Stability and local bifurcation of parameter-excited vibration of pipes conveying pulsating fluid under thermal loading

The parametric excited vibration of a pipe under thermal loading may occur because the fluid is often transported heatedly. The effects of thermal loading on the pipe stability and local bifurcations have rarely been studied. The stability and the local bifurcations of the lateral parametric resonance of the pipe induced by the pulsating fluid velocity and the thermal loading are studied. A mathematical model for a simply supported pipe is developed according to the Hamilton principle. Two partial differential equations describing the lateral and longitudinal vibration are obtained. The singularity theory is utilized to anMyze the stability and the bifurcation of the system solutions. The transition sets and the bifurcation diagrams are obtained both in the unfolding parameter space and the physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The frequency response and the relationship between the critical thermal rate and the pulsating fluid velocity are obtained. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and the stability and local bifurcation analyses. It also confirms the existence of the chaos. The presented work can provide valuable information for the design of the pipeline and the controllers to prevent the structural instability.

Sub-Harmonic Resonances of Periodic Parameter Excited Oscillators with Discontinuities

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.

SURFACE EXCITATION PARAMETER IN QUANTITATIVE SURFACE ANALYSIS BY ELECTRON SPECTROSCOPY

The investigation of influence of surface effects on the energy spectra of elect rons is essential for comprehensive understanding of electron-solid interactions as well as quantitative analysis. The accuracy of the analysis depends on the m odels for elastic and inelastic interactions. Electrons impinging on a solid or escaping from it suffer losses in the surface layer. The energy loss spectra the refore have contributions from surface excitations. The role of surface excitati ons is characterized by surface excitation parameter (SEP), which indicates the number of surface plasmons created by an electron crossing the surface. The imag inary part of complex self-energy of an electron is related to the energy loss c ross section. SEP is numerically computed using self-energy formalism and compar ed with the results as described and calculated by different workers.

Calculation of Surface Excitation Parameters by a Monte Carlo Method

Electron inelastic mean free path （IMFP） is an important parameter for surface chemical quantification by surface electron spectroscopy techniques. It can be obtained from analysis of elastic peak electron spectroscopy （EPES） spectra measured on samples and a Monte Carlo simulation method. To obtain IMFP parameters with high accuracy, the surface excitation effect on the measured EPES spectra has to be quantified as a surface excitation parameter （SEP）, which can be calculated via a dielectric response theory. However, such calculated SEP does not include influence of elastic scattering of electrons inside samples during their incidence and emission processes, which should not be neglected simply in determining IMFP by an EPES method. In this work a Monte Carlo simulation method is employed to determine surface excitation parameter by taking account of the elastic scattering effect. The simulated SEPs for different primary energies are found to be in good agreement with the experiments particularly for larger incident or emission angles above 60° where the elastic scattering effect plays a more important role than those in smaller incident or emission angles. Based on these new SEPs, the IMFP measurement by EPES technique can provide more accurate data.

Nonlinear identification of systems with parametric excitation

In this paper, the incremental harmonic balance nonlinear identification (IHBNID) is presented for modelling and parametric identification of nonlinear systems. The effects of harmonic balance nonlinear identification (HBNID) and IHBNID are also studied and compared by using numerical simulation. The effectiveness of the IHBNID is verified through the Mathieu-Duffing equation as an example. With the aid of the new method, the derivation procedure of the incremental harmonic balance method is simplified. The system responses can be represented by the Fourier series expansion in complex form. By keeping several lower-order primary harmonic coefficients to be constant, some of the higher-order harmonic coefficients can be self-adaptive in accordance with the residual errors. The results show that the IHBNID is highly efficient for computation, and excels the HBNID in terms of computation accuracy and noise resistance.