永磁体同性磁极相吸现象的研究

永磁体的磁极同性相斥异性相吸现象是人所共知的常识,但在一定条件下却能表现出同性磁极相吸现象．本文对这一现象进行了讨论．     

互相垂直方向的非正弦周期信号的合成

通过复变函数和傅里叶级数，分析了2个互相垂直的非正弦周期信号的合成，得出了类似于李萨如曲线的规律.     

Resonance frequencies and mode shapes of elastically restrained,prestressed annular plates attached together by flexible cores

The free vibrations of annular plates attached together by flexible cores are studied analytically. Both axisymmetric and non-axisymmetric vibrations are considered. The plates are elastically constrained against rotation at the inner and outer edges. At the same time, the plates are subjected to initial radial tensions. Detailed analysis is worked out for systems consisting of five through two identical plates with identical boundary conditions and a uniform radial tension. General frequency equations and mode shapes are developed. The first nine eigenvalues are calculated for a plate system having identically constrained inside and outside edges and are tabulated as functions of the initial tension parameter, the elastic edge constraint parameter and the ratio of inner to outer radius. The orthogonality property of the mode function is also discussed.     

带电粒子在正交恒定电磁场中运动状态的分析

由洛伦兹力公式出发,分析带电粒子在相互垂直的恒定电磁场中运动的方程,由此得到一些常见的运动轨迹,并给出带电粒子在电磁场中的一种新的轨迹——长辐旋轮线．     

Resonance frequencies of finite circular cylinders

Reference is made to a 1971 paper by Rumerman and Raynor in which the free vibration of finite circular cylinders was treated by expanding the displacement fields in terms of the pure axial and radial modes of the infinite cylinder.     

Dynamic analysis of very flexible beams

The dynamic analysis of flexible beams with large deformations is difficult and few studies have been performed. In this paper, the vibration analysis of several very flexible beams with large deflections using the finite element approach is studied. The examples were a cantilever beam and rotating flexible robot arms. The results were compared with the results available in the published literature. Several successful checks on the finite element results were performed to ensure the accuracy of the solutions. Due to the geometrical nonlinearity, several static equilibrium shapes can exist for large deflections of a cantilever beam for a given load. Nonlinear dynamic finite element analysis was implemented to investigate the stability of these shapes.     

A successive scattering methodology with application to two cylinders in the Fresnel region of each other

We present an efficient approach to compute the second-order scattering of an electromagnetic wave by two discrete scatterers in proximity to each other. Such a two-body system represents the simplest canonical arrangement to address near-field volume scattering phenomena in microwave remote sensing models of vegetation. Using an analytical wave-based approach, a successive scattering methodology is employed to derive the first interaction term in multiple scattering by two arbitrary scatterers in terms of their transition operators. The general formulation is applied to find the second-order bistatic scattering amplitude for a pair of finite length thin cylinders at arbitrary interaction distances using the exact Green's function. To improve computational efficiency, the solution is then specialized to the Fresnel region. These second-order bistatic scattering amplitude results are in agreement with the exact Green's function model when the scatterers are in the Fresnel region of each other. Additionally, it is demonstrated that using the far field approximation in the Fresnel region can yield significant deviations from the exact results. The Fresnel model, unlike the far field approximation, accurately predicts the scattering amplitude peak values and null locations, and is suited to fast solutions in realistic canopy simulations.     

Vibration and stability of cracked hollow-sectional beams

This paper presents simple tools for the vibration and stability analysis of cracked hollow-sectional beams. It comprises two parts. In the first, the influences of sectional cracks are expressed in terms of flexibility induced. Each crack is assigned with a local flexibility coefficient, which is derived by virtue of theories of fracture mechanics. The flexibility coefficient is a function of the depth of a crack. The general formulae are derived and expressed in integral form. It is then transformed to explicit form through 128-point Gauss quadrature. According to the depth of the crack, the formulae are derived under two scenarios. The first is for shallow cracks, of which the penetration depth is contained within the top solid-sectional region. The second is for deeper penetration, in which the crack goes into the middle hollow-sectional region. The explicit formulae are best-fitted equations generated by the least-squares method. The best-fitted curves are presented. From the curves, the flexibility coefficients can be read out easily, while the explicit expressions facilitate easy implementation in computer analysis. In the second part, the flexibility coefficients are employed in the vibration and stability analysis of hollow-sectional beams. The cracked beam is treated as an assembly of sub-segments linked up by rotational springs. Division of segments are made coincident with the location of cracks or any abrupt change of sectional property. The crack's flexibility coefficient then serves as that of the rotational spring. Application of the Hamilton's principle leads to the governing equations, which are subsequently solved through employment of a simple technique. It is a kind of modified Fourier series, which is able to represent any order of continuity of the vibration/buckling modes. Illustrative numerical examples are included.     

Chaotic dynamics of flexible beams with piezoelectric and temperature phenomena

The Euler–Bernoulli kinematic model as well as the von Kármán geometric non-linearity are used to derive the PDEs governing flexible beam vibrations. The beam is embedded into a 2D temperature field, and its surface is subjected to action of the electric potential. We report how an increase of the exciting load amplitude yields the beam turbulent behavior, and how the temperature changes a scenario from a regular/laminar to spatio-temporal/turbulent dynamics. Both classical Fourier analysis and Morlet wavelets are used to monitor a strong influence of temperature on regular and chaotic beam dynamics.     

Dynamic stability of two rigid rotors connected by a flexible coupling with angular misalignment

The effect of misalignment on the stability of two rotors connected by a flexible mechanical coupling subjected to angular misalignment is examined. The study performed is to understand the effect of angular misalignment on the stability of rotating machinery. The dimensionless stability criteria of the non-linear system of differential equations of two misaligned rigid rotors are derived using Liapunov's direct method. A rigid disk is attached at the middle of each rotor, where the rotor-disk assembly is mounted on two hydrodynamic bearings with four stiffness and four damping coefficients. Sets of dimensionless conditions for sufficient whirl stability of the two misaligned rotors are derived. The stability conditions are presented in graphical form for deeper understanding of the effect of the flexible mechanical coupling stiffness and angular misalignment on rotating machinery stability. The results show that an increase in angular misalignment or mechanical coupling stiffness terms leads to an increase of the model stability region.     

Resonance frequencies of piezoelectric plates surrounded by solid and fluid half-spaces

The design of ultrasound transducers, resonators and other piezoelectric devices usually requires the calculation of the resonance frequencies of piezoelectric plates. Recent studies have shown that the resonance frequencies for plates in vacuum correspond to frequencies where the waveguide group velocity vanishes (zero-group-velocity points). However, those studies are limited to vacuum boundary conditions. The objective of the present study is to analyze the resonance frequencies of layered piezoelectric plates in contact with solid and fluid half-spaces and their relation to the dispersion behavior of the elastic guided wave propagation. Theoretical analysis using partial-wave approach of leaky Lamb waves is performed to study wave propagation in, and resonance behavior of, multilayered plates in contact with solid and fluid half-spaces. A novel observation resulted from this analysis is that, for plates in contact with solid and fluid half-spaces, the resonance frequencies occur at points where the magnitude of the wavenumber reaches a minimum. This frequency is named as a ‘transition frequency’. Such observations are important because they allow an easy identification of resonance frequencies with high amplitude response directly from the dispersion curves. This study will be helpful for the design of piezoelectric components used for resonators and sensors.     

Galerkin methods for natural frequencies of high-speed axially moving beams

In this paper, natural frequencies of planar vibration of axially moving beams are numerically investigated in the supercritical ranges. In the supercritical transport speed regime, the straight equilibrium configuration becomes unstable and bifurcate in multiple equilibrium positions. The governing equations of coupled planar is reduced to two nonlinear models of transverse vibration. For motion about each bifurcated solution, those nonlinear equations are cast in the standard form of continuous gyroscopic systems by introducing a coordinate transform. The natural frequencies are investigated for the beams via the Galerkin method to truncate the corresponding governing equations without nonlinear parts into an infinite set of ordinary-differential equations under the simple support boundary. Numerical results indicate that the nonlinear coefficient has little effects on the natural frequency, and the three models predict qualitatively the same tendencies of the natural frequencies with the changing parameters and the integro-partial-differential equation yields results quantitatively closer to those of the coupled equations.     

On the natural frequencies and modes of beams loaded by sloshing liquids

Equations of motion for a beam carrying a channel of free surface liquid of rectangular cross section have been formulated and solved analytically in closed form for the case where the beam is simply supported and the liquid is connected at both ends to large reservoirs. Various special situations are discussed and effects that govern the interaction are pointed out.