Vibration analysis of a beam with PCLD Patch

An analytical approach for vibration response analysis of a beam with single passive constrained layer damping (PCLD) patch is presented. The governing equation of motion of the beam is firstly derived on the basis of an energy approach and the Lagrange equation. The noval contribution is that a third admissible function is introduced to represent the longitudinal displacements of the constraining layer in the PCLD patch when the assumed-modes method is applied for discretizing the governing equation. In conventional analytical approaches, only two admissible functions are used together with a longitudinal static equilibrium equation of a section of base beam or constraining layer. Comparison of the computational results from the proposed analytical approach and the conventional analytical approach as well as a commercial FEM code reveals that the proposed analytical approach can describe the vibration responses of the damped beam more accurately for commonly used viscoelastic material (VEM) layer in the PCLD patch while the conventional analytical approach, in general, overestimates the damping effects of the PCLD patch. The advantages and disadvantages of the proposed analytical approach and conventional analytical approach are discussed through some case studies.     

Effects of laser intensity on the emission direction of fast electrons in laser-solid interactions

The dependence of emission direction of fast electrons on the laser intensity has been investigated. The experimental results show that, at nonrelativistic laser intensities, the emission of fast electrons is mainly in the polarization plane. With the increase of the laser intensity, fast electrons emit towards the laser propagation direction from laser polarization direction. At relativistic laser intensities, fast electrons move away from the laser polarization plane, closely to the reflection direction of the incident laser beam.     

质子化丙酮分子团簇的结构和振动光谱

用密度泛函B3LYP/ 6 3 1G(d)方法 ,对质子化丙酮分子团簇 (CH3COCH3) nH+ (n =1～ 7)弱相互作用体系进行了全自由度能量梯度优化 ,得到了该系列团簇的稳定结构及其对应的体系能量 .通过对构型的分析得出了质子化丙酮分子团簇 (CH3COCH3) nH+ (n =1～ 7)的生长规律 .计算了中性丙酮分子团簇体系的质子亲合能并总结出其变化趋势 .分析讨论了质子化团簇的红外振动光谱 ,发现质子化团簇的振动光谱普遍较中性环型团簇的振动光谱复杂 ,最强的振动峰来源于质子在溶剂壳中两个氧原子之间的振动 ,而且随着团簇尺寸的增加羰基的伸缩振动峰的数目也随之增多     

Study of a vibrating plate: comparison between experimental (ESPI) and analytical results

Real-time electronic speckle pattern interferometry (ESPI) was used for tuning and visualization of natural frequencies of a trapezoidal plate. The plate was excited to resonant vibration by a sinusoidal acoustical source, which provided a continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plate—corresponding to several resonant frequencies—were registered. From these interferograms, calculations of vibrational amplitudes by means of zero-order Bessel functions were performed in some particular cases. The system was also studied analytically. The analytical approach developed is based on the Rayleigh–Ritz method and on the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated by using the Gram–Schmidt procedure. A high degree of correlation between computational analysis and experimental results was observed.     

从一道运动学题目的求解谈坐标系选取的重要性

通过比较一道典型运动学题目的近似求解方法与精确求解方法，探讨坐标系选取对研究曲线运动的重要性．     

牛顿第二定律实验中的误差分析

本文是通过对加速度的实验值和理论值进行比较和分析，给出误差的合理范围。     

Transfer matrix approach of vibration isolation analysis of periodic composite structure

The transmission properties of elastic waves propagating in a three-dimensional composite structure embedded periodically with spherical inclusions are analyzed by the transfer matrix method in this paper. Firstly, the periodic composite structures are divided into many layers, the transfer matrix of monolayer structure is deduced by the wave equations, and the transfer matrix of the entire structure is obtained in the case of boundary conditions of displacement and stress continuity between layers. Then, the effective impedance of the structure is analyzed to calculate its reflectivity and transmissivity of vibration isolation. Finally, numerical simulation is carried out; the experiment results validate the accuracy and feasibility of the method adopted in the paper and some useful conclusions are obtained. Project (No. 50075029) supported by the National Natural Science Foundation of China.     

Skin-Depth Theory Explaining Anomalous Picosecond-Terawatt Laser Plasma Interaction II

The anomaly of ion emission at laser irradiation of targets measured by Badziak et al. was analyzed on the background of the extensive research in the past. In contrast to the irradiation with lasers of longer than 100 ps pulse duration, a drastic decrease of the maximum ion energies was measured with ps pulses. Very strange was the observation that the number of emitted fast ions was intensity independent. The usual ponderomotive or relativistic self-focusing theory and related processes could not explain the results. Instead a direct interaction within the skin depth of the irradiated target was concluded. This model confirms the plane geometry nonlinear force interaction in the ps range producing fast plasma blocks moving perpendicular off or into the target. The block moving into the target opens a new scheme of laser fusion by modifying the experiments of Norreys et al. The use of relatively low subrelativistic laser intensities for the new scheme of laser fusion is evaluated on the background of the long years studies of nonlinear force driven plasma blocks and earlier interpenetration fusion reactions for providing the parameters for expected fusion gains much higher than the experiment of Norreys et al. for a fusion power scheme.     

Propagation of thickness-twist waves in a multi-sectioned piezoelectric plate of 6 mm crystals

We study thickness-twist vibrations and waves in an unbounded, multi-sectioned piezoelectric plate of crystals with 6 mm symmetry or polarized ceramics. An exact solution from the three-dimensional equations of piezoelectricity is obtained. Basic vibration and wave propagation characteristics are calculated based on the solution. The results are useful in the understanding and design of plate resonators, filters and acoustic wave sensors of ZnO, AlN and polarized ceramics.     

Geometrically qualified ESPI vibration analysis of an engine

This paper presents an application in the automotive industry where a combination of electronic speckle-pattern interferometry and laser doppler velocimetry were used at a critical stage in the design process of an internal combustion engine. Combined deformation and surface relief measurements were used to study the phase and amplitude of deformation of a vibrating engine. The relief data was combined with the interferometer geometry and used to geometrically correct the deformation data, in an effort to improve accuracy. The measurements allowed rapid identification and quantification of design weaknesses, particularly those causing undesirable resonances. This led to a significant reduction in the design time and lowering of costs, when compared with existing design optimisation methods.