Karl-Evert Fällström

Transient bending waves in plates studied by hologram interferometry

Propagating bending waves are studied in plates made of aluminum and wood. The waves are generated by the impact of a ballistic pendulum. Hologram interferometry, with a double pulsed ruby laser as the light source, is used to record the out of plane motion of the waves. Elliptic-like fringes visualize differences in wave speed for different directions in the anisotropic plate and circular ones are obtained for the isotropic plate. The experimental data for the isotropic plate compare favorably with analytical results derived from the Kirchhoff-plate equation with a point impact of finite duration. A similarity variable is found when starting conditions are modeled as a Dirac pulse in space and time, that brings new understanding to the importance of specific parameters for wave propagation in plates. A formal solution is obtained for a point force with an arbitrary time dependence. For times much larger than the contact time, the plate deflection is shown to be identical to that from a Dirac pulse applied at the mean contact time. A method for determining material parameters, and the mean contact time, from the interferograms is hence developed.

Dynamic material parameters in an anisotropic plate estimated by phase-stepped holographic interferometry

Abstract Material parameters in an anisotropic plate are determined using two non-destructive measuring techniques: real-time phase-stepped electronic speckle pattern interferometry and dual-reference-beam pulsed holographic interferometry. The first technique is used to measure the lower modes of vibration of the plate with free-free boundary conditions. Finite element analysis is then used to determine two effective Youngs moduli and the in-plane shear modulus. The second technique is used to detect transient bending waves propagating in the plate and acoustic waves propagating in the surrounding air. A double-pulsed laser is used both to generate the waves and to make holographic recordings of the wave fields. The stiffness of the plate is estimated using the measured deformation field and an analytical solution to the plate impact problem.

A nondestructive method to detect delaminations and defects in plates

Abstract Double exposure holographic interferometry, with a ruby laser as the light source, is used to study the influence of local changes in thickness, of delaminations and variations in damping upon propagating transient bending waves in plates and shells. The bending waves are created by the impact of a pendulum. Defects cause changes in the wave impedance of the plate, which will give rise to changes relative to the undisturbed fringe pattern, by reflected and transmitted waves. The size of a defect has to be of the same size or larger than the wavelength of the bending wave to be visible. Since bending waves are dispersive, high frequency components travelling faster than low frequency ones, a small defect is most likely to be observed shortly after impact. The influence of local changes in thickness and delaminations upon the fringe pattern is presented, together with a method to interpret the fringe pattern when several defects are present.

MECHANICAL AND THERMAL EFFECTS IN A STEEL PLATE IMPACTED BY A FOCUSED LASER PULSE

A short laser pulse from a 1 J ruby laser is focused at a steel plate. The effect will be that the material surface at the impact point becomes very rapidly heated. Metal vapour leaves the surface at a very high velocity. That is, both a mechanical impulse and local thermal energy are transferred to the plate. The mechanical impulse creates propagating bending waves in the plate, which in turn creates transient sound waves in the surrounding air. The heated spot at the plate surface creates thermal stresses in the plate which g\ve rise to an out-of-plane deformation of the plate. This deformation is added up to the propagating bending waves. These effects are studied in experiments using pulsed holographic interferometry.

Laser Generated and Recorded Transient Bending Waves in Composite Tubes

Propagating bending waves are studied in three different composite tubes by holographic interferometry. A conical mirror is placed axially inside the tubes. Axial illumination and observation directions make it possible to view the circumference of the tube, with a high sensitivity to radial deformation. It is shown how the deformation field can be numerically evaluated using a phase stepping and unwrapping technique. Transient bending waves in the tubes are both generated and recorded by the same pulsed laser, which makes the experiments easy to perform. Finite element simulations of the impacted tubes are compared to corresponding experiments. Both the geometry and the material properties of the tubes affect the wave propagation. For unidirectional composite tubes, the 0-deg and 90-deg directions have different dynamic behavior. The proposed method could be used in nondestructive testing of tubes.

Determination of paper stiffness and anisotropy from recorded bending waves in paper subjected to tensile forces

Experiments and theory for bending wave propagation of paper sheets in tension are presented. An all-electronic pulsed TV holography technique is used to record the bending wave field initiated by a laser pulse. A theory for bending wave propagation in tensile-loaded paper is developed. The bending waves are influenced by mechanical properties such as density, thickness, bending stiffness, anisotropy and also by tensile forces in the paper. The paper stiffnesses are determined by matching the measured deformation field with the calculated theoretical field. The results show that the bending wave pattern is strongly influenced by the tensile force. For a non-destructive on-line measurement of, e.g. stiffnesses and anisotropy in the paper machine the tensile force must be considered.

A study of bending waves in infinite and anisotropic plates

In this paper we present a unified approach to obtain integral representation formulas for describing the propagation of bending waves in infinite plates. The general anisotropic case is included and both new and well-known formulas are obtained in special cases (e.g. the classical Boussinesq formula). The formulas we have derived have been compared with experimental data and the coincidence is very good in all cases.

Material Parameters in Anisotropic Plates

Material parameters, that is, the two Youngs moduli, the in-plane shear modulus and the Poisson’s ratio, in anisotropic rectangular plates are determined in three different ways.