Torsional vibrations of prismatic shells
TL;DR: In this paper, a method of analysis of prismatic shells having different internal ribbing for their torsional vibrations was proposed. And the results for some wellknown boundary conditions with the results obtained by classical methods were compared.
Abstract: Prismatic shells find wide application in mechanical, civil and aeronautical engineering. The object of this paper is to propose a method of analysing such shells having different internal ribbing for their torsional vibrations. The governing equations of motion are derived by using a finite difference method and solved by the simultaneous iteration technique. The accuracy of the method is ascertained by comparing the results for some wellknown boundary conditions with the results obtained by classical methods. Shells of square cross-section and rectangular shells of variable and constant cross-section have been analysed. The effects of introduction of diaphragms on the eignefrequencies have been analysed. The effects of variations in shell thickness and length on the dynamic behaviour also have been studied.
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TL;DR: In this article, the first few mode shapes and the respective natural frequencies of a submerged cantilever plate are found by using a finite element procedure, eigenvalues being obtained by a simultaneous iteration technique.
Abstract: The added mass of the fluid surrounding it plats an important role in the dynamic behaviour of a submerged structure. The first few mode shapes and the respective natural frequencies of a submerged cantilever plate are found by using a finite element procedure, eigenvalues being obtained by a simultaneous iteration technique. The influence of the water depth below the plate and also of the water's lateral extent is considered, in order to test the convergency of the results. Results on the effects of the depth of immersion on the natural frequencies and mode shapes of the cantilever plate for different aspect ratios are presented.
32Â citations
TL;DR: In this article, the dynamic free response of thin rectangular plates subjected to one and two dimensional steady state temperature distributions satisfying Laplace's equation is analyzed and the governing equations of motion are derived by a finite difference method and solved by a simultaneous iteration technique to obtain eigenvalues and eigenvectors.
Abstract: The dynamic free response of thin rectangular plates subjected to one and two dimensional steady state temperature distributions satisfying Laplace's equation is analyzed. The governing equations of motionare derived by a finite difference method and solved by a simultaneous iteration technique to obtain eigenvalues and eigenvectors. The accuracy of the method is assessed by comparing the results for some typical cases with those obtained by classical methods. The finite element method is also employed for the problem and the results obtained compare well with those of the finite difference method. From the results an attempt is made to correlate the non-dimensional frequency parameter and the temperature. Plates of different boundary conditions, with at least one edge clamped, free to expand or contract in their planes, are studied.
28Â citations
TL;DR: In this article, the effect of dampers on the maximum strain produced in transmission lines with and without a damper has been studied, and a comparative study of the maximum strains produced is also made for various wind power input assumptions.
Abstract: Various forms of dampers are used to suppress vibrations in transmission lines. In the present paper a study has been made on vibrations of transmission lines having one or more dampers (Stockbridge type) near each end of the span for different cable lengths. An attempt is made here to study the effect of the location of dampers on maximum strains produced in the line. A comparative study of the maximum strains produced is also made for various wind power input assumptions. In addition, a finite difference method is used to find the natural frequency and a finite element method is used to find the natural frequency and mode shapes of the cable with and without a damper.
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TL;DR: In this paper, the method is based on the following theorem: if A is a positive definite matrix of band form such that A = 0, then there exists a real non-singular lower triangular matrix L such that L{L^T} = A,
Abstract: The method is based on the following theorem. If A is a positive definite matrix of band form such that
$${a_{ij}} = 0{\rm{ (|}}i - j| >m{\rm{)}}$$
(1)
then there exists a real non-singular lower triangular matrix L such that
$$L{L^T} = A,{\rm{ where }}{l_{ij}} = 0{\rm{ (}}i - j >m{\rm{)}}{\rm{.}}$$
(2)
76Â citations
TL;DR: In this paper, the simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems, and a method of allowing for body freedom is given and some numerical tests are discussed.
Abstract: The simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems. This method is of significance when a few of the dominant eigenvalues and eigenvectors are required from a large matrix, and hence is particularly suitable for vibration problems involving a large number of degrees of freedom. It is shown that advantage may be taken of both the symmetry and the band form of the mass and stiffness matrices, thus making it feasible to process on a computer larger order vibration problems than can be processed using transformation methods. A method of allowing for body freedom is given and some numerical tests are discussed.
69Â citations
TL;DR: In this article, a forced-flow interchannel mixing model is presented for rod-bundles containing helical-wire spacer systems, which can be incorporated into the COBRA-II and COBLRA-III B lumped-parameter computer codes.
Abstract: A forced-flow interchannel mixing model is presented which is applicable to LMFBR fuel assemblies containing helical-wire spacer systems. The model accounts for the directional nature of the interchannel mixing mechanism, and can be incorporated into the COBRA-II and COBRA-III B lumped-parameter computer codes. Predictions based on this model are compared with available experimental data, and with results computed using turbulent mixing models. Recommendations are made for designing future mixing experiments in rod-bundles containing helical-wire spacer systems.
15Â citations
TL;DR: In this paper, the problem of unsymmetric bending of cylindrical conical shell junction has been analyzed and an exact solution has also been worked out in order to indicate how such problems can be tackled by non-numerical methods and the results of this solution have been compared with the results obtained by the numerical method.
Abstract: The problem of unsymmetric bending of cylindrical conical shell junction has been analysed. In the method presented here the classical assumption of Geckeler's approach has not been made. In the first instance a numerical method has been adopted to solve the shell equations and detailed numerical results have been given for those diameter to thickness ratios and angles of discontinuity which are of practical interest. An exact solution has also been worked out in order to indicate how such problems can be tackled by non-numerical methods and the results of this solution have been compared with the results obtained by the numerical method. The effect of the presence of of fillet at the cylinder cone junction has also been investigated.
8Â citations
TL;DR: In this paper, a shape function for the circumferential displacement distribution has been proposed which reduces the three-dimensional problem to a two-dimensional one, and the accuracy of the method has been checked by verifying the results of known cases.
Abstract: The simultaneous iteration method to determine the eigenfrequencies and eigenvectors is utilized for solving the flexural vibration problems of rotationally symmetric bodies. The finite element approach is used to predict the behaviour of the system. A suitable shape function for the circumferential displacement distribution has been proposed which reduces the three-dimensional problem to a two-dimensional one. The accuracy of the method has been checked by verifying the results of known cases. It has been applied to a complicated structure and results have been compared with experimental ones.
8Â citations