In this paper an attempt has been made to find the aperture field distribution in a rectangular waveguide for non-sinusoidal, periodic excitations using Multiple Cavity Modeling Technique. The excitation functions, co...In this paper an attempt has been made to find the aperture field distribution in a rectangular waveguide for non-sinusoidal, periodic excitations using Multiple Cavity Modeling Technique. The excitation functions, considered, are square, trapezoidal and clipped sine wave in nature. In the present analysis these time domain excitation functions have been represented in terms of a truncated Fourier series consisting of the fundamental frequency and its higher harmonics. Within the waveguide the fundamental frequency will give rise to a dominant mode excitation whereas the higher order modes will excite dominant as higher order modes. If the higher harmonics are assumed suppressed then the waveguide is subjected only to a dominant mode excitation. Results for dominant mode reflection coefficient (magnitude), VSWR and complex transmission coefficient have been computed and compared with theoretical data. The excellent agreement between them validates the analysis.展开更多
Consider the KdV equations with the external periodic excitation u t+uu x+u xxx +γu=f(t) , with f(t+T)=f(t). Prove the existence of attractors of resulting discrete semigroup ｛S(τ+mT)｝ m∈N .
The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing...The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.展开更多
The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the ...The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper, which makes it more convenient to calculate the Lyapunov exponent spectrum of the dynamical system periodically excited. Following the definition of the Lyapunov dimension D-L((A)) of the autonomous system, the definition of the Lyapunov dimension D-L of the non-autonomous dynamical system is also given, and the difference between them is the integer 1, namely, D-L((A)) - D-L = 1. For a quasi-periodically excited dynamical system, similar conclusions are formed.展开更多
It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study ...It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study the sub-harmonic resonances of highly nonlinear parameter excited oscillating systems with absolute value terms. The non-smoothness of absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach. The square residuals of the homotopy-approximations of the two examples decrease to 10-6and 10-5,respectively. Thus,the HAM combining with other methods gives hope to solve complex singular oscillating systems analytically.展开更多
The focusing phenomena of SAW excited by an IDT with sinusoidal wavefront and linearly chirped periodic distribution has been explored.Some experimental results are compared with theoretical one and agree with it fair...The focusing phenomena of SAW excited by an IDT with sinusoidal wavefront and linearly chirped periodic distribution has been explored.Some experimental results are compared with theoretical one and agree with it fairly well.展开更多
The line side winding is under the fundamental frequency AC voltage, while the valve side winding contains not only fundamental AC voltage component, but also the DC voltage component, fundamental AC voltage component...The line side winding is under the fundamental frequency AC voltage, while the valve side winding contains not only fundamental AC voltage component, but also the DC voltage component, fundamental AC voltage component, and higher harmonic voltage components when the converter transformer is at its normal operating condition, and the electric field of converter transformer is a non-sinusoidal steady one. To analyze the non-sinusoidal steady electric field containing the DC component, fundamental AC and higher harmonic components, the voltage spectrum of the valve winding in a ±500 kV converter transformer is firstly analyzed, and the non-sinusoidal periodic steady electric field is obtained by the fast discrete Fourier transform. Different resistivity of the oil and oil-immersed paper is adopted to simulate the aging of oil paper insulation at operation, and get the non-sinusoidal steady electric field.展开更多
An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcat...An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcation. A pseudoclosed form complete solution for parametrically excited systems subjected to inhomogeneous generalized forcing is developed, based on the Fourier expansion of periodic matrices and the substitution of matrix exponential terms via Lagrange-Sylvester theorem. A Mathieu type of equation with large amplitude is presented to demonstrate the method of formulating state transition matrix and Floquet multipliers. A two-degree-of-freedom system with irregular time periodic stiffness characterized by spiral bevel gear mesh vibration is presented to find forced response in stability and instability. The obtained results are presented and discussed.展开更多
A new method for the solution of non-sinusoidal periodic states in linear fractionally damped oscillators is presented. The oscillator is forced by a periodic discontinuous waveform and a viscous element is taken into...A new method for the solution of non-sinusoidal periodic states in linear fractionally damped oscillators is presented. The oscillator is forced by a periodic discontinuous waveform and a viscous element is taken into account. The presented method avoids completely the Fourier series calculations of the input and output oscillator waveforms. In the proposed method, the steady-state response of fractionally damped oscillator is formulated directly in the time domain as a superposition of the zero-input and forced responses for each continuous piecewise segments of the forcing waveform, separately. The whole periodic response is reached by taking into account the continuity and periodicity conditions at instants of discontinuities of the excitation and then using the concatenation procedure for all segments. The method can be applied efficiently to discontinuous and continuous non-harmonic excitations equally well. Solutions are exact and there is no need to apply any of the widely up-to-date used frequency approaches. The Fourier series is completely cut out of the oscillator analysis.展开更多
A class of new doubly periodic wave solutions for （2＋1）-dimensional KdV equation are obtained by introducing appropriate Jacobi elliptic functions and Weierstrass elliptic functions in the general solution（contain...A class of new doubly periodic wave solutions for （2＋1）-dimensional KdV equation are obtained by introducing appropriate Jacobi elliptic functions and Weierstrass elliptic functions in the general solution（contains two arbitrary functions） got by means of multilinear variable separation approach for （2＋1）-dimensional KdV equation. Limiting cases are considered and some localized excitations are derived, such as dromion, multidromions, dromion-antidromion, multidromions-antidromions, and so on. Some solutions of the dromion-antidromion and multidromions-antidromions are periodic in one direction but localized in the other direction. The interaction properties of these solutions, which are numerically studied, reveal that some of them are nonelastic and some are completely elastic. Furthermore, these results are visualized.展开更多
文摘In this paper an attempt has been made to find the aperture field distribution in a rectangular waveguide for non-sinusoidal, periodic excitations using Multiple Cavity Modeling Technique. The excitation functions, considered, are square, trapezoidal and clipped sine wave in nature. In the present analysis these time domain excitation functions have been represented in terms of a truncated Fourier series consisting of the fundamental frequency and its higher harmonics. Within the waveguide the fundamental frequency will give rise to a dominant mode excitation whereas the higher order modes will excite dominant as higher order modes. If the higher harmonics are assumed suppressed then the waveguide is subjected only to a dominant mode excitation. Results for dominant mode reflection coefficient (magnitude), VSWR and complex transmission coefficient have been computed and compared with theoretical data. The excellent agreement between them validates the analysis.
文摘Consider the KdV equations with the external periodic excitation u t+uu x+u xxx +γu=f(t) , with f(t+T)=f(t). Prove the existence of attractors of resulting discrete semigroup ｛S(τ+mT)｝ m∈N .
基金Project supported by the National Natural Science Foundation of China (Grant No. 60927005)the 2012 Innovation Foundation of BUAA for PhD Graduatesthe Fundamental Research Funds for the Central Universities,China (Grant No. YWF-10-01-A17)
文摘The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.
基金the National Natural Science Foundation of China(No.19772027)the Science Foundation of Shanghai Municipal Commission of Education(99A01)the Science Foundation of Shanghai Municipal Commission of Science and Technology(No.98JC14032)
文摘The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper, which makes it more convenient to calculate the Lyapunov exponent spectrum of the dynamical system periodically excited. Following the definition of the Lyapunov dimension D-L((A)) of the autonomous system, the definition of the Lyapunov dimension D-L of the non-autonomous dynamical system is also given, and the difference between them is the integer 1, namely, D-L((A)) - D-L = 1. For a quasi-periodically excited dynamical system, similar conclusions are formed.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11272209)the State Key Laboratory of Ocean Engineering(Grant No.GKZD010059)
文摘It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study the sub-harmonic resonances of highly nonlinear parameter excited oscillating systems with absolute value terms. The non-smoothness of absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach. The square residuals of the homotopy-approximations of the two examples decrease to 10-6and 10-5,respectively. Thus,the HAM combining with other methods gives hope to solve complex singular oscillating systems analytically.
文摘The focusing phenomena of SAW excited by an IDT with sinusoidal wavefront and linearly chirped periodic distribution has been explored.Some experimental results are compared with theoretical one and agree with it fairly well.
文摘The line side winding is under the fundamental frequency AC voltage, while the valve side winding contains not only fundamental AC voltage component, but also the DC voltage component, fundamental AC voltage component, and higher harmonic voltage components when the converter transformer is at its normal operating condition, and the electric field of converter transformer is a non-sinusoidal steady one. To analyze the non-sinusoidal steady electric field containing the DC component, fundamental AC and higher harmonic components, the voltage spectrum of the valve winding in a ±500 kV converter transformer is firstly analyzed, and the non-sinusoidal periodic steady electric field is obtained by the fast discrete Fourier transform. Different resistivity of the oil and oil-immersed paper is adopted to simulate the aging of oil paper insulation at operation, and get the non-sinusoidal steady electric field.
基金supported by the National Natural Science Foundation of China (Grant No. 50875009)the Defense Industrial Technology Development Program of China (Grant No. B0620060424)the Aviation Science Foundation of China (Grant No. 20090451009)
文摘An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcation. A pseudoclosed form complete solution for parametrically excited systems subjected to inhomogeneous generalized forcing is developed, based on the Fourier expansion of periodic matrices and the substitution of matrix exponential terms via Lagrange-Sylvester theorem. A Mathieu type of equation with large amplitude is presented to demonstrate the method of formulating state transition matrix and Floquet multipliers. A two-degree-of-freedom system with irregular time periodic stiffness characterized by spiral bevel gear mesh vibration is presented to find forced response in stability and instability. The obtained results are presented and discussed.
文摘A new method for the solution of non-sinusoidal periodic states in linear fractionally damped oscillators is presented. The oscillator is forced by a periodic discontinuous waveform and a viscous element is taken into account. The presented method avoids completely the Fourier series calculations of the input and output oscillator waveforms. In the proposed method, the steady-state response of fractionally damped oscillator is formulated directly in the time domain as a superposition of the zero-input and forced responses for each continuous piecewise segments of the forcing waveform, separately. The whole periodic response is reached by taking into account the continuity and periodicity conditions at instants of discontinuities of the excitation and then using the concatenation procedure for all segments. The method can be applied efficiently to discontinuous and continuous non-harmonic excitations equally well. Solutions are exact and there is no need to apply any of the widely up-to-date used frequency approaches. The Fourier series is completely cut out of the oscillator analysis.
基金Foundation item： Supported by the National Natural Science Foundation of China（10647112, 10871040） Acknowledgement The authors are in debt to thank the helpful discussions with Prof Qin and Dr A P Deng.
文摘A class of new doubly periodic wave solutions for （2＋1）-dimensional KdV equation are obtained by introducing appropriate Jacobi elliptic functions and Weierstrass elliptic functions in the general solution（contains two arbitrary functions） got by means of multilinear variable separation approach for （2＋1）-dimensional KdV equation. Limiting cases are considered and some localized excitations are derived, such as dromion, multidromions, dromion-antidromion, multidromions-antidromions, and so on. Some solutions of the dromion-antidromion and multidromions-antidromions are periodic in one direction but localized in the other direction. The interaction properties of these solutions, which are numerically studied, reveal that some of them are nonelastic and some are completely elastic. Furthermore, these results are visualized.
