The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear...The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.展开更多
The active-passive hybrid piezoelectric network (APPN) is investigated to reduce the vibration of cantilever beam. Hamilton's principle with the Rayleigh-Ritz method is used to derive the equations of motion of th...The active-passive hybrid piezoelectric network (APPN) is investigated to reduce the vibration of cantilever beam. Hamilton's principle with the Rayleigh-Ritz method is used to derive the equations of motion of the beam with the APPN. Only one piezoelectric actuator is bonded on the cantilever beam, so in the segment of the beam where the piezoelectric actuator is attached, the neutral axis is not the geometric center of the beam. This change on the neutral axis is considered in the process of deriving equations. Selecting RL circuit as passive shunt circuit, open-loop analysis is performed to gain insight into the passive damping features. Velocity feedback control is then employed to analyze the characteristics of the closed-loop system. Numerical results show that the APPN has a significant effect on vibration suppression, especially at narrow frequency bands. On this basis, variable RL circuit is proposed and analyzed for broadband vibration attenuation. Numerical simulations illustrate that this scheme is effective and feasible.展开更多
The classical theory of mass-spring-damper-type dynamical systems on the ordinary flat space R^3 may be generalized to higher-dimensional Riemannian manifolds by reformulating the basic underlying physical principles ...The classical theory of mass-spring-damper-type dynamical systems on the ordinary flat space R^3 may be generalized to higher-dimensional Riemannian manifolds by reformulating the basic underlying physical principles through differential geometry.Nonlinear dynamical systems have been studied in the scientific literature because they arise naturally from the modeling of complex physical structures and because such dynamical systems constitute the basis for several modern applications such as the secure transmission of information.The flows of nonlinear dynamical systems may evolve over time in complex,non-repeating(although deterministic) patterns.The focus of the present paper is on formulating the general equations that describe the dynamics of a point-wise particle sliding on a Riemannian manifold in a coordinate-free manner.The paper shows how the equations particularize in the case of some manifolds of interest in the scientific literature,such as the Stiefel manifold and the manifold of symmetric positive-definite matrices.展开更多
基金supported by the National Natural Science Foundation of China (No.10662003)Educational Commission of Guangxi Province of China (No.200807MS109)
文摘The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.
文摘The active-passive hybrid piezoelectric network (APPN) is investigated to reduce the vibration of cantilever beam. Hamilton's principle with the Rayleigh-Ritz method is used to derive the equations of motion of the beam with the APPN. Only one piezoelectric actuator is bonded on the cantilever beam, so in the segment of the beam where the piezoelectric actuator is attached, the neutral axis is not the geometric center of the beam. This change on the neutral axis is considered in the process of deriving equations. Selecting RL circuit as passive shunt circuit, open-loop analysis is performed to gain insight into the passive damping features. Velocity feedback control is then employed to analyze the characteristics of the closed-loop system. Numerical results show that the APPN has a significant effect on vibration suppression, especially at narrow frequency bands. On this basis, variable RL circuit is proposed and analyzed for broadband vibration attenuation. Numerical simulations illustrate that this scheme is effective and feasible.
基金supported by the Grant 'Ricerca Scientifica di Ateneo(RSA-B)2014'
文摘The classical theory of mass-spring-damper-type dynamical systems on the ordinary flat space R^3 may be generalized to higher-dimensional Riemannian manifolds by reformulating the basic underlying physical principles through differential geometry.Nonlinear dynamical systems have been studied in the scientific literature because they arise naturally from the modeling of complex physical structures and because such dynamical systems constitute the basis for several modern applications such as the secure transmission of information.The flows of nonlinear dynamical systems may evolve over time in complex,non-repeating(although deterministic) patterns.The focus of the present paper is on formulating the general equations that describe the dynamics of a point-wise particle sliding on a Riemannian manifold in a coordinate-free manner.The paper shows how the equations particularize in the case of some manifolds of interest in the scientific literature,such as the Stiefel manifold and the manifold of symmetric positive-definite matrices.
