Natural frequencies and modes of tapered skew plates

The vibration of simply supported skew plates having a linear variation in thickness in one direction is considered. Approximate analysis is made by using Lagrange's equations employing the double Fourier sine series in oblique co-ordinates to represent the deflected surface. Natural frequencies are obtained for rhombic plates for several ranges of thickness variation and skew angle. The nodal patterns plotted for a few typical configurations show interesting metamorphoses with variation in thickness and skew angle.

A weighted mean square method of linearization in non-linear oscillations

The paper deals with a linearization technique in non-linear oscillations for systems which are governed by second-order non-linear ordinary differential equations. The method is based on approximation of the non-linear function by a linear function such that the error is least in the weighted mean square sense. The method has been applied to cubic, sine, hyperbolic sine, and odd polynomial types of non-linearities and the results obtained are more accurate than those given by existing linearization methods.

Vibration of simply-supported trapezoidal plates II. Unsymmetric trapezoids

This paper deals with the investigation of the vibration characteristics of simply-supported unsymmetric trapezoidal plates. For numerical calculations, the relationship between the eigenvalue problems of a polygonal simply-supported plate and polygonal membrane is again effectively utilized. The Galerkin method is applied, with the deflection surface expressed in terms of a Fourier sine series in transformed coordinates. Numerical values for the first seven to eight frequencies for different geometries of the unsymmetric trapezoid are presented in the form of tables. Also the nodal patterns for a few representative configurations are presented.

Capillary-gravity waves against a corrugated vertical cliff

An analysis involving a transformation of the velocity potential and a Fourier Sine Transform technique is described to study the effect of surface tension on incoming surface waves against a vertical cliff with a periodic wall perturbation. Known results are recovered as particular cases of the general problem considered. An analytical expression is derived for the surface elevation, at far distances from the shore-line, by using Watson's lemma and a representative table of numerical values of the coefficients of the resulting asymptotic expansion is also presented.

Developement of DSP based educational kit for power electronics and drives

The educational kit was developed for power electronics and drives. The need and purpose of this kit is to train engineers with current technology of digital control in power electronics. The DSP is the natural choice as it is able to perform high speed calculations required in power electronics. The educational kit consists of a DSP platform using TI DSP TMS320C50 starter kit, an inverter and an induction machine-dc machine set. A set of experiments have been prepared so that DSP programming can be learned easily in a smooth fashion. Here the application presented is open loop V/F control of three phase induction using sine pulse width modulation technique.

NMR of bicyclic diazines oriented in a lyotropic mesophase

Restricted Access.. Proton NMR spectra of bicyclic diazines such as phthalazine and quinoxaline have been studied in lyotropic liquid crystalline solvents. Values of the indirect spin-spin couplings which could not be derived from studies in the isotropic medium have been obtained. Geometrical information has been obtained in both the cases. The results are indicative of significant solvcntsolute interactions in phthalazine but not in quinoxaline.

Extended gravitational action and novel consequences

It is found that the inclusion of higher derivative terms in the gravitational action along with concepts of phase transition and spontaneous symmetry breaking leads to some novel consequence. The Ricci scalar plays the dual role, like a physical field as well as a geometrical field. One gets Klein-Gordon equation for the emerging field and the corresponding quanta of geometry are called Riccions. For the early universe the model removes singularity along with inflation. In higher dimensional gravity the Riccions can break into spin half particle and antiparticle along with breaking of left-right symmetry. Most tantalizing consequences is the emergence of the physical universe from the geometry in the extreme past. Riccions can Bose condense and may account for the dark matter.

High Yield Room Temperature Synthesis And Spectral Studies Of Tri(Amino)Silanes: (R2n)3SIH

Tri(amino)silanes were prepared by the condensation of trichlorosilane with secondary amines in 1:6 molar ratio. Reactions of trichlorosilane with pyrrolidine, piperidine, hexamethyleneimine, morpholine, N-methylpiperazine and diethylamine afford the tri(amino)silanes in nearly quantitative yields. Their physical and spectroscopic properties are discussed. All these compounds are highly sensitive to moisture and hydrolyse to silica and the respective amine with the evolution of hydrogen. The compounds have been characterised by IR, 1H NMR, [1H]29Si NMR spectroscopic methods and CHN elemental analysis.

Exact free-surface flows for shallow-water equations .1. - the incompressible case

A comprehensive exact treatment of free surface flows governed by shallow water equations (in sigma variables) is given. Several new families of exact solutions of the governing PDEs are found and are shown to embed the well-known self-similar or traveling wave solutions which themselves are governed by reduced ODEs. The classes of solutions found here are explicit in contrast to those found earlier in an implicit form. The height of the free surface for each family of solutions is found explicitly. For the traveling or simple wave, the free surface is governed by a nonlinear wave equation, but is arbitrary otherwise. For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed; in another case, the free surface is a horizontal plane while the flow underneath is a sine wave. The existence of simple waves on shear flows is analytically proved. The interaction of large amplitude progressive waves with shear flow is also studied.

ADC Static Nonlinearity Estimation Using Linearity Property of Sinewave

Prohibitive test time, nonuniformity of excitation, and signal nonlinearity are major concerns associated with employing dc, sine, and triangular/ramp signals, respectively, while determining static nonlinearity of analog-to-digital converters (ADCs) with high resolution (i.e., ten or more bits). Attempts to overcome these issues have been examined with some degree of success. This paper describes a novel method of estimating the ``true'' static nonlinearity of an ADC using a low-frequency sine signal (for example, less than 10 Hz) by employing the histogram-based approach. It is based on the well-known fact that the variation of a sine signal is ``reasonably linear'' when the angle is small, for example, in the range of +/- 5 degrees to +/- 7 degrees. In the proposed method, the ADC under test has to be ``fed'' with this ``linear'' portion of the sinewave. The presence of any harmonics and offset in input excitation makes this linear part of the sine signal marginally different compared with that of an ideal ramp signal of equal amplitude. However, since it is a sinusoid, this difference can be accurately determined and later compensated from the measured ADC output. Thus, the corrected ADC output will correspond to the true ADC static nonlinearity. The implementation of the proposed method is discussed along with experimental results for two 8-b ADCs and one 10-b ADC which are then compared with the static characteristics estimated by the conventional DC method.

Vibration and buckling of hybrid laminated curved panels

Vibration and buckling of curved plates, made of hybrid laminated composite materials, are studied using first-order shear deformation theory and Reissner's shallow shell theory. For an initial study, only simply-supported boundary conditions are considered. The natural frequencies and critical buckling loads are calculated using the energy method (Lagrangian approach) by assuming a combination of sine and cosine functions in the form of double Fourier series. The effects of curvature, aspect ratio, stacking sequence and ply-orientation are studied. The non-dimensional frequencies and critical buckling load of a hybrid laminate lie in between the values for laminates made of all plies of higher strength and lower strength fibres. Curvature enhances natural frequencies and it is more predominant for a thin panel than a thick one.

Screw dynamo and the generation of nonaxisymmetric magnetic fields

A mechanism is presented here for the amplification of large-scale nonaxisymmetric magnetic fields as a manifestation of the dynamo effect. We generalize a result on restrictions of dynamo actions due to laminar flow originally derived by Zeldovich, Ruzmaikin, and Sokolov [Magnetic Fields in Astrophysics (Gordon and Breach, New York, 1983)]. We show how a screwlike motion having phi and z components of velocity can help to grow a magnetic field. This model postulates a large-scale flow having phi and z components with radial dependences (helical flow). Shear in the radial field, because of a near-flux-freezing condition, causes amplification of the phi component of the magnetic field. The radial and axial components grow due to the presence of turbulent diffusion. The shear in the large scale flow induces an indefinite growth of magnetic field without the a effect; nevertheless, turbulent diffusion forms an important part in the overall mechanism.

Space vector pulsewidth modulation — A status review

The technique of space vector pulsewidth modulation (SVM) is reviewed. The basic principle of SVM is derived and is compared with sine-triangle PWM. Operation in the overmodulation range is explained. Extension of SVM to other inverter-motor combinations such as three level inverters and split phase motors are discussed.

Dodecagonal space vector diagram using cascaded H-Bridge inverters

This paper proposes the development of dodecagonal (12-sided) space vector diagrams from cascaded H-Bridge inverters. As already reported in literatures, dodecagonal space vector diagrams have many advantages over conventional hexagonal ones. Some of them include the absence of 6n±1, (n=odd) harmonics from the phase voltage, and the extension of the linear modulation range. In this paper, a new power circuit is proposed for generating multiple dodecagons in the space vector plane. It consists of two cascaded H-Bridge cells fed from asymmetric dc voltage sources. It is shown that, with proper PWM timing calculation and placement of active and zero vectors, a very high quality of sine-wave can be produced. At the same time, the switching frequency of individual cells can be reduced substantially. Detailed PWM analysis, one design example and an elaborate simulation study is presented to support the proposed idea.