Bending Of Circular Plate On Elastic-Foundation

The governing differential equation of linear, elastic, thin, circular plate of uniform thickness, subjected to uniformly distributed load and resting on Winkler-Pasternak type foundation is solved using ``Chebyshev Polynomials''. Analysis is carried out using Lenczos' technique, both for simply supported and clamped plates. Numerical results thus obtained by perturbing the differential equation for plates without foundation are compared and are found to be in good agreement with the available results. The effect of foundation on central deflection of the plate is shown in the form of graphs.

Vertical uplift resistance of circular plate anchors in clays under undrained condition

The vertical uplift resistance of circular plate anchors, embedded horizontally in a clayey stratum whose cohesion increases linearly with depth, has been obtained under undrained (phi = 0) condition. The axi-symmetric static limit analysis formulation in combination with finite elements proposed recently by the authors has been employed. The variation of the uplift factor (F,) with changes in the embedment ratio (H/B) has been computed for several rates of increases of soil cohesion with depth. It is noted that in all the cases, the magnitude of F-c increases continuously with depth up to a certain value of H-cr/B beyond which the uplift factor becomes essentially constant. The proposed static limit analysis formulation is seen to provide acceptable results even for the two other simple chosen axi-symmetric problems.

A Lagrangian for von Karman Equations of Large Deflection Problem of Thin Circular Plate

By the semi-inverse method proposed by He, a Lagrangian is established for the large deflection problem of thin circular plate. Ritz method is used to obtain an approximate analytical solution of the problem. First order approximate solution is obtained, which is similar to those in open literature. By Mathematica a more accurate solution can be deduced.

Transient bending of a piezoelectric circular plate

Thin, piezoelectric circular plates are frequently used as active components in transducer and smart materials applications. This paper reports on the exact, explicit solution for the transient motion of a piezoelectric circular plate, built-in or simply supported on the edge and electrically grounded over the entire surface. Expressed by elementary Bessel functions and obtained via exact inverse Laplace transforms, the solution enables the efficient calculation of accurate system parameters. (C) 2004 Elsevier Ltd. All rights reserved.

A semi- analytic finite element approach to the stress analysis of circular plate

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Elasto-Electrostatic Analysis of Circular Microplates Used in Capacitive Micromachined Ultrasonic Transducers

The active structural component of a capacitive micromachined ultrasonic transducer (CMUT) is the top plate which vibrates under the influence of a time-varying electrostatic force thereby producing ultrasound waves of the desired frequency in the surrounding medium. Analysis of MEMS devices which rely on electrostatic actuation is complicated due to the fact that the structural deformations alter the electrostatic forces, which redistribute and modify the applied loads. Hence, it becomes imperative to consider the electrostatics-structure coupling aspect in the design of these devices. This paper presents an approximate analytical solution for the static deflection of a thin, clamped circular plate caused by electrostatic forces which are inherently nonlinear. Traditionally, finite element simulations using some commercial software such as ANSYS are employed to determine the structural deflections caused by electrostatic forces. Since the structural deformation alters the electrostatic field, a coupled-field simulation is required wherein the electrostatic mesh is continuously updated to coincide with the deflection of the structure. Such simulations are extremely time consuming, in addition to being nontransparent and somewhat hard to implement. We employ the classical thin-plate theory which is adequate when the ratio of the diameter to thickness of the plate is very large, a situation commonly prevalent in many MEMS devices, especially the CMUTs. We solve the thin-plate electrostatic-elastic equation using the Galerkin-weighted residual technique, under the assumption that the deflections are small in comparison to the thickness of the plate. The evaluation of the electrostatic force between the two plates is simplified due to the fact that the electrostatic gap is much smaller than the lateral dimensions of the device. The results obtained are compared to those found from ANSYS simulations and an excellent agreement is observed between the two. The pull-in voltage predicted by our model is close to the value predicted by ANSYS simulations.

Estimation of low-velocity impact damage in laminated composite circular plates using nonlinear finite element analysis

Nonlinear finite element analysis is used for the estimation of damage due to low-velocity impact loading of laminated composite circular plates. The impact loading is treated as an equivalent static loading by assuming the impactor to be spherical and the contact to obey Hertzian law. The stresses in the laminate are calculated using a 48 d.o.f. laminated composite sector element. Subsequently, the Tsai-Wu criterion is used to detect the zones of failure and the maximum stress criterion is used to identify the mode of failure. Then the material properties of the laminate are degraded in the failed regions. The stress analysis is performed again using the degraded properties of the plies. The iterative process is repeated until no more failure is detected in the laminate. The problem of a typical T300/N5208 composite [45 degrees/0 degrees/-45 degrees/90 degrees](s) circular plate being impacted by a spherical impactor is solved and the results are compared with experimental and analytical results available in the literature. The method proposed and the computer code developed can handle symmetric, as well as unsymmetric, laminates. It can be easily extended to cover the impact of composite rectangular plates, shell panels and shells.

Influence of a liquid on the natural frequencies of almost circular plates

In this work, the influence of the surrounding fluid on the dynamic characteristics of almost circular plates is investigated. First the natural frequencies and normal modes for the plates in vacuum are calculated by a perturbation procedure. The method is applied for the case of elliptical plates with a low value of eccentricity. The results are compared with other available methods for this type of plates with good agreement. Next, the effect of the fluid is considered. The normal modes of the plate in vacuum are used as a base to express the vibration mode of the coupled plate-fluid system. By applying the Hankel transformation the nondimensional added virtual mass 2 increment (NAVMI) are calculated for elliptical plates. Results of the NAVMI factors and the effect of the fluid on the natural frequencies are given and it is shown that when the eccentricity of the plate is reduced to zero (circular plate) the known results of the natural frequencies for circular plates surrounded by liquid are recovered.

Induced Damping on Vibrating Circular Plates Submerged in still Fluid

When a structure vibrates immersed in a fluid it is known that the dynamic properties of the system are modified. The surrounding fluid will, in general, contribute to the inertia, the rigidity and the damping coefficient of the coupled fluid-structure system. For light structures, like spacecraft antennas, even when the fluid is air the contribution to the dynamic properties can be important. For not so light structures the ratio of the equivalent fluid/structure mass and rigidity can be very small and the fluid contribution could be neglected. For the ratio of equivalent fluid/structure damping both terms are of the same order and therefore the fluid contribution must be studied. The working life of the spacecraft structure would be on space and so without any surrounding fluid. The response of a spacecraft structure on its operational life would be attenuated by the structural damping alone but when the structure is dynamically tested on the earth the dynamic modal test is performed with the fluid surrounding it. The results thus are contaminated by the effects of the fluid. If the damping added by the fluid is of the same order as the structural damping the response of the structure in space can be quite different to the response predicted on earth. It is therefore desirable to have a method able to determine the amount of damping induced by the fluid and that should be subtracted of the total damping measured on the modal vibration test. In this work, a method for the determination of the effect of the surrounding fluid on the dynamic characteristics of a circular plate has been developed. The plate is assumed to vibrate harmonically with the vacuum modes and the generalized forces matrix due to the fluid is thus computed. For a compressible fluid this matrix is formed by complex numbers including terms of inertia, rigidity and damping. The matrix due to the fluid loading is determined by a boundary element method (BEM). The BEM used is of circular rings on the plate surface so the number of elements to obtain an accurate result is very low. The natural frequencies of the system are computed by an iteration procedure one by one and also the damping fluid contribution. Comparisons of the present method with various experimental data and other theories show the efficiency and accuracy of the method for any support condition of the plate.

On limiting cases in the flexure of simply supported regular polygonal plates

Limiting solutions are derived for the flexure of simply supported many-sided regular polygons, as the number of sides is increased indefinitely. It is shown that these solutions are different from those for simply supported circular plates. For axisymmetric loading, circular plate solutions overestimate the deflexions and the moments by significant factors.

激光辐照下圆薄板的动态屈曲研究

对强激光辐照下薄板（铜片）的动态热失稳过程进行了分析，得出了简支圆薄板在热冲击下发生的屈曲及后屈曲过程，并给出了临界激光功率密度与薄板厚径比的关系曲线，方法计入了温度分布、惯性项和缺陷大小对于失稳过程的影响。这一工作有利于人们对强激光引起的硬目标破坏机理的认识。

Asymptotic analysis of thin plates under normal load and horizontal edge thrust

We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions.

We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solution approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes.

We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.

A design strategy in the propulsion system attachment to a submarine hull to minimise radiated noise

Vibration modes of a submerged hull are excited by fluctuating forces generated at the propeller and transmitted to the hull via the propeller-shafting system. The low frequency hull vibrational modes result in significant sound radiation. This work investigates the reduction of the far-field radiated sound pressure by optimising the connection point of the shafting system to the hull. The submarine hull is modelled as a fluid loaded cylindrical hull with truncated conical shells at each end. The propeller-shafting system consists of the propeller, shaft, thrust bearing and foundation, and is modelled in a modular approach using a combination of spring-mass-damper elements and continuous systems (beams, plates, shells). The foundation is attached to the stern side end plate of the hull, which is modelled as a circular plate coupled to an annular plate. By tuning the connection radius of the foundation to the end plate, the maximum radiated noise in a given frequency range can be minimised.

Direct measurement of powder flavour adhesion on to a food surface using a novel adhesion tester

The firm adhesion of flavouring particles onto crisp surfaces during coating processes is a major concern in the snack production industry. Detachment of flavouring powders from products during handling and production stages can lead to substantial financial losses for the industry, in terms of variable flavour performance and extended cleaning down time of fugitive particle build-up on process equipment. Understanding the adhesion strength of applied bulk particulates used for flavouring formulations will help analysts to evaluate the efficiency of coating processes and potentially enable them to assess the adhesion strength of newly formulated flavouring powder prior to commitment to full scale plant trials. A rapid prototype of a novel adhesion tester has been designed and constructed. The apparatus operates according to the principle of impact force acting on particles attached to the surface of the food substrate. The main component is a circular plate to which four sample holders are attached and which is subjected to vertical travel down a guide shaft. Several flavouring powders have been tested extensively. By plotting the detachment versus impact force, the difference obtained between adhesion strength of different flavouring powders (which is a strong function of particle size) has been discussed.

Reinforced Stone Columns in Weak Deposits – A Laboratory Model Study

This paper investigates the performance of stone columns in a weak deposit such as peat. It evaluates the effects of reinforcing stone columns by jacketing with a tubular wire mesh and bridging reinforcement with a metal rod and a concrete plug. A series of plate loading tests was conducted on isolated stone columns installed in a soil bed consisting of a peat layer sandwiched between two layers of sand. The load–displacement characteristics of footings supported by stone columns were investigated by applying load to a circular plate supported on: (a) untreated soil; (b) soil treated with stone columns; and (c) soil treated with stone columns reinforced with the above reinforcing techniques. The work has shown that the settlement characteristics of the soil can be improved by installing stone columns and that a significant enhancement in the load–settlement response is achieved when the columns are reinforced by the various methods.