The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first tr...The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first transformed into the time independent one. And then exact wave function is found in terms of solutions of the classical equation of motion of the oscillator.展开更多
The dynamics of an axially accelerating beam subjected to axial flow is studied.Based on the Floquet theory and the Runge-Kutta algorithm,the stability and nonlinear vibration of the beam are analyzed by considering t...The dynamics of an axially accelerating beam subjected to axial flow is studied.Based on the Floquet theory and the Runge-Kutta algorithm,the stability and nonlinear vibration of the beam are analyzed by considering the effects of several system parameters such as the mean speed,flow velocity,axial added mass coefficient,mass ratio,slenderness ratio,tension and viscosity coefficient.Numerical results show that when the pulsation frequency of the axial speed is close to the sum of first-and second-mode frequencies or twice the lowest two natural frequencies,instability with combination or subharmonic resonance would occur.It is found that the beam can undergo the periodic-1 motion under subharmonic resonance and the quasi-periodic motion under combination resonance.With the change of system parameters,the stability boundary may be widened,narrowed or drifted.In addition,the vibration amplitude of the beam under resonance can also be affected by changing the values of system parameters.展开更多
Long-period ground motion has become an important consideration because of the increasing number of large and long-period structures.Therefore,a thorough investigation on the formation and characteristics of longperio...Long-period ground motion has become an important consideration because of the increasing number of large and long-period structures.Therefore,a thorough investigation on the formation and characteristics of longperiod ground motion is desirable for engineering applications.In this work,an analytical study is performed to examine the effect of several parameters and the combining mode for equivalent harmonic components on the dynamic response of systems.The results of the work show that the harmonic components in equivalent ground motion are evidently influenced by the intensity rise time,duration,phase and combining mode.Moreover,the long-period ground motions are simplified and simulated by separate harmonic components through proper combination.The findings of the work are believed to be useful in the selection of input ground motion in structural seismic analysis.展开更多
The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As...The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.展开更多
Based on a theoretical motion equation of encapsulated microbubbles within an ultrasound field, the subharmonic characterizations of microbubbles are optimally designed and analyzed by a computer aided design system. ...Based on a theoretical motion equation of encapsulated microbubbles within an ultrasound field, the subharmonic characterizations of microbubbles are optimally designed and analyzed by a computer aided design system. The effects of size, shell elasticity and acoustic pressure on subharmonic response of microbubbles are calculated theoretically to obtain the optimal parameters for nondestructive subharmonic imaging. In addition, microbubbles with different shell elasticity are prepared, and their subharmonic responses are measured in vitro. The results of theoretical calculation and acoustic measurement show that good subharmonic enhancement can be obtained by using the encapsulated microbubbles with the mean size of 3 μm, which were prepared from the surfactant solution with the proper ratio of shell material. It is also shown that the best operating acoustic pressure is 200 to 400 kPa for nondestructive subharmonic imaging based on such kind of microbubbles.展开更多
基金National Natural Science Foundation (K19972 0 11)
文摘The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first transformed into the time independent one. And then exact wave function is found in terms of solutions of the classical equation of motion of the oscillator.
基金supported by the National Natural Science Foundation of China(Nos.11972167,12072119,12102139).
文摘The dynamics of an axially accelerating beam subjected to axial flow is studied.Based on the Floquet theory and the Runge-Kutta algorithm,the stability and nonlinear vibration of the beam are analyzed by considering the effects of several system parameters such as the mean speed,flow velocity,axial added mass coefficient,mass ratio,slenderness ratio,tension and viscosity coefficient.Numerical results show that when the pulsation frequency of the axial speed is close to the sum of first-and second-mode frequencies or twice the lowest two natural frequencies,instability with combination or subharmonic resonance would occur.It is found that the beam can undergo the periodic-1 motion under subharmonic resonance and the quasi-periodic motion under combination resonance.With the change of system parameters,the stability boundary may be widened,narrowed or drifted.In addition,the vibration amplitude of the beam under resonance can also be affected by changing the values of system parameters.
基金Supported by Major Research Plan of National Natural Science Foundation of China(No.91215301)National Natural Science Foundation of China(No.51238012,No.51178152,No.51008208)the Special Fund for Earthquake Scientific Research in the Public Interest(No.201208013)
文摘Long-period ground motion has become an important consideration because of the increasing number of large and long-period structures.Therefore,a thorough investigation on the formation and characteristics of longperiod ground motion is desirable for engineering applications.In this work,an analytical study is performed to examine the effect of several parameters and the combining mode for equivalent harmonic components on the dynamic response of systems.The results of the work show that the harmonic components in equivalent ground motion are evidently influenced by the intensity rise time,duration,phase and combining mode.Moreover,the long-period ground motions are simplified and simulated by separate harmonic components through proper combination.The findings of the work are believed to be useful in the selection of input ground motion in structural seismic analysis.
基金Supported by the Program for New Century Excellent Talents in University under Grant No.NCET-10-0702the National Basic Research Program of China(973 Program)under Grant No.2013CB328904the Ph.D.Programs Foundation of Ministry of Education of China under Grant No.20110184110016
文摘The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.
基金This work was supported by the National Natural Science Foundation of China (30270404) High Technology Research and Development Program of China (863 Program, 2004AA218022).
文摘Based on a theoretical motion equation of encapsulated microbubbles within an ultrasound field, the subharmonic characterizations of microbubbles are optimally designed and analyzed by a computer aided design system. The effects of size, shell elasticity and acoustic pressure on subharmonic response of microbubbles are calculated theoretically to obtain the optimal parameters for nondestructive subharmonic imaging. In addition, microbubbles with different shell elasticity are prepared, and their subharmonic responses are measured in vitro. The results of theoretical calculation and acoustic measurement show that good subharmonic enhancement can be obtained by using the encapsulated microbubbles with the mean size of 3 μm, which were prepared from the surfactant solution with the proper ratio of shell material. It is also shown that the best operating acoustic pressure is 200 to 400 kPa for nondestructive subharmonic imaging based on such kind of microbubbles.
