Lowell hydraulic experiments, being a selection from experiments on hydraulic motors, on the flow of water over weirs, and in canals of uniform rectangular section and of short length.

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The book of the marine aquarium, or, Practical instructions on the formation, stocking, and management in all seasons, of collections of marine animals and plants /

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Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

Winding patterns for biplanar MRI shim coils with rectangular and circular target-field regions

A method is presented for calculating the winding patterns required to design independent zonal and tesseral biplanar shim coils for magnetic resonance imaging. Streamline, target-field, Fourier integral and Fourier series methods are utilized. For both Fourier-based methods, the desired target field is specified on the surface of the conducting plates. For the Fourier series method it is possible to specify the target field at additional depths interior to the two conducting plates. The conducting plates are confined symmetrically in the xy plane with dimensions 2a x 2b, and are separated by 2d in the z direction. The specification of the target field is symmetric for the Fourier integral method, but can be over some asymmetric portion pa < x < qa and sb < y < tb of the coil dimensions (-1 < p < q < 1 and -1 < s < t < 1) for the Fourier series method. Arbitrary functions are used in the outer sections to ensure continuity of the magnetic field across the entire coil face. For the Fourier series case, the entire field is periodically extended as double half-range sine or cosine series. The resultant Fourier coefficients are substituted into the Fourier series and integral expressions for the internal and external magnetic fields, and stream functions on both the conducting surfaces. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis of field calculations from a ZX shim coil indicates that example designs and theory are well matched.

Investigations into a wideband spatial beamformer employing a rectangular array of planar monopoles

This paper presents a rectangular array antenna with a suitable signal-processing algorithm that is able to steer the beam in azimuth over a wide frequency band. In the previous approach, which was reported in the literature, an inverse discrete Fourier transform technique was proposed for obtaining the signal weighting coefficients. This approach was demonstrated for large arrays in which the physical parameters of the antenna elements were not considered. In this paper, a modified signal-weighting algorithm that works for arbitrary-size arrays is described. Its validity is demonstrated in examples of moderate-size arrays with real antenna elements. It is shown that in some cases, the original beam-forming algorithm fails, while the new algorithm is able to form the desired radiation pattern over a wide frequency band. The performance of the new algorithm is assessed for two cases when the mutual coupling between array elements is both neglected and taken into account.

Fully spatial wide-band beamforming using a rectangular array of planar monopoles

This paper describes a spatial beamformer which by using a rectangular array antenna steers a beam in azimuth over a wide frequency band without frequency filters or tap-delay networks. The weighting coefficients are real numbers which can be realized by attenuators or amplifiers. A prototype including a 4 x 4 array of square planar monopoles and a feeding network composed of attenuators, power divider/combiners and a rat-race hybrid is developed to test the validity of this wide-band beamforming concept. The experimental results prove the validity of this wide-band spatial beamformer for small size arrays.

Wideband beam and steering using a rectangular array of planar monopoles

This article presents the design of a wideband rectangular array of planar monopoles, which is able to steer its beam and nulls over a wide frequency band using real-valued weights. These weights can be realized in practice by amplifiers or attenuators leading to a low cost development of a wideband array antenna with beam and null steering capability. The weights are determined by applying an inverse discrete Fourier transform to an assumed radiation pattern. This wideband beam and null forming concept is verified by full electromagnetic simulations which take into account mutual coupling effects between the array elements.

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.

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.