The smart magneto-rheological visco-elastomer (MRVE) has a promising application to vibration control.Its dynamic characteristics are described by complex moduli which are applicable to linear dynamics.However,experim...The smart magneto-rheological visco-elastomer (MRVE) has a promising application to vibration control.Its dynamic characteristics are described by complex moduli which are applicable to linear dynamics.However,experimental results show remarkable nonlinear relations between force and deformation for certain large deformations,and the nonlinear dynamic modeling needs to be developed.The present study focuses on the nonlinear dynamic characteristics of MRVE.The MRVE was fabricated and specimens were tested to show nonlinear mechanical properties and dynamic behaviors.The nonlinear effect induced by applied magnetic fields was investigated.A phenomenological model for the dynamic behaviors of MRVE was proposed to describe the nonlinear elasticity,linear damping and hysteretic effect,and the corresponding equivalent linear model in the frequency domain was also given for small deformations.The proposed model is applicable to the dynamics and control analysis of composite structures with MRVE.展开更多
We investigate the nonlinear instability of a smooth steady density profile solution to the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field,inclu...We investigate the nonlinear instability of a smooth steady density profile solution to the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field,including a Rayleigh-Taylor steady-state solution with heavier density with increasing height(referred to the Rayleigh-Taylor instability).We first analyze the equations obtained from linearization around the steady density profile solution.Then we construct solutions to the linearized problem that grow in time in the Sobolev space H k,thus leading to a global instability result for the linearized problem.With the help of the constructed unstable solutions and an existence theorem of classical solutions to the original nonlinear equations,we can then demonstrate the instability of the nonlinear problem in some sense.Our analysis shows that the third component of the velocity already induces the instability,which is different from the previous known results.展开更多
The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian c...The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian coordinates. To deal with the free surface, instead of using the transformation to Lagrangian coordinates, the perturbed equations in Eulerian coordinates are transformed to an integral form and the two-fluid flow is formulated as a single-fluid flow in a fixed domain, thus offering an alternative approach to deal with the jump conditions at the free interface. First, the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with a free interface separating the two fluids, both fluids being in(unstable) equilibrium is analyzed. By a general method of studying a family of modes, the smooth(when restricted to each fluid domain) solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces are constructed, thus leading to a global instability result for the linearized problem.Then, by using these pathological solutions, the global instability for the corresponding nonlinear problem in an appropriate sense is demonstrated.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 11072215)the Fundamental Research Funds for the Central Universitiesthe Hong Kong Polytechnic University through the Development of Niche Areas Programme (Grant No. 1-BB95)
文摘The smart magneto-rheological visco-elastomer (MRVE) has a promising application to vibration control.Its dynamic characteristics are described by complex moduli which are applicable to linear dynamics.However,experimental results show remarkable nonlinear relations between force and deformation for certain large deformations,and the nonlinear dynamic modeling needs to be developed.The present study focuses on the nonlinear dynamic characteristics of MRVE.The MRVE was fabricated and specimens were tested to show nonlinear mechanical properties and dynamic behaviors.The nonlinear effect induced by applied magnetic fields was investigated.A phenomenological model for the dynamic behaviors of MRVE was proposed to describe the nonlinear elasticity,linear damping and hysteretic effect,and the corresponding equivalent linear model in the frequency domain was also given for small deformations.The proposed model is applicable to the dynamics and control analysis of composite structures with MRVE.
基金supported by National Natural Science Foundation of China (Grant Nos. 11101044,11271051,11229101 and 91130020)National Basic Research Program of China (Grant No.2011CB309705)
文摘We investigate the nonlinear instability of a smooth steady density profile solution to the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field,including a Rayleigh-Taylor steady-state solution with heavier density with increasing height(referred to the Rayleigh-Taylor instability).We first analyze the equations obtained from linearization around the steady density profile solution.Then we construct solutions to the linearized problem that grow in time in the Sobolev space H k,thus leading to a global instability result for the linearized problem.With the help of the constructed unstable solutions and an existence theorem of classical solutions to the original nonlinear equations,we can then demonstrate the instability of the nonlinear problem in some sense.Our analysis shows that the third component of the velocity already induces the instability,which is different from the previous known results.
基金supported by the National Natural Science Foundation of China(Nos.11101044,11271051,11229101,11301083,11371065,11471134)the Fujian Provincial Natural Science Foundation of China(No.2014J01011)+1 种基金the National Basic Research Program(No.2011CB309705)the Beijing Center for Mathematics and Information Interdisciplinary Sciences
文摘The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian coordinates. To deal with the free surface, instead of using the transformation to Lagrangian coordinates, the perturbed equations in Eulerian coordinates are transformed to an integral form and the two-fluid flow is formulated as a single-fluid flow in a fixed domain, thus offering an alternative approach to deal with the jump conditions at the free interface. First, the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with a free interface separating the two fluids, both fluids being in(unstable) equilibrium is analyzed. By a general method of studying a family of modes, the smooth(when restricted to each fluid domain) solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces are constructed, thus leading to a global instability result for the linearized problem.Then, by using these pathological solutions, the global instability for the corresponding nonlinear problem in an appropriate sense is demonstrated.
