Encouraging problem-solving disposition in a Singapore classroom

In this article, we share our learning experience as a Lesson Study team. The Research Lesson was on Figural Patterns taught in Year 7. In addition to helping students learn the skills of the topic, we wanted them to develop a problem-solving disposition. The management of these two objectives was a challenge to us. From the lesson observation and the students’ classwork, it turned out better than we expected.     

Generalized eigenproblem of hybrid matrix for Floquet wave propagation in one-dimensional phononic crystals with solids and fluids

A method based on the solution to a generalized eigenproblem of hybrid matrix is presented for stable analysis of Floquet wave propagation in one-dimensional phononic crystals with solids and fluids. The method overcomes the numerical instability in the standard eigenproblem of transfer matrix, thus enabling Floquet waves to be determined reliably. The recursion relations of hybrid matrix for periodic multilayered structure of various solid and/or fluid phases are formulated. Dispersion relation and omnidirectional reflection for one-dimensional phononic crystals with solids and fluids are discussed. The frequency-thickness range of phononic bandgap is determined conveniently based on the Floquet wavenumbers.     

Generalized three-dimensional windowed Fourier transform for fringe analysis

A 3D windowed Fourier transform is proposed for fringe sequence analysis, which processes the joint spatial and temporal information of the fringe sequence simultaneously. The 2D windowed Fourier transform in the spatial domain and the 1D windowed Fourier transform in the temporal domain are two special cases of the proposed method. The principles of windowed Fourier filtering and windowed Fourier ridges are developed. Experimental verification shows encouraging results despite a longer processing time.     

Optical time-domain reflectometry for distributed sensing of the structural strain and deformation

A unique structure of microbend optical fiber sensor (MOFS) for measuring tensile and compressive strain is described in this paper. The average measuring sensitivity for tensile strain is 35μ using 3 MOFS arrays. The repeatability and stability of MFOS are better than 18μ. The loss sensitivity of single-mode (SM) fiber and multi-mode (MM) fiber used in MOFS, as well as the relationship between the pulse width of diode laser and loss sensitivity are also studied in this paper. From these studies, some conclusions have been obtained. They are (1) the loss sensitivity and repeatability of SM fiber are better when compared to MM fiber in MOFS, and (2) the variation of pulse width of laser would only influent the signal-to-noise ratio and dynamic range, but has no contribution to loss sensitivity. Experimental results also show that loss of SM fiber highly depends on the wavelength of laser, but MM fiber has no such property. The loss of SM fiber between the wavelength of 1550 and 1310 nm is about the ratio of 6.5. Therefore, the experiments reported in this paper used a wavelength of 1310 nm to measure tensile strain and 1550 nm to measure compressive strain based on the above property of SM fiber, without changing the configuration of MOFS.