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At least 37 records · Page 2

Ultrasonic input-output for transmitting and receiving longitudinal transducers coupled to same face of isotropic elastic plate

The quantitative understanding of ultrasonic nondestructive evaluation parameters such as the stress wave factor were studied. Ultrasonic input/output characteristics for an isotropic elastic plate with transmitting and receiving longitudinal transducers coupled to the same face were analyzed. The asymptotic normal stress is calculated for an isotropic elastic half space subjected to a uniform harmonic normal stress applied to a circular region at the surface. The radiated stress waves are traced within the plate by considering wave reflections at the top and bottom faces. The output voltage amplitude of the receiving transducer is estimated by considering only longitudinal waves. Agreement is found between the output voltage wave packet amplitudes and times of arrival due to multiple reflections of the longitudinal waves.

Williams, J. H., Jr.

Flexural models of trench/outer rise topography of coronae on Venus with axisymmetric spherical shell elastic plates

Magellan altimetry has revealed that many coronae on Venus have trenches or moats around their peripheries and rises outboard of the trenches. This trench/outer rise topographic signature is generally associated with the tectonic annulus of the corona. Sandwell and Schubert have interpreted the trench/outer rise topography and the associated tectonic annulus around coronae to be the result of elastic bending of the Venus lithosphere (though the tectonic structures are consequences of inelastic deformation of the lithosphere). They used two-dimensional elastic plate flexure theory to fit topographic profiles across a number of large coronae and inferred elastic lithosphere thicknesses between about 15 and 40 km, similar to inferred values of elastic thickness for the Earth's lithosphere at subduction zones around the Pacific Ocean. Here, we report the results of using axisymmetric elastic flexure theory for the deformation of thin spherical shell plates to interpret the trench/outer rise topography of the large coronae modeled by Sandwell and Schubert and of coronae as small as 250 km in diameter. In the case of a corona only a few hundred kilometers in diameter, the model accounts for the small planform radius of the moat and the nonradial orientation of altimetric traces across the corona. By fitting the flexural topography of coronae we determine the elastic thickness and loading necessary to account for the observed flexure. We calculate the associated bending moment and determine whether the corona interior topographic load can provide the required moment. We also calculate surface stresses and compare the stress distribution with the location of annular tectonic features.

Moore, W.

The nonlinear transient response of thin, rectangular elastic plates

The results of experiments and theoretical analysis of the nonlinear, transient response of thin, rectangular, elastic, simply supported plates are presented. In the experiments, a plane wave tube with a special pulse generator at one end and a thin glass plate mounted at the other end was used to subject the glass plate to pressure pulses of different magnitudes. Whole-field measurements of the response of the plate were obtained by the reflected moire grid technique. The largest ratio of center deflection to thickness of the plate during the experiments was 5.6. The theoretical response of the glass plate to the pressure pulses was computed by solving the von Karman equations governing large deflections in elastic plates by two methods - (1) the finite-difference method, and (2) Galerkin's method. Good agreement was found between theoretically predicted and experimentally measured response.

Rajagopal, G.

Contact problem for an elastic reinforcement bonded to an elastic plate

The stiffening layer is treated as an elastic membrane and the base plate is assumed to be an elastic continuum. The bonding between the two materials is assumed to be either one of direct adhesion ro through a thin adhesive layer which is treated as a shear spring. The solution for the simple case in which both the stiffener and the base plate are treated as membranes is also given. The contact stress is obtained for a series of numerical examples. In the direct adhesion case the contact stress becomes infinite at the stiffener ends with a typical square root singularity for the continuum model, and behaving as a delta function for the membrane model. In the case of bonding through an adhesive layer the contact stress becomes finite and continuous along the entire contact area.

Erdogan, F.

Estimates of elastic plate thicknesses beneath large volcanos on Venus

Megellan radar imaging and topography data are now available for a number of volcanos on Venus greater than 100 km in radius. These data can be examined to reveal evidence of the flexural response of the lithosphere to the volcanic load. On Earth, flexure beneath large hotspot volcanos results in an annual topographic moat that is partially to completely filled in by sedimentation and mass wasting from the volcano's flanks. On Venus, erosion and sediment deposition are considered to be negligible at the resolution of Magellan images. Thus, it may be possible to observe evidence of flexure by the ponding of recent volcanic flows in the moat. We also might expect to find topographic signals from unfilled moats surrounding large volcanos on Venus, although these signals may be partially obscured by regional topography. Also, in the absence of sedimentation, tectonic evidence of deformation around large volcanos should be evident except where buried by very young flows. We use analytic solutions in axisymmetric geometry for deflections and stresses resulting from loading of a plate overlying an inviscid fluid. Solutions for a set of disk loads are superimposed to obtain a solution for a conical volcano. The deflection of the lithosphere produces an annular depression or moat, the extent of which can be estimated by measuring the distance from the volcano's edge to the first zero crossing or to the peak of the flexural arch. Magellan altimetry data records (ARCDRs) from data cycle 1 are processed using the GMT mapping and graphics software to produce topographic contour maps of the volcanos. We then take topographic profiles that cut across the annular and ponded flows seen on the radar images. By comparing the locations of these flows to the predicted moat locations from a range of models, we estimate the elastic plate thickness that best fits the observations, together with the uncertainty in that estimate.

Mcgovern, Patrick J.

Active control of sound transmission/radiation from elastic plates by vibration inputs. II - Experiments

Actively controlled harmonic force inputs were applied experimentally to reduce the sound transmitted through an elastic circular plate. The control implementation used a time domain least mean square adaptive algorithm with two error sensors. The control forces were applied directly to the plate by point force vibration inputs, while the error information and performance were measured in the radiated acoustic field by microphones. Test cases were also performed in which the error sensors were accelerometers mounted on the plate. When accelerometers were used as error sensors, the controller performance was degraded; leading to the conclusion that minimizing plate motion does not necessarily lead to an associated decrease in radiated sound levels. In contrast, the results show excellent attenuation of the transmitted sound field when microphone error sensors were used. This result was consistent over a range of frequencies. In addition, the experimental results are compared to previously derived analytical results and the effect of using a point or global minimization scheme is discussed.

Metcalf, V. L.

Elastic plate spallation

The dynamic finite element method was used to investigate elastic stress waves in a plate. Strain displacement and stress strain relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of finite element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.

Oline, L.

Active control of sound transmission/radiation from elastic plates by vibration inputs. I - Analysis

Active control of sound radiation from vibrating plates by oscillating forces applied directly to the structure is analytically studied. The model consists of a plane acoustic wave incident on a clamped elastic circular thin plate. Control is achieved by point forces, and quadratic optimization is used to calculate the optimal control gains necessary to minimize a cost function proportional to the radiated acoustic power (the transmitted field). The results show that global attenuation of broadband radiated sound levels for low to mid-range frequencies can be achieved with one or two control forces, irrespective of whether the system is on or off resonance. The efficiency of the control strategy is demonstrated to be related to the nature of the coupling between the plate modes of response and the radiated field.

Fuller, C. R.

Thermal stresses and buckling of elastic plates with reinforced edges

An approximation method based on the method of Kantorovich is used to calculate the critical thickness necessary to prevent thermal buckling of a rectangular cantilever plate with edge stiffeners. The case where no external loads are applied is considered, and the only stresses are those due to the prescribed thermal profile. Stiffeners are found to play an important role in the thermal buckling by affecting the overall distribution of the in-plane stresses within the plate. Results show that edge stiffeners can cause less or more buckling, and that in most situations the edge stiffeners hinder buckling because a thicker plate is required than if the stiffeners were not present.

Ahmed, M.

Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory. I - Stress and displacement

A simple theory for bending of composite anisotropic plates that are laminated symmetrically about their mid-plane is presented. This theory incorporates transverse shear deformation and transverse normal stress as well as the higher-order effects and fulfills the static conditions on the external boundary planes. Further on, by using Levy-type solutions considered in conjunction with the state space concept, the state of stress and displacement of rectangular plates for a variety of edge conditions is determined and the results are compared to their first-order shear deformation and classical counterparts, obtained by using the same state-space technique.

Librescu, L.

Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory. II - Buckling and free vibration

A previously developed higher-order plate theory and a technique based on the state space concept are used to investigate free vibration and buckling problems of rectangular cross-ply laminated plates. Unified results are presented for the case of arbitrary boundary conditions on two opposite edges. Good agreement is obtained with previous data for simply supported edge conditions. It is pointed out that classical laminated plate theory tends to overpredict both eigenfrequencies and buckling loads, leading to an increase of the degree of orthotropicity of individual layers and of the thickness ratio of the plate.

Khdeir, A. A.

A geometrically nonlinear theory of elastic plates

A set of kinematic and intrinsic equilibrium equations is derived for plates undergoing large deflection and rotation but with small strain. The large rotation is treated by the general finite rotation of a frame in which the material points that are originally along a normal line in the undeformed plate undergo only small displacements. Exact intrinsic virtual strain-displacement relations are derived; using a reduced 2-D strain energy function from which the warping has been systematically eliminated, a set of intrinsic equilibrium equations follows. It is demonstrated that only five equilibrium equations can be derived in this way, because the component of virtual rotation about the normal is not independent. These equations include terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories.

Hodges, Dewey H.