Plates Of Non-uniform Thickness Research Articles

Branched flows of flexural waves in non-uniform elastic plates

Flexural elastic waves and sound in solids are of great interest in wide-ranging contexts such as ultrasound in plates, geophysics, ocean engineering, aerospace and automotive structures, and musical acoustics. Despite bending waves being the most important elastic waves for such surface structures, their propagation in the presence of the inevitable non-uniformity is poorly understood. Here we show the branching and focusing behaviour of highly dispersive flexural waves travelling in elastic plates of non-uniform thickness. The thickness profile has isotropically correlated spatial randomness. The correlation length is much larger than the wavelength. The location of wave focusing shows a scaling relationship with randomness, which is consistent with those previously reported in other random media. We show this analytically and numerically. This suggests a universality in the scaling between the location of wave focusing with randomness and the correlation length, regardless of the physics of the waves in question.

Geometrical Influences on the Vibration of Layered Plates

This paper aims to study the influence of different geometric properties and support conditions on the vibration of layered plates of nonuniform thickness under shear deformation theory. The layered plates are supposed to have arbitrarily nonuniform thickness as linear, exponential, and sinusoidal. The spline approximation is used to approximate translational and angular displacement functions. Eigen frequency parameters are calculated by solving eigenvalue problem. The geometrical influences such as number of lay-ups, different ply orientations, each ply consisting of different material, side-to-thickness ratio, and aspect ratio are taken into consideration to examine the frequency variation of plates for two different support conditions.

Vibrations of a rectangular plate of non-uniform thickness partially embedded in a Winkler medium

Vibrations of a rectangular plate of non-uniform thickness partially embedded in a Winkler medium

Effect of transverse shear strain on the stress state of plates of nonuniform thickness

Effect of transverse shear strain on the stress state of plates of nonuniform thickness

Analytical and experimental investigation on vibrating, continuous rectangular plates of non-uniform thickness

This paper is concerned with the determination of the fundamental frequency of vibration of plates having stepped thickness. The planforms considered include rectangular and rectangular with a rectangular corner cut-out. The plate may carry an elastically mounted mass. Results of presumably good accuracy are obtained by using polynomial co-ordinate functions and the Rayleigh approach. An experimental investigation is also described for plates of uniform thickness.

Surface Crack in a Clamped Circular Plate Subjected to Uniform Lateral Pressure

The bending of a clamped circular plate containing a surface crack along its edge is discussed. An approximate method of solution, which is based on the classical plate theory, is proposed to obtain the asymptotic behavior of bending stresses along the tip of the crack. The flexural rigidity of the plate is reduced by the crack. The distribution of bending stresses is therefore changed. A plate of nonuniform thickness is introduced which has the equivalent of the flexural rigidity of the cracked plate under consideration. The bending stress intensity factor is evaluated with the aid of the equivalent plate. It is found that the stress intensity factor increases with the crack depth for shallow cracks, and it decreases when the depth exceeds a certain value.

Minimum Reinforcement of Nonuniform Plates

Considerable attention has been given to the plastic design of plates and grillages of uniform depth for minimum reinforcement material consumption, but very little has been given to nonuniform depth structures. This paper attempts to fill some of this gap. It will be shown that the optimality conditions for plates of nonuniform thickness can be derived quite simply from the Marcal-Prager-Shield “associated structure” optimization theory. These conditions are applied to an axisymmetric plate or grillage with predefined thickness variation, a square simply supported flat plate with differing reinforcement depths and to the more practical problem of an infinite flat plate with drop panels, supported on finite columns. Some remarks about the practical application of the results close the paper.

Bending of fibre-reinforced composite circular plates of non-uniform thickness

By use of classical plate theory complete analytical solutions are obtained for the bending of thin fibre-reinforced composite circular plates of radially varying thickness exhibiting rectangular orthotropy. The plate equations are solved for three specific cases of axisymmetric loading and boundary conditions. The solutions are presented in non-dimensional form. Numerical results are presented graphically for glass-epoxy composite plates.

Stress Distribution in a Plate of Non-uniform Thickness, subject to Non-Uniformly Distributed Transverse Load : (Case of Axial Symmetry) II.

We take a circular plate of external radius R, its thickness being non-uniform and varying according to the law : h=h0(R1-r)/R1, where R1>R. The transverse load acting on this plate is distributed by a linear law : p=p0(1+kr/R1). Stress distribution in such a plate of non-uniform thickness and subject to non-uniformly distributed transverse load, has been calculated and the result was shown as numerical tables and curves.