Acoustic radiation and scattering from cylindrical bodies and analysis of transducer arrays

New mathematical methods to analytically investigate linear acoustic radiation and scattering from cylindrical bodies and transducer arrays are presented. Three problems of interest involving cylinders in an infinite fluid are studied. In all the three problems, the Helmholtz equation is used to model propagation through the fluid and the beam patterns of arrays of transducers are studied. In the first problem, a method is presented to determine the omni-directional and directional far-field pressures radiated by a cylindrical transducer array in an infinite rigid cylindrical baffle. The solution to the Helmholtz equation and the displacement continuity condition at the interface between the array and the surrounding water are used to determine the pressure. The displacement of the surface of each transducer is in the direction of the normal to the array and is assumed to be uniform. Expressions are derived for the pressure radiated by a sector of the array vibrating in-phase, the entire array vibrating in-phase, and a sector of the array phase-shaded to simulate radiation from a rectangular piston. It is shown that the uniform displacement required for generating a source level of 220 dB ref. μPa @ 1m that is omni directional in the azimuthal plane is in the order of 1 micron for typical arrays. Numerical results are presented to show that there is only a small difference between the on-axis pressures radiated by phased cylindrical arrays and planar arrays. The problem is of interest because cylindrical arrays of projectors are often used to search for underwater objects. In the second problem, the errors, when using data-independent, classical, energy and split beam correlation methods, in finding the direction of arrival (DOA) of a plane acoustic wave, caused by the presence of a solid circular elastic cylindrical stiffener near a linear array of hydrophones, are investigated. Scattering from the effectively infinite cylinder is modeled using the exact axisymmetric equations of motion and the total pressures at the hydrophone locations are computed. The effect of the radius of the cylinder, a, the distance between the cylinder and the array, b, the number of hydrophones in the array, 2H, and the angle of incidence of the wave, α, on the error in finding the DOA are illustrated using numerical results. For an array that is about 30 times the wavelength and for small angles of incidence (α<10), the error in finding the DOA using the energy method is less than that using the split beam correlation method with beam steered to α; and in some cases, the error increases when b increases; and the errors in finding the DOA using the energy method and the split beam correlation method with beam steered to α vary approximately as a7 / 4 . The problem is of interest because elastic stiffeners – in nearly acoustically transparent sonar domes that are used to protect arrays of transducers – scatter waves that are incident on it and cause an error in the estimated direction of arrival of the wave. In the third problem, a high-frequency ray-acoustics method is presented and used to determine the interior pressure field when a plane wave is normally incident on a fluid cylinder embedded in another infinite fluid. The pressure field is determined by using geometrical and physical acoustics. The interior pressure is expressed as the sum of the pressures due to all rays that pass through a point. Numerical results are presented for ka = 20 to 100 where k is the acoustic wavenumber of the exterior fluid and a is the radius of the cylinder. The results are in good agreement with those obtained using field theory. The directional responses, to the plane wave, of sectors of a circular array of uniformly distributed hydrophones in the embedded cylinder are then computed. The sectors are used to simulate linear arrays with uniformly distributed normals by using delays. The directional responses are compared with the output from an array in an infinite homogenous fluid. These outputs are of interest as they are used to determine the direction of arrival of the plane wave. Numerical results are presented for a circular array with 32 hydrophones and 12 hydrophones in each sector. The problem is of interest because arrays of hydrophones are housed inside sonar domes and acoustic plane waves from distant sources are scattered by the dome filled with fresh water and cause deterioration in the performance of the array.

Role of academic bodies with special references to the academic programmes in the universities in Kerala

This makes a thorough study of Role of Academic Bodies with Special Reference to the Academic Programmes in the Universities in Kerala. The present study has dealt with the constitution, powers and functions of the authorities of the universities in Kerala, especially the academic bodies which have well-defined powers and function. This thesis gives in detail the role and functions of the academic bodies in the four universities in Kerala, under study: and examines the role-effectiveness of these bodies. To sum up, it can be concluded that the academic bodies in the universities in Kerala do not function as effectively as envisaged in the laws of the universities. They have a maintenance-oriented approach rather than a dynamic one, without thinking in terms of introducing innovations. They need improvement in the various aspects of their constitution, selection of members and their mode of functioning

Foreign exchange reserves in India and China

Professor Irma Glicman Adelman, an Irish Economist working in California University at Berkely, in her research work on ‘Development Over Two Centuries’, which is published in the Journal of Evolutionary Economics, 1995, has identified that India, along with China, would be one of the largest economies in this 21st Century. She has stated that the period 1700 - 1820 is the period of Netherlands, the period 1820 - 1890 is the period of England the period 1890 - 2000 is the period of America and this 21st Century is the century of China and India. World Bank has also identified India as one of the leading players of this century after China. India will be third largest economy after USA and China. India will challenge the Global Economic Order in the next 15 years. India will overtake Italian economy in 2015, England economy in 2020, Japan economy in 2025 and USA economy in 2050 (China will overtake Japan economy in 2016 and USA economy in 2027). India has the following advantages compared with other economies. India is 4th largest GDP in the world in terms of Purchasing Power. India is third fastest growing economy in the world after China and Vietnam. Service sector contributes around 57% of GDP. The share of agriculture is around 17% and Manufacture is 16% in 2005 - 2006. This is a character of a developed country. Expected GDP growth rate is 10% shortly (It has come down from 9.2% in 2006 - 2007 to 6.2% during 2008 - 2009 due to recession. It is only a temporary phenomenon). India has $284 billion as Foreign Exchange Reserve as on today. India had just $1 billion as Foreign Exchange Reserve when it opened its economy in the year 1991. In this research paper an attempt has been made to study the two booming economies of the globe with respect to their foreign exchange reserves. This study mainly based on secondary data published by respective governments and various studies done on this area

A crack on the interface of piezo-electric bodies

Singularities of elastic and electric fields are investigated at the tip of a crack on the interface of two anisotropic piezo-electric media under various boundary conditions on the crack surfaces. The Griffith formulae are obtained for increments of energy functionals due to growth of the crack and the notion of the energy release matrix is introduced. Normalization conditions for bases of singular solution are proposed to adapt them to the energy, stress, and deformation fracture criteria. Connections between these bases are determined and additional properties of the deformation basis related to the notion of electric surface enthalpy are established.