The vibrational spectra of rectangular plates

The wire drive pulse-echo system has been extensively used to excite and measure modes of vibration of thin rectangular plates. The frequency spectra of different modes have been investigated as a function of the material elastic moduli and the plate geometry. Most of the work was carried out on isotropic materials. For square plates a wide selection of materials were used. These were made isotropic in their in-plane dimensions where the displacements are taking place. The range of rnaterials enabled the dependence on Poisson's ratio to be investigated. A method of determining the value of Poisson's ratio resulted from this investigation. Certain modes are controlled principally by the shear modulus. Of these the fundamental has two nodal lines across the plate surface. One of them, which has nodes at the corners, (the Lame mode) is uniquely a pure shear mode where the diagonal is a full wave length. One controlled by the Young's modulus has been found. The precise harmonic relationship of the Lame mode series in square and rectangular plates was established. Use of the Rayleigh-Lamb equation has extended the theoretical support. The low order modes were followed over a wide range of sides ratios. Two fundamental types of modes have been recognised; These are the longitudinal modes where the frequency is controlled by the length of the plate only and the 2~f product has an asymptotic value approaching the rod velocity. The other type is the in-plane flexural modes (in effect a flexurally vibrating bar where the -2/w is the geometrical parameter). Where possible the experimental work was related to theory. Other modes controlled by the width dimension of the plate were followed. Anisotropic materials having rolled sheet elastic symmetry were investigated in terms of the appropriate theory. The work has been extended to examine materials from welds in steel plates.

Vibration analysis of submerged rectangular microplates with distributed mass loading

This paper investigates the vibration characteristics of the coupling system of a microscale fluid-loaded rectangular isotropic plate attached to a uniformly distributed mass. Previous literature has, respectively, studied the changes in the plate vibration induced by an acoustic field or by the attached mass loading. This paper investigates the issue of involving these two types of loading simultaneously. Based on Lamb's assumption of the fluid-loaded structure and the Rayleigh–Ritz energy method, this paper presents an analytical solution for the natural frequencies and mode shapes of the coupling system. Numerical results for microplates with different types of boundary conditions have also been obtained and compared with experimental and numerical results from previous literature. The theoretical model and novel analytical solution are of particular interest in the design of microplate-based biosensing devices.

Deflection of jets discharged into a reservoir with a free surface

Deflections of jets discharged into a reservoir with a free surface are investigated numerically. The jets are known to deflect towards either side of the free surface or the bottom, whose direction is not determined uniquely in some experimental conditions, i.e. there are multiple stable states realizable in the same condition. The origin of the multiple stable states is explored by utilizing homotopy transformations in which the top boundary of the reservoir is transformed from a rigid to a free boundary and also the location of the outlet throat is continuously moved from mid-height to the top. We depicted bifurcation diagrams of the flow compiling the data of numerical simulations, from which we identified the origin as an imperfect pitchfork bifurcation, and obtained an insight into the mechanism for the direction to be determined. The parameter region where such multiple stable states are possible is also delimited. © 2011 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

Non-rectangular perfect reconstruction pulse shaping based ICI reduction in CO-OFDM

In this paper, we propose to increase residual carrier frequency offset tolerance based on short perfect reconstruction pulse shaping for coherent optical-orthogonal frequency division multiplexing. The proposed method suppresses the residual carrier frequency offset induced penalty at the receiver, without requiring any additional overhead and exhaustive signal processing. The Q-factor improvement contributed by the proposed method is 1.6 dB and 1.8 dB for time-frequency localization maximization and out-of-band energy minimization pulse shapes, respectively. Finally, the transmission span gain under the influence of residual carrier frequency offset is ̃62% with out-of-band energy minimization pulse shape. © 2014 Optical Society of America.

Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating

In this paper, we present a technique for the shaping of short pulses based on the use of superstructured fiber Bragg gratings (SSFBGs), We apply this technique to demonstrate the generation of 20-ps rectangular pulses by phase and amplitude profiling of 2.5-ps soliton pulses. Numerical calculations validate our experimental findings.

Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM

We propose a new nonlinear optical loop mirror based configuration capable of regenerating regular rectangular quadrature amplitude modulated (QAM) signals. The scheme achieves suppression of noise distortion on both signal quadratures through the realization of two orthogonal regenerative Fourier transformations. Numerical simulations show the performance of the scheme for high constellation complexities (including 256-QAM formats).

Theoretical modeling and experimental validation of fluid-loaded micro rectangular plates

This paper presents a theoretical model on the vibration analysis of micro scale fluid-loaded rectangular isotropic plates, based on the Lamb's assumption of fluid-structure interaction and the Rayleigh-Ritz energy method. An analytical solution for this model is proposed, which can be applied to most cases of boundary conditions. The dynamical experimental data of a series of microfabricated silicon plates are obtained using a base-excitation dynamic testing facility. The natural frequencies and mode shapes in the experimental results are in good agreement with the theoretical simulations for the lower order modes. The presented theoretical and experimental investigations on the vibration characteristics of the micro scale plates are of particular interest in the design of microplate based biosensing devices. Copyright © 2009 by ASME.