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One thousand orthopantomograms (OPGs) of patients 20-40 years old were examined. Where impacted third molars were present, the angle and depth of impaction were recorded. Results were analysed using the Pearson chi2 test. 68.6% of OPGs showed at least one impacted third molar. The frequency was three-fold higher in the mandible (1024/1079=90%) than in the maxilla (306/1077=28%), with a significantly higher frequency (P<0.05) in females (56%) than males (44%). The mesioangular impaction was the most common, and 80% of all impacted third molars were partially buried in bone. Of the 429 bilateral occurrence of impacted third molars, 423 were in the mandible. It was concluded that the frequency of impacted third molars in the Singapore Chinese population studied was generally two to three times that reported in races of the Caucasian stock. There was also double the frequency of impacted third molars when compared to a previous study in a Chinese population published in 1932 with females being more frequently affected than males.

SUMMARYA random process can be represented as a series expansion involving a complete set of deterministic functions with corresponding random coe cients. Karhunen-Loeve (K-L) series expansion is based on the eigen-decomposition of the covariance function. Its applicability as a simulation tool for both stationary and non-stationary Gaussian random processes is examined numerically in this paper. The study is based on ÿve common covariance models. The convergence and accuracy of the K-L expansion are investigated by comparing the second-order statistics of the simulated random process with that of the target process. It is shown that the factors a ecting convergence are: (a) ratio of the length of the process over correlation parameter, (b) form of the covariance function, and (c) method of solving for the eigen-solutions of the covariance function (namely, analytical or numerical). Comparison with the established and commonly used spectral representation method is made. K-L expansion has an edge over the spectral method for highly correlated processes. For long stationary processes, the spectral method is generally more e cient as the K-L expansion method requires substantial computational e ort to solve the integral equation. The main advantage of the K-L expansion method is that it can be easily generalized to simulate non-stationary processes with little additional e ort.

This study on the vibration control of smart piezoelectric composite plates investigates the effect of the stretching-bending coupling of the piezoelectric sensor/actuator pairs on the system stability of smart composite plates. Based on first-order shear theory and consistent methodology, a smart isoparametric finite element is formulated and the classical negative velocity feedback control method is adopted for the active vibration control analysis of smart composite plates with bonded or embedded distributed piezoelectric sensors and actuators. It is shown mathematically and demonstrated numerically that generally the coupling effect tends to result in system instability unless the sensor/actuator pairs are collocated or the plate simply supported. The result of this study can be used to aid the placement of piezoelectric sensor/actuator pairs of smart composite plates as well as for robust controller design.

In this paper, a comprehensive methodology for locating and determining the extent of linear cracks in homogeneous plates based on the time-of-flight analysis of Lamb wave propagation is proposed. Piezoelectric sensors and actuators (PZTs) placed on a square grid configuration are used to excite and receive direct and reflected waves. The actuation frequency, spacing of PZTs and length of the signal to analyze are first determined. The grid is used to sweep across the plate to identify the location of a crack, if there is one. Elliptical loci of possible crack positions are constructed based on the flight time of crack-reflected waves estimated using energy spectra from the Hilbert–Huang transform of the sensor signals. A detailed procedure for obtaining the ellipses is described, including the blind zones. After identifying the crack position, the crack orientation is determined by varying the positions of the PZTs and observing the strength of the energy peaks in the Hilbert spectra. This provides the basis for moving the PZTs to estimate the extent of the crack. Experimental results obtained using aluminum plates with through, half-through and concealed cracks showed that the proposed method is feasible and accurate.

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This paper deals with the vibration analysis of a circular plate surface bonded by two piezoelectric layers, based on the Kirchhoff plate model. The form of the electric potential field in the piezoelectric layer is assumed such that the Maxwell static electricity equation is satisfied. The validation of the theoretical model is done by comparing the resonant frequencies of the piezoelectric coupled circular plate obtained by the theoretical model and those obtained by finite-element analysis. The mode shape of the electric potential obtained from free vibration analysis is generally shown to be non-uniform in the radial direction in contrast to what is commonly assumed. The piezoelectric layer is shown to have an effect on the frequencies of the host structure. The proposed model for the analysis of a coupled piezoelectric circular plate provides a means to obtain the distribution of electric potential in the piezoelectric layer. The model provides design reference for piezoelectric material application, such as an ultrasonic motor.

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