NON-DESTRUCTIVE EVALUATION OF HORIZONTAL CRACK DETECTION IN BEAMS USING TRANSVERSE IMPACT

Numerical and experimental studies for crack detection in beam employing transverse impact are presented. In the numerical study, a beam model of wave propagation is developed to calculate the time history of beam response before, over and after the crack region. It is expected that the resulting wave in the beam will be scattered by the crack and will carry information on the location and geometry of the crack. Experiments using a scanning laser vibrometer on specimens containing simulated crack are then conducted to verify the numerical results. Comparison study between the numerical results and experimental observations are conducted; good correlation between theory and experiment is observed. The beam model of wave propagation and adaptive multilayer perceptron networks (MLP) are then used for inverse identification of crack parameters (i.e., crack location, depth and length) in the beams. Time-domain displacement responses calculated using the present beam model containing predetermined crack parameters are used as training data for the MLP. Once the MLP is trained, the MLP networks are then employed for inverse determination of an unknown crack in a beam using experimental displacement responses measured with a scanning laser vibrometer. Examples show that the procedure performs well for the determination of a wide range of values for the location, depth and length of the crack.     

Complete Solution of Sun Tracking for Heliostat

A general solution of sun tracking for an arbitrarily oriented heliostat towards an arbitrarily located target on the earth is published. With the most general form of solar tracking formulae, it is seen that the used azimuth-elevation, spinning-elevation tracking formulae etc. are the special cases of it. The possibilities of utilizing the general solution and its significance in solar energy engineering are discussed.     

VIBRATIONAL POWER TRANSMISSION FROM A MACHINE TO ITS SUPPORTING CYLINDRICAL SHELL

Power flows from a vibratory machine to its supporting structure are of primary concern in a passive or active isolation system design. Although in the literature there is a fair number of investigations on the power inputs to beams, plates or the like, few attempts have been made for other commonly used structures such as cylindrical shells. In this paper, the vibratory power flows from a rigid-body machine to an elastic cylindrical shell are studied considering the contributions of the non-radial (tangential and axial) displacements and forces. In particular, it is argued that the notion that the motion of a thin shell is primarily radial does not necessarily dictate that the power transmissions are predominantly carried out by the radial displacement. This point is subsequently illuminated through numerical examples. Another issue discussed here is concerned with the effects on the power flows of the cross couplings of the (different) displacement components. It is shown that even though the contributions of the cross couplings are usually insignificant, they may become important if the vibration isolators are substantially hard as compared with the local shell stiffness or impedance. This assertion is particularly useful when an experimental technique is used to measure the vibratory power flows into a supporting structure.     

DYNAMICAL ANALYSIS OF A CYLINDRICAL PIEZOELECTRIC TRANSDUCER

In the present paper, the vibration of a cylindrical piezoelectric transducer induced by applied voltage, which can be used as the stator transducer of a cylindrical micromotor, is studied based on shell theory. The transducer is modelled as a thin elastic cylinder. The properties of the vibration modes of the transducer, such as mode frequencies and amplitude ratios of the mode shapes, are determined following Galerkin method. The response of the transducer under the four electric sources with 90° phase difference is then obtained by the modal summation method. With the results, the performance of the transducer under the electric sources can be estimated. The present work provides a general and precise theoretical modelling on the dynamical movement of the transducer.     

电动力学中衰减机械系统的非线性振荡方法

衰减机械系统的非线性振荡可用来研究长约瑟夫逊结的电动力学方程式，而这方程式等同于弱衰减机械系统的非线性振荡。本文应用的方法是将控制方程线性化及结合谐波平衡法（线性谐波平衡法）而产生色散关系，再把平均法应用在弱非线性的耗散系统中得到非常准确的瞬变反应。在此提出的方法不仅考虑能量耗散，而且利用简单的线性代数等式关系来代替冗长及复杂的分析近似解。     

Explicit expressions for linearly independent spin eigenfunctions

Both the spin-free and the spin-dependent spin eigenfunctions with λ-double occupancy and their reverse relations are produced explicitly. The orthogonal spin coefficients for λ-double occupancy are just some linear sums of 2^λ orthogonal spin coefficients for zero-double occupancy. Their linear independence is shown.