Plates Of Different Shapes Research Articles

Calculation of the Acoustic Field of a Direct Transducer with Piezoelectric Plates of Different Shapes

For a direct transducer with a circular piezoelectric plate, a comparative analysis of acoustic field calculations by the Helmholtz–Huygens and Fourier–Bessel formulas is performed. The equivalence of these calculations is demonstrated. A refined expression is obtained for the pressure on the transducer axis as a function of distance. The field calculations are also performed for square and triangular piezoelectric plates. A comparison of numerical results is carried out.

Experimental investigation of alternative pre-stress components for a 3-1 connectivity multilayer piezoelectric-polymer composite ultrasonic transducer

The most popular configuration for piezoelectric-polymer composites has pillars of piezoelectric ceramic supported by a polymer matrix and material with this structure is now widely available commercially. However, it has significant disadvantages for use in multilayer devices for non-mass-loaded operation below approximately 50 kHz. An alternative configuration is therefore reported here, in which interconnected fingers of piezoelectric ceramic surround polymer plates. This can be termed 3-1 connectivity, since the piezoceramic is fully connected in three dimensions and the polymer in only one. The configuration has been found to have significant manufacturing advantages which feed through to enhanced performance compared with practical 1-3 connectivity multilayer devices. For many potential applications, high-power operation is required, and it is unclear if the multilayer structure has sufficient internal strength to maintain its integrity at high strains. Therefore, an investigation has been carried out into alternative pre-stressing component designs. These comprise back and front stainless steel plates of different shapes, connected by a number of stainless steel rods. In this paper, the fundamental performance of a multilayer device is illustrated with electrical impedance and surface displacement measurements in air, without pre-stressing. Then measurements are reported from three different clamping configurations. It is shown that good results can be achieved at spot frequencies with a suitable clamp, but that unsuitable clamps prevent even this, and broadband performance is unlikely to be achieved easily.

A high precision shear deformable element for the analysis of laminated composite plates of different shapes

A high precision triangular element developed by the last author is upgraded for the analysis of laminated composite plates. In this element the effect of shear deformation is considered by taking transverse displacement and bending rotations as independent field variables. The interpolation function used to approximate transverse displacement is one order higher than that used for bending rotations. This has made the element free from locking in shear. For the analysis of unsymmetric laminates, in-plane displacements are also taken as the field variables. Plates having different shapes, boundary conditions, thickness ratios, number of layers, fibre orientations and something else are analysed by this element and the results obtained are compared with those obtained from other sources in most of the cases. A number of new results are presented, which are expected to be useful in future research.

Plate on cross-anisotropic foundation analyzed by the finite element method

Abstract The isoparametric element method is used for a plate on a cross-anisotropic foundation. The surface displacement due to a point force acting on a cross-anisotropic foundation is taken as the fundamental solution. Based on this analysis, the interaction between the foundation and plate can be determined, and the reaction of the foundation can be treated as the external forces of the plate. Therefore, only the plate needs to be divided into a number of elements. The present method can be applied to thin or thick plates, plates of different shapes, plates under various loading, and to isotropic or cross-anisotropic foundation. The examples in this paper show that this method is versatile, highly accurate, and can reduce preparation and computing work.

Investigation into thin-walled structures at the technical University of Łódź

The behaviour of thin-walled structures has been a very important area of research activity in the Department of Strength of Materials and Structures (previously the Institute of Applied Mechanics) of the Technical University of Łódź in Poland for over 30 years. The investigations concerned many kinds of thin-walled structures: plates of different shapes including trapezoidal and circular, girder and column structures composed of flat plates, cylindrical and conical shells, and composite multi-layer structures subjected to a variety of load types. The analyses included buckling and post-buckling behaviour, assessment of ultimate loads and the behaviour of the structure in post post failure range. This necessitated usage of the theory of elasticity and elasto plasticity in the constitutive relations describing phenomena of the materials behaviour. All the works done at our Department resulted in a number of papers and books, achieved academic degrees and titles (PhD, DSc, Professor). They were also presented in numerous conferences, symposia and seminars. It is our academic duty and a pleasure to mention that for about 20 years we have been accompanied in our thin-walled research activity by our sister unit from the University of Strathclyde-the Department of Mechanical Engineering. Some of our achievements would not be possible without this valuable collaboration, which was part of a more general scheme of academic link initiated between our universities almost 30 years ago.

Predicted natural frequencies of two‐dimensional elastodynamic problems: a practical error estimator

Based on the asymptotic solution for predicted natural frequencies of a two‐dimensional elastodynamic problem from the finite element analysis, presents the concept of the asymptotic error, which is an approximate error but tends to the exact error when the characteristic length of elements approaches zero, and a practical error estimator. The present practical error estimator contains two criteria: one is the error estimator criterion, the other the finite element mesh design criterion. Using this practical error estimator, not only can the accuracy of a finite element solution for natural frequencies of a two‐dimensional elastodynamic problem be directly evaluated without any further finite element calculation, but also a new target finite element mesh for the desired accuracy of solution can be immediately designed from the relevant information of an original finite element solution. Generally, for the purpose of designing a new target finite element mesh, this original finite element solution is obtainable from a very coarse mesh of a few elements and usually does not satisfy the accuracy requirement. Since the new target finite element mesh could result in a finite element solution with a desire accuracy, the finite element solution so obtained can be used for a structural design in engineering practice. The related numerical results from vibration problems of three representative plates of different shapes under plane stress conditions have demonstrated the correctness and applicability of the present practical error estimator.

Vibrations of thin elastic plates with point supports: A comparative study

Point-supported structural elements are commonly found in several fields of engineering: from civil and naval engineering applications to electronic systems (mainly point-supported printed circuit boards). The present paper deals with vibrating plates of different shapes and different support arrangements. Natural frequencies are determined using a finite element algorithm and compared with results available in the literature where possible. It is also shown that in the case of clamped and simply supported plates of regular polygonal shape with a central clamping support simple polynomial expressions yield accurate values for the fundamental frequency coefficient when the Ritz method is used.

Symmetrical configurations by capillary forces

The equilibrium positions of aluminium plates of different shapes floating by capillary forces on water surface in glass cells of various forms are investigated. In the centre of the cells the floating plates have an equilibrium orientation for which the symmetry elements of the cell and those of the floating plate coincide with each other as far as possible.

Amplitude response of finite plates and the characteristic admittance theory

Frequency response curves of rectangular plates and of plates of different shapes will be presented and the results compared with the predictions of the Characteristic Admittance Theory. Regardless of the point of excitation, the mean line through the driving-point response curve seems to always coincide with the predicted mean line as closely as this line can be drawn. The accuracy is not quite as great if the driving point and the point of observation are separated. [Work supported by ONR, Task No. 064-475.]

Natural convection heat transfer from isothermal horizontal plates of different shapes

Experiments were carried out on natural convection heat transfer from isothermal plates facing upwards in air in the range of Gr·Pr from 2 × 10 5 m ̊ to 10 9 , Both the average and local heat transfer were determined. Plates of different shapes (square, rectangular and circular) were used and “corner” and “edge” effects were investigated. Dimensionless equations are suggested for the laminar and turbulent regions.

Vibration and sound radiation of a plate

Because of their many vibratory resonances, plates are mechanically soft and their suspending structures have considerable effect on their vibration and sound radiation. Experimental evaluation of acoustic properties of plates is therefore difficult. Plates of different shapes and dimensions were supported in such a way as to eliminate the effects of the supports on the vibrations and the velocity amplitudes due to point forces were recorded by phonograph cartridges and microphones in the near sound field. The results show that the many vibratory modes generate “hotspots” on the plates. The attachment of ribs and supports disturbs the vibration field and leads to localized areas of increased sound radiation. Long wavelength acoustic holography was used to locate on the vibrating plates the sources of farfield sound. These regions were also investigated by recording the vibratory and nodal line patterns of the plates by a nearfield microphone method. This combination of techniques has a unique capability to locate acoustic sources on vibrating structure. [Work supported by NASA and ONR.]