Exact analysis of simply supported rhombic plates under uniform pressure

The simply supported rhombic plate under transverse load has received extensive attention from elasticians, applied mathematicians and engineers. All known solutions are based on approximate procedures. Now, an exact solution in a fast converging explicit series form is derived for this problem, by applying Stevenson's tentative approach with complex variables. Numerical values for the central deflexion and moments are obtained for various corner angles. The present solution provides a basis for assessing the accuracy of approximate methods for analysing problems of skew plates or domains.

Natural frequencies of polar orthotropic annular plates

The classical Rayleigh-Ritz method with simple polynomials as admissible functions has been used for obtaining natural frequencies of transversely vibrating polar orthotropic annular plates. The method in conjunction with transformations introduced in the analysis has been found to be quite effective, particularly for large hole sizes. Estimates of natural frequencies corresponding to modes with one as well as two nodal diameters are obtained for the nine combinations of clamped, simply supported and free edge conditions and for various values of rigidity ratio and hole sizes. Based on the variation of eigenvalue parameter with rigidity ratio, the frequencies of these modes as well as those of axisymmetric modes have been expressed by means of simple formulae in terms of rigidity ratio and the frequencies of corresponding modes in the isotropic case. These formulae have been used in determining the fundamental frequencies of orthotropic plates.

Natural frequencies of circumferentially truncated sector plates with simply supported straight edges

The classical Rayleigh-Ritz method in conjunction with suitable co-ordinate transformations is found to be effective for accurate estimation of natural frequencies of circumferentially truncated circular sector plates with simply supported straight edges. Numerical results are obtained for all the nine combinations of clamped, simply supported and free boundary conditions at the circular edges and presented in the form of graphs. The analysis confirms an earlier observation that the plate behaves like a long rectangular strip as the width of the plate in the radial direction becomes small.

Estimation of higher natural frequencies of polar orthotropic annular plates

A method based on an assumption that the radial bending moment is zero at a nodal circle is shown to yield accurate estimates of natural frequencies corresponding to higher modes of transversely vibrating polar orthotropic annular plates for various combinations of clamped, simply supported and free edge conditions. This method is found to be convenient for the determination of locations of nodal circles as well. Numerical investigations revealed that for small holes, nodal circles tend to move towards the outer edge with increasing number of nodal diameters. For large holes, it has been shown that the plate behaves like a long rectangular strip.

Vibration of generally orthotropic skew plates

Vibration problem of generally orthotropic plates with particular attention to plates of skew geometry is studied. The formulation is based on orthotropic plate theory with arbitrary orientation of the principal axes of orthotropy. The boundary conditions considered are combinations of simply supported, clamped, and free-edge conditions. Approximate solution for frequencies and modes is obtained by the Ritz method using products of appropriate beam characteristic functions as admissible functions. The variation of frequencies and modes with orientation of the axes of orthotropy is examined for different skew angles and boundary conditions. Features such as "crossings" and "quasi-degeneracies" of the frequency curves are found to occur with variation of the orientation of the axes of orthotropy for a given geometry of the skew plate. It is also found that for each combination of skew angle and side ratio, a particular orientation of the axes gives the highest value for the fundamental frequency of the plate.

Vibration of skew plates

The vibration problems of skew plates with different edge conditions involving simple support and clamping have been considered by using the variational method of Ritz, a double series of beam characteristic functions being employed appropriate to the combination of the edge conditions. Natural frequencies and modes of vibration have been obtained for different combinations of side ratio and skew angle. These detailed studies reveal several interesting features concerning the frequency curves and nodal patterns. The results presented should, in addition, be of considerable value and practical significance in design applications.

Natural frequencies of circumferentially truncated sector plates with simply supported straight edges

The classical Rayleigh-Ritz method in conjunction with suitable co-ordinate transformations is found to be effective for accurate estimation of natural frequencies of circumferentially truncated circular sector plates with simply supported straight edges. Numerical results are obtained for all the nine combinations of clamped, simply supported and free boundary conditions at the circular edges and presented in the form of graphs. The analysis confirms an earlier observation that the plate behaves like a long rectangular strip as the width of the plate in the radial direction becomes small.

A comprehensive study of interference and clearance fit pins in large plates

Pin joints in structures are designed for interference, push or clearance fits. That is, the diameter of the pin is made greater than, equal to or less than the hole diameter. Consider an interference fit pin in a plate subjected to a continuously increasing in-plane load.

Vibrations of annular plates with linear thickness profiles

Abstract is not vailable.

Analysis of vibration of clamped square plates by the Rayleigh-Ritz method with asymptotic solutions from a modified Bolotin method

Estimates of flexural frequencies of clamped square plates are initially obtained by the modified Bolotin's method. The mode shapes in “each direction” are then determined and the product functions of these mode shapes are used as admissible functions in the Rayleigh-Ritz method. The data for the first twenty eigenvalues in each of the three (four) symmetric groups obtained by the (i) Bolotin, (ii) Rayleigh and (iii) Rayleigh-Ritz methods are reported here. The Rayleigh estimates are found to be much closer to the true eigenvalues than the Bolotin estimates. The present product functions are found to be much superior to the conventional beam eigenmodes as admissible functions in the Rayleigh-Ritz method of analysis.

Free vibration of rectangular plates of arbitrary thickness

Free vibration of thick rectangular plates is investigated by using the “method of initial functions” proposed by Vlasov. The governing equations are derived from the three-dimensional elastodynamic equations. They are obtained in the form of series and theories of any desired order can be constructed by deleting higher terms in the infinite order differential equations. The numerical results are compared with those of classical, Mindlin, and Lee and Reismann solutions.

Estimation of higher natural frequencies of polar orthotropic annular plates

A method based on an assumption that the radial bending moment is zero at a nodal circle is shown to yield accurate estimates of natural frequencies corresponding to higher modes of transversely vibrating polar orthotropic annular plates for various combinations of clamped, simply supported and free edge conditions. This method is found to be convenient for the determination of locations of nodal circles as well. Numerical investigations revealed that for small holes, nodal circles tend to move towards the outer edge with increasing number of nodal diameters. For large holes, it has been shown that the plate behaves like a long rectangular strip.