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

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

Inverse Elastostatics Boundary Element Approach Applied To Nondestructive Evaluation

The elastostatics boundary element method is applied in an inverse problem approach to the nondestructive detection of subsurface cavities in structures. The approach relies on the overspecification of the boundary conditions at the exposed surface. The traction is specified there, and displacements are used as additional data for solving the inverse problem. The displacements are numerically simulated in this study; however in practice they may be experimentally determined, for instance by the laser speckle photography technique. In the developed iterative procedure, an initial guess is made for the shape of the cavity and a grid pattern is laid out

Detection Of Cavities By An Inverse Elastostatics Boundary Element Method: Experimental Results

An inverse elastostatics boundary element approach is developed for the nondestructive detection of subsurface cavities in structures. The method relies on the overspecification of the boundary conditions at the exposed surface. The traction is specified there, and displacements are used as additional data for solving the inverse problem. These displacements are experimentally determined by the laser speckle photography technique. An iterative process is used to locate the cavity by driving surface residuals to zero. Iterative updates of the cavity geometry are kept within a physically realistic feasible region using an anchored grid pattern. The detection of a circular hole is presented

Deformation And Strain Fields In Pin Specimens In Sliding Contact By Laser Speckle And Metallographic Techniques

This paper describes the application of laser speckle photography to the measurement of deformations associated with sliding wear. The deformations and the associated strains are those which occur on the side of a rectangular-sectioned pin which is in sliding contact against a counterface disc. The side of the pin is exposed to a pulsed ruby laser beam, and a double exposure specklegram is made to record deformations which occur between laser pulses. Strain fields are obtained from displacement data by use of the Lagrangian description, and neglecting out-of-plane displacement gradients. By appropriately sequencing pulses, deformation histories can be obtained, in situ. And since the exposed side of the thin pin specimen represents the cover layer under which subsurface sections lie, the deformation history observable through the laser speckle method reflects the deformation behavior which is occurring on subsurface planes. By post-test metallography on planes close to this side face, the degree of correspondence between surface and subsurface deformation fields is demonstrated. The paper discusses the materials, apparatus and experimental techniques employed, and presents results obtained with several metallic specimens. Of particular interest is the extent of the plastically deformed subsurface zone, and its development as a function of time. © 1990 by ASME