Development of basic theories and techniques for determining stresses in rotating turbine or compressor blades

A method for measuring in-plane displacement of a rotating structure by using two laser speckle photographs is described. From the displacement measurements one can calculate strains and stresses due to a centrifugal load. This technique involves making separate speckle photographs of a test model. One photograph is made with the model loaded (model is rotating); the second photograph is made with no load on the model (model is stationary). A sandwich is constructed from the two speckle photographs and data are recovered in a manner similar to that used with conventional speckle photography. The basic theory, experimental procedures of this method, and data analysis of a simple rotating specimen are described. In addition the measurement of in-plane surface displacement components of a deformed solid, and the application of the coupled laser speckle interferometry and boundary-integral solution technique to two dimensional elasticity problems are addressed

Modal testing using two speakers and application to the space shuttle tiles bond evaluation

This paper concerns the application of two-speaker acoustic excitation in modal testing. Single-speaker excitation is first reviewed, and it is shown that anti-symmetric modes can not be adequately excited and measured when a uniform sound pressure is applied to the structure since the generalized forces are zeros. However, the two-speaker excitation method is shown to be effective in modal testing conducted on an aluminum plate and on the Space Shuttle tiles. The excitation signals are from the same function generator, but 180° out of phase. A laser vibrometer is used to measure the induced vibration. Data is acquired and processed using a two-channel spectrum analyzer, modal analysis software, and other instrumentation. The mode shapes (both symmetric and anti-symmetric) of the aluminum plate are determined experimentally and by finite element analysis. These results are shown to be in close agreement. This method of excitation, along with an inverse approach, is successfully implemented in the Space Shuttle tile bond evaluation. In this, the size and location of the disbonded regions are computed and displayed. The developed system for tile testing is shown to be quick, accurate, and user-friendly

An Inverse Vibration Method Applied To Bond Evaluation Of Space Shuttle Tiles

This paper describes an inverse vibration method for determining unknown parameters of the physical system by using partial modal information. The method is based on knowing the complete mass matrix of the system and part of its stiffness matrix. The unknown parameters in the stiffness matrix are related to the physical system. This method is applied to the bond evaluation of the space shuttle tiles. The tiles are excited by audible acoustic energy and the response is measured by a noncontact laser vibrometer. The inverse solution is incorporated into a user-friendly computer program to determine the size and location of disbanded regions in the tile assembly. The program allows for any tile geometry as well as the orthotropic properties of the tile material. Both simulated data, provided by finite element analysis, and experimentally acquired data are used to verify the proposed method. © 1996 by ASME

Model Analysis Of Plates Using The Dual Reciprocity Boundary Element Method

This paper presents a new method for determining the natural frequencies and mode shapes for the free vibration of thin elastic plates using the boundary element and dual reciprocity methods. The solution to the plate\u27s equation of motion is assumed to be a separable form. The problem is further simplified by using the fundamental solution of an infinite plate in the reciprocity theorem. Except for the inertia term, all domain integrals are transformed into boundary integrals using the reciprocity theorem. However, the inertia domain integral is evaluated in terms of the boundary nodes by using the dual reciprocity method. In this method, a set of interior points are selected and the deflection at these points is assumed to be a series of approximating functions. The reciprocity theorem is applied to reduce the domain integrals to a boundary integral. To evaluate the boundary integrals, the displacements and rotations are assumed to vary linearly along the boundary. The boundary integrals are discretized and evaluated numerically. The resulting matrix equations are significantly smaller than the finite element formulation for an equivalent problem. Mode shapes for the free vibration of circular and rectangular plates are obtained and compared with analytical and finite element results

Modal analysis of plates using the dual reciprocity boundary element method

This paper presents a new method for determining the natural frequencies and mode shapes for the free vibration of thin elastic plates using the boundary element and dual reciprocity methods. The solution to the plate\u27s equation of motion is assumed to be of separable form. The problem is further simplified by using the fundamental solution of an infinite plate in the reciprocity theorem. Except for the inertia term, all domain integrals are transformed into boundary integrals using the reciprocity theorem. However, the inertia domain integral is evaluated in terms of the boundary nodes by using the dual reciprocity method. In this method, a set of interior points is selected and the deflection at these points is assumed to be a series of approximating functions. The reciprocity theorem is applied to reduce the domain integrals to a boundary integral. To evaluate the boundary integrals, the displacements and rotations are assumed to vary linearly along the boundary. The boundary integrals are discretized and evaluated numerically. The resulting matrix equations are significantly smaller than the finite element formulation for an equivalent problem. Mode shapes for the free vibration of circular and rectangular plates are obtained and compared with analytical and finite element results. © 1995

Model For Friction In Quasi-Steady-State Sliding Part I. Derivation

This paper presents the derivation of a model for the prediction of the coefficient of friction for two elasto-plastic surfaces in quasi-steady-state sliding. A companion paper presents numerical results and a discussion on the implications of the model\u27s predictions in comparison with selected experimental data. The model considers the separate effects of asperity interaction and deformation, debris interaction and plowing, and adhesion, with partitioning of normal load (and contact areas) between different contacting elements. The analysis is restricted to nominally \u27steady state\u27 sliding where the contact parameters are statistically invariant. The modifier \u27quasi\u27 is used to emphasize that in tribodynamic systems, there is no true equilibrium condition in which the frictional effects are \u27constant.\u2

A Boundary Element Method For Stress Reduction By Optimal Auxiliary Holes

Stress concentration reduction in a plate with a hole is accomplished by introducing optimally sized and placed circular holes. This paper presents a method based on boundary elements and mathematical programming to determine these auxiliary holes. The mathematical programming method consists of a modified Newton\u27s method and subsequent parallel tangents method (PARTAN). A solution is presented for an elliptical hole in a tension strip. © 1995