Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering. The researches concentrate on the rigid finite dimensional models which are described...Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering. The researches concentrate on the rigid finite dimensional models which are described by ordinary differential equations (ODEs) .Complete rigidity is the approximation of practical models ; Elasticity should be introduced into mathematical models in the analysis of system dynamics and integration of highly precise controller. A new kind of inverted pendulum, elastic inverted pendulum was proposed, and elasticity was considered. Mathematical model was derived from Hamiltonian principle and variational methods, which were formulated by the coupling of partial differential equations (PDE) and ODE. Because of infinite dimensional, system analysis and control of elastic inverted pendulum is more sophisticated than the rigid one.展开更多
The methods of multiple scales and approximate potential are used to study pendulums with linear damping and variable length. According to the order of the coefficient of friction compared with that of the slowly vary...The methods of multiple scales and approximate potential are used to study pendulums with linear damping and variable length. According to the order of the coefficient of friction compared with that of the slowly varying parameter of length, three different cases are discussed in details. Asymptotic analytical expressions of amplitude, frequency and solution are obtained. The method of approximate potential makes the results effective for large oscillations. A modified multiple scales method is used to get more accurate leading order approximations when the coefficient friction is not small. Comparisons are also made with numerical results to show the efficiency of the present method.展开更多
An analysis of the sensitive mechanism of silicon micromachined gas pendulum tilt sense organ is made.Adopting the method of FEA (finite element analysis),the temperature field at two points heat source,when the two-d...An analysis of the sensitive mechanism of silicon micromachined gas pendulum tilt sense organ is made.Adopting the method of FEA (finite element analysis),the temperature field at two points heat source,when the two-dimensional enclosure was inclined,was obtained by application of the program ANSYS-FLOTRAN CFD and a series of procedures,such as modeling,meshing,loading and equation solving.The numerical results show that in the level state,the temperatures at two points heat source are two points in the same isotherm;however,the temperatures are not the same when the enclosure is inclined.The difference of the temperatures will increase with the augment of the tilt angle,and contrarily it will decrease.That is the characteristic used to sense the transformation of obliquity.展开更多
Based on two- and three-dimensional potential flow theories, the width effects on the hydrodynamics of a bottom-hinged trapezoidal pendulum wave energy converter are discussed. The two-dimensional eigenfunction expans...Based on two- and three-dimensional potential flow theories, the width effects on the hydrodynamics of a bottom-hinged trapezoidal pendulum wave energy converter are discussed. The two-dimensional eigenfunction expansion method is used to obtain the diffraction and radiation solutions when the converter width tends to be infinity. The trapezoidal section of the converter is approximated by a rectangular section for simplification. The nonlinear viscous damping effects are accounted for by including a drag term in the two- and three-dimensional methods. It is found that the three- dimensional results are in good agreement with the two-dimensional results when the converter width becomes larger, especially when the converter width is infinity, which shows that both of the methods are reasonable. Meantime, it is also found that the peak value of the conversion efficiency decreases as the converter width increases in short wave periods while increases when the converter width increases in long wave periods.展开更多
基金This worie was supported by Ningbo Institute of Technology, Zhejiang University (No. 1051157G301).
文摘Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering. The researches concentrate on the rigid finite dimensional models which are described by ordinary differential equations (ODEs) .Complete rigidity is the approximation of practical models ; Elasticity should be introduced into mathematical models in the analysis of system dynamics and integration of highly precise controller. A new kind of inverted pendulum, elastic inverted pendulum was proposed, and elasticity was considered. Mathematical model was derived from Hamiltonian principle and variational methods, which were formulated by the coupling of partial differential equations (PDE) and ODE. Because of infinite dimensional, system analysis and control of elastic inverted pendulum is more sophisticated than the rigid one.
文摘The methods of multiple scales and approximate potential are used to study pendulums with linear damping and variable length. According to the order of the coefficient of friction compared with that of the slowly varying parameter of length, three different cases are discussed in details. Asymptotic analytical expressions of amplitude, frequency and solution are obtained. The method of approximate potential makes the results effective for large oscillations. A modified multiple scales method is used to get more accurate leading order approximations when the coefficient friction is not small. Comparisons are also made with numerical results to show the efficiency of the present method.
文摘An analysis of the sensitive mechanism of silicon micromachined gas pendulum tilt sense organ is made.Adopting the method of FEA (finite element analysis),the temperature field at two points heat source,when the two-dimensional enclosure was inclined,was obtained by application of the program ANSYS-FLOTRAN CFD and a series of procedures,such as modeling,meshing,loading and equation solving.The numerical results show that in the level state,the temperatures at two points heat source are two points in the same isotherm;however,the temperatures are not the same when the enclosure is inclined.The difference of the temperatures will increase with the augment of the tilt angle,and contrarily it will decrease.That is the characteristic used to sense the transformation of obliquity.
基金supported by the Special Fund for Marine Renewable Energy of the Ministry of Finance of China(No.GD2010ZC02)
文摘Based on two- and three-dimensional potential flow theories, the width effects on the hydrodynamics of a bottom-hinged trapezoidal pendulum wave energy converter are discussed. The two-dimensional eigenfunction expansion method is used to obtain the diffraction and radiation solutions when the converter width tends to be infinity. The trapezoidal section of the converter is approximated by a rectangular section for simplification. The nonlinear viscous damping effects are accounted for by including a drag term in the two- and three-dimensional methods. It is found that the three- dimensional results are in good agreement with the two-dimensional results when the converter width becomes larger, especially when the converter width is infinity, which shows that both of the methods are reasonable. Meantime, it is also found that the peak value of the conversion efficiency decreases as the converter width increases in short wave periods while increases when the converter width increases in long wave periods.
