This thesis details the development and validation of a laser Doppler vibrometer-based measurement system that is capable of quantifying not only the normal vibration of a solid body but also the component of vibration that is parallel to the plane containing the surface of interest. LDV manufacturers produce various devices that capture 3D measurements in a beam configuration that can be used to decompose the measured signals into not only the normal velocity of the surface of an object but also two orthogonal in-plane components of the vibration. It was a slightly simplified two-dimensional version of this approach that was chosen for implementation in the Wave Physics Lab using individual components to create a cheaper, more flexible system than those produced by companies such as Polytec. The goal of this system is to facilitate the exploration and discovery of areas and applications where 2D measurement may provide a more complete and precise view of the physics of different phenomena. Upon completion of the system development and validation, a study was done that sought to measure the acoustoelastic effect in an Aluminum plate by measuring how increasing loads alter both the normal and in-plane components of Lamb wave propagation in the plate. The acoustoelastic effect is the effect of stress on wave speed caused by non-linearity in the propagation medium.

Ultrasonic measurements of the preload in bolted joints is a very accurate method since it does not depend on the friction and other factors which cause difficulties for common methods. The ultrasonic method works by emitting an ultrasonic pulse into the bolt which is reflected at the end and returned to the transducer, the change in the time of flight (TOF) can be related to the elongation of the bolt and therefore the preload. One must account for the acoustoelastic effect which is the change in sound speed due to an initial stress state. The goal of this thesis project was to implement a Murnaghan hyperelastic material model in order to account for the acoustoelastic effect when conducting a numerical simulation using the finite element method (FEM). An experiment was also performed to validate the numerical simulation. The DeltaTOF as a function of a tensile force was obtained for an M8 and M10 test piece from the experiment. The material model was implemented by creating a user subroutine written in Fortran for the explicit solver Radioss. Hypermesh was used to set-up the numerical simulation. The material model has shown an expected behavior with an increased sound speed with compressive stresses and a decreased speed with tensile stresses. The numerical simulation showed a good correspondence to the experimental results. / Ultraljudsmätning av klämklraften i skruvförband är en väldigt noggrann metod eftersom att metoden inte påverkas av friktion eller andra faktorer som innebär svårigheter för vanliga metoder. Ultraljudsmetoden fungerar genom att skicka in en ultraljudsvåg i skruven som reflekteras i botten och återvänder tillbaka till sensorn. Skillnaden i tiden för ekot att återvända kan relateras till förlängningen av skruven och därmed klämkraften. Det är viktigt att ta hänsyn till den akustoelastiska effekten, som är fenomenet där ljudhastigheten av en våg i en solid förändras med spänningstillståndet. Målet med det här arbetet är att implementera en hyperelastisk Murnaghan modell som tar hänsyn till den akustoelastiska effekten med FEM simuleringar. Ett experiment har också genomförts för att validera beräkningsmodellen. Tidsfördröjningen som en funktion av förspänningskraften togs fram för ett M8 och M10 provobjekt. Murnaghans hyperelastiska materialmodell implementerades genom att skapa ett användar material skriven i programmeringsspråket Fortran för den explicita lösaren Radioss. Hypermesh användes för att ställa upp FEM simuleringen. Materialmodellen har visat ett väntat beteende med en ökad ljudhastighet med tryckspänningar och minskad ljudhastighet med dragspänningar. Beräkningsmodellen visade en god överenstämmelse med resultatet från experimentet.