequency of the damped oscillation and the relation between the critical rupture radius and initial outer radius. The normal stress in the tangential direction plays the principal role in the rupture and buckling of the encapsulating shell, resulting in likely rupture for a larger microbubble and resistance to rupture for a thicker-shell microbubble. Comparison of proposed dynamical model with Marmottant's model has been given. The dynamical model can be employed in ultrasound medical diagnostics and therapy of drug incorporation or extravasation through further understanding the influence of the encapsulating shell.展开更多
基金supported by the National Natural Science Foundation of China(Nos.10772106 and 11072138)the Natural Science Foundation of Shanghai(No.15ZR1416100)the Shanghai Leading Academic Discipline Project(No.S30106)
文摘A new continuum model is developed to study the influence of surface stress on the behaviors of piezoelectric nanobeams. Different from existing piezoelectric surface models which only consider the surface properties, the proposed model takes surfaceinduced initial fields into consideration. Due to the fact that the surface-induced initial fields are totally different under various boundary conditions, two kinds of beams, the doubly-clamped beam and the cantilever beam, are analyzed. Furthermore, boundary conditions can affect not only the initial state of the piezoelectric nanobeam but also the forms of the governing equations. Based on the Euler-Bernoulli beam theory, the nonlin- ear Green-Lagrangian strain-displacement relationship is applied. In addition, the surface area change is also considered in the proposed model. The governing equations of the doubly-clamped and cantilever beams are derived by the energy variation principle. Com- pared with existing Young-Laplace models, the proposed model for the doubly-clamped beam is similar to the Young-Laplace models. However~ the governing equation of the cantilever beam derived by the proposed model is very different from that derived by the Young-Laplace models. The behaviors of piezoelectric nanobeams predicted by these two models Mso have significant discrepancies, which is owing to the surface-induced initial fields in the bulk beam.
基金supported by the National Natural Science Foundation of China(Nos.10772106 and11072138)the Shanghai Leading Academic Discipline Project(No.S30106)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China(No.20113108110005)the Natural Science Foundation Project of Shanghai(No.15ZR1416100)
文摘In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magnetomelectro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.
基金supported by the National Natural Science Foundation of China(Grant Nos.11102105,and 11072138)Shanghai Leading Academic Discipline Project(Grant No.S30106)+1 种基金Natural Science Foundation of Shanghai(Grant No.15ZR1416100)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20113108110005)
文摘Based on the theory of elastic mechanics, a dynamical model of an encapsulated gas microbubble under ultrasound is presented.The dynamical motion of the microbubble is divided into three states: buckled, elastic, and ruptured. The model describes the compression-only behavior appropriately and derives the transient variation of the resonance frequency of the damped oscillation and the relation between the critical rupture radius and initial outer radius. The normal stress in the tangential direction plays the principal role in the rupture and buckling of the encapsulating shell, resulting in likely rupture for a larger microbubble and resistance to rupture for a thicker-shell microbubble. Comparison of proposed dynamical model with Marmottant's model has been given. The dynamical model can be employed in ultrasound medical diagnostics and therapy of drug incorporation or extravasation through further understanding the influence of the encapsulating shell.