Model reduction for parametric instability analysis in shells conveying fluid

Flexible pipes conveying fluid are often subjected to parametric excitation due to time-periodic flow fluctuations. Such systems are known to exhibit complex instability phenomena such as divergence and coupled-mode flutter. Investigators have typically used weighted residual techniques, to reduce the continuous system model into a discrete model, based on approximation functions with global support, for carrying out stability analysis. While this approach is useful for straight pipes, modelling based on FEM is needed for the study of complicated piping systems, where the approximation functions used are local in support. However, the size of the problem is now significantly larger and for computationally efficient stability analysis, model reduction is necessary. In this paper, model reduction techniques are developed for the analysis of parametric instability in flexible pipes conveying fluids under a mean pressure. It is shown that only those linear transformations which leave the original eigenvalues of the linear time invariant system unchanged are admissible. The numerical technique developed by Friedmann and Hammond (Int. J. Numer. Methods Eng. Efficient 11 (1997) 1117) is used for the stability analysis. One of the key research issues is to establish criteria for deciding the basis vectors essential for an accurate stability analysis. This paper examines this issue in detail and proposes new guidelines for their selection.     

The vibration and stability of orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure

In this paper, the vibration and stability of orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure are studied. At first, the basic relations have been obtained for orthotropic truncated conical shells, Young's moduli and density of which vary continuously in the thickness direction. By applying the Galerkin method to the foregoing equations, the buckling pressure and frequency parameter of truncated conical shells are obtained from these equations. Finally, carrying out some computations, the effects of the variations of conical shell characteristics, the effects of the non-homogeneity and the orthotropy on the critical dimensionless hydrostatic pressure and lowest dimensionless frequency parameter have been studied, when Young's moduli and density vary together and separately. The results are presented in tables, figures and compared with other works.     

Combinational parametric resonance under imperfectly periodic excitation

Conditions for mean square stability of a two-degree-of-freedom system have been obtained for the case of sum combinational resonance due to sinusoidal parametric excitation with constant amplitude and white-noise random temporal variations in the instantaneous frequency. Analysis is based on the asymptotic Krylov–Bogoliubov averaging method. The resulting set of ten deterministic differential equations for second-order moments of the four new state variables (inphase and quadrature modal responses) was solved analytically for its neutral stability boundary. The imperfections in periodicity may lead to either stabilization or destabilization of the system and the corresponding conditions have been clearly established from the solution obtained. Furthermore, conditions for almost sure stability have been obtained for a special symmetric case of identical modal damping factors and identical modal excitation amplitudes.     

Self-action of electromagnetic wave in plasma under parametric instability

The self-action of a strong electromagnetic wave in an inhomogeneous plasma is considered near the plasma resonance.     

Axial and conical parametric emissions from potassium atoms under two-photon fs excitation

We report on the emissions near the 5P_3/2,1/2–4S_1/2 and 4P_3/2,1/2–4S_1/2 transitions of potassium atoms which are excited by a fs laser beam. The field at the transition 5P_3/2,1/2–4S_1/2 is mainly the result of a parametric process with an axial profile when the excitation frequency is tuned above resonance and a conical one below resonance. Similar but not identical far-field patterns were also observed for the 4P_3/2,1/2–4S_1/2 emission. No amplified spontaneous emission was observed for the fs case, in contrast to the ns excitation for the 4P_3/2,1/2–4S_1/2 transition.     

Lagrangian approach for analysis of radiation pressure induced parametric instability in micro-resonators

We introduce a new scheme for determining radiation pressure coupling to microresonator devices. It is shown that for the input pump powers there exists a threshold value for instability behavior. Radiation pressure can couple mechanical modes of a cavity to it's optical modes, leading to parametric oscillation instability. Here we present an approximate analysis of such nonlinear effect with Hamilton's least action principle. Our Lagrangian includes no interaction term, but interaction between optical and mechanical modes has been taken into account through integration limit.     

Axisymmetric vibrations of laminated conical shells of variable thickness

Axisymmetric free vibrations of laminated conical shells with a linear thickness variation in the meridional direction are studied. A Rayleigh-Ritz procedure is adopted for the analysis. A general stacking arrangement with orthotropic layers is considered. Classical thin shell theory is used. Assumed displacement functions are algebraic polynomials in transformed meridional co-ordinate. Parametric studies are presented to illustrate the effects of geometric, material and coupling parameters and of the boundary conditions on the frequencies and mode shapes.     

Non-linear interaction of bending deformations of free-oscillating cylindrical shells

A method is proposed for the calculation of free oscillations of circular cylindrical shells taking into account the non-linear interaction of their bending deformations. Cases are studied in which a shell is characterized by eigenfrequencies, which are in close proximity or multiple frequencies. Based on analysis of the averaged equations, a number of solutions have been constructed. These solutions are used to investigate the particular qualities of the energy exchange and interaction of the modes of the shell. Phase patterns corresponding to interaction of conjugate forms (2-D model) and forms of various wave-forming parameters (4-D model) are studied. The impact of initial conditions on deformation shapes of free multi-mode-oscillating shells is considered.     

Asymptotic solutions for Mathieu instability under random parametric excitation and nonlinear damping

A theoretical analysis is presented of the response of a lightly and nonlinearly damped mass-spring system in which the spring constant contains a small randomly fluctuating component. Damping is represented by a combination of linear and nonlinear power-law damping. System response to some initial disturbance at time zero is described by a sinusoidal wave whose amplitude and phase vary slowly and randomly with time. Leading order formulations for the equations of amplitude and phase are obtained through the application of methods of stochastic averaging of Stratonovich. The equations of amplitude and phase are given in two versions: Fokker-Planck equations for transient probability and Langevin equations for response in the time-domain. Solutions in closed-form of these equations are derived by methods of mathematical and theoretical physics involving higher transcendental functions. They are used to study the behavior of system response for ever increasing time applying asymptotic methods of analysis such as the method of steepest descent or saddle-point method. It is found that system behavior depends on the power density of the parametric excitation at twice the natural frequency and on the magnitude and form of the damping. Depending on these parameters different types of system behavior are found to be possible: response which decays exponentially to zero, response which leads to a stationary state of random behavior, and response which can either grow unboundedly or which approaches zero in a finite time.     

Structural instability of PbSe/SnSe superlattices under pressure

Abstract

PbSe/SnSe superlattice, phase transition, high pressure, SR x-ray diffraction)

Synchrotron x-ray diffraction experiments have revealed successive phase transitions in epitaxially-grown PbSe/SnSe superlattices. The transition pressures from the low-pressre cubic B1- to the high-pressure orthorhombic B16-type structures are observed to vary systematically depending upon thickness of the PbSe layer. For example, a [PbSe(36A)/SnSe(12A)]₁₉, with the B1 structure in both layers stabilized in its asgrown state, undergoes the [B1/B1]-to-[B1/B16] and [B1/B16]-to-[B16/B16] structural transitions at 1.9 and 3.8GPa, respectively. This result is in contrast to their bulk data that the B1-to-B16 transition takes place at 5.3GPa in PbSe while the B16 phase is stable in SnSe at atmospheric pressure.     

无阀微泵腔内气泡对周期驱动压力的影响

气泡的存在使无阀微泵的工作性能和使用寿命大大降低, 甚至无法正常工作. 为了合理地预测无阀微泵腔内气泡对周期驱动压力的影响, 给出了用来描述收缩管/扩张管型无阀压电微泵的数学模型, 包括泵腔体积变化、连续性方程、流体有效体积弹性模量以及锥管阻力系数的计算. 同时, 分析了腔内不同气泡体积对无阀微泵周期驱动压力的影响, 并对两个气泡进入无阀微泵泵腔时压力脉动过程进行了仿真和试验研究. 通过仿真结果与试验数据的比较表明, 所提出的存在气泡时无阀微泵数学模型及仿真方法是合理的. 关键词： 无阀微泵 气泡 压力脉动