Ultrasonic Attenuation in Polycrystalline Materials in 2D

Grains in a polycrystalline material, typically a metal, act as scatterers of ultrasonic waves and thus give rise to attenuation of the waves. Grains have anisotropic stiffness properties, typically orthotropic or cubic. A new approach is proposed to calculate attenuation in a 2D setting starting from the scattering by an anisotropic circle in an isotropic surrounding. This problem has recently been solved, giving explicit, simple expressions for the elements of the transition (T) matrix (which gives the relation between the the incoming and scattered fields) when the circle is small compared to the ultrasonic wavelengths. The T matrix can be used to calculate the total scattering cross section, which in turn can be used to estimate the attenuation in the material. Explicit expressions for the attenuation coefficient for longitudinal and transverse waves are obtained for a cubic material, and contrary to results in the literature these expressions are valid also for strong anisotropy. For the longitudinal attenuation coefficient a comparison with recent FEM results for Inconel 600 gives excellent agreement

Scattering of elastic waves by a transversely isotropic sphere and ultrasonic attenuation in hexagonal polycrystalline materials

The scattering of elastic waves by a transversely isotropic sphere in an isotropic medium is considered. The elastodynamic equations inside the sphere are transformed to spherical coordinates and the displacement field is expanded in the vector spherical harmonics in the angular coordinates and powers in the radial coordinate. The governing equations inside the sphere then give recurrence relations among the expansion coefficients. Then all the remaining expansion coefficients for the fields outside and inside the sphere are found using the boundary conditions on the surface of the sphere. As a result, the transition (T) matrix elements are calculated and given explicitly for low frequencies. Using the T matrix and the theory of Foldy an explicit expression for the effective complex wave number of transversely isotropic (hexagonal) polycrystalline materials are presented for low frequencies. Numerical comparisons are made with previously published results and with recent FEM results and show a very good correspondence with FEM for low frequencies. As opposed to other published methods there is no limitation on the degree of anisotropy with the present approach

COMPUTATIONAL MODELLING OF GUIDED WAVE PROPAGATION FOR ICE DETECTION ON COMPOSITE MATERIALS

Guided waves are an efficient non-destructive tool in inspection and fault detection of elongated structures. Due to the special characteristics of composite materials, study of guided wave propagation in them has been an interest. Icing condition is a well-known problem in wind turbine industry and in this work application of guided wave propagation for ice detection on composite materials is studied.A 3D shell model is developed in which ice is placed on the plate by changing the properties of specific elements in the icing region. The excitation is applied to the middle of one side of the plate with a low angle of inclination and the centre frequencies varying from 3 kHz to 7 kHz. The signal is received in 24 nodes equally distributed on the plate known as the measurement nodes. The model with a patch of ice is validated using a 3D solid model in which ice is placed as a second solid layer. Comparison shows the model can be simplified using this method without significant change in the results.The Baseline Signal Stretch with the mode decomposition method is applied to the model for temperature variations. Effects of ice accretion on a composite plate is studied in time, frequency and wavenumber domains. In each case post-processing approaches are introduced for this specific application. Moreover, icing index is introduced which is sensitive to accumulated ice on the plate.The model is calibrated and final results are validated using an experimental work which is performed in a cold climate lab.Using the model and introduced criteria both thickness and location of ice on the plate are identified. All the results show that application of guided waves is a promising and accurate tool in ice detection on composite plates

Application of low frequency guided waves to delamination detection in large composite structures: a numerical study

The aim of the current work is to identify the challenges in computational modelling of ultrasonic guidedwave propagation in large structures and developing methods to overcome them. The work includesinvestigating the application of GW in composite laminates and sandwich materials with the aim ofdelamination detection. Moreover, phased array systems are introduced as a method of overcoming thenegative effect of high damping properties in such structures. Propagation of GW in a wind turbine bladeis studied as an example of large structure with the aim of defect detection. Results that show GW canbe used as a potential tool for structural health monitoring of wind turbine blades

Scattering of elastic waves by a sphere with cubic anisotropy with application to attenuation in polycrystalline materials

Scattering of elastic waves by an anisotropic sphere with cubic symmetry inside an isotropic medium is studied. The waves in the isotropic surrounding are expanded in the spherical vector wave functions. Inside the sphere, the elastodynamic equations are first transformed to spherical coordinates and the displacement field is expanded in terms of the vector spherical harmonics in the angular directions and a power series in the radial direction. The governing equations inside the sphere give recursion relations among the expansion coefficients in the power series. The boundary conditions on the sphere then determine the expansion coefficients of the scattered wave. This determines the transition (T) matrix elements which are calculated explicitly to the leading order for low frequencies. Using the theory of Foldy, the T matrix elements of a single sphere are used to study attenuation and phase velocity of polycrystalline materials with cubic symmetry, explicitly for low frequencies and numerically for intermediate frequencies. Numerical comparisons of the present method with previously published results and recent finite element method (FEM) results show a good correspondence for low and intermediate frequencies. The present approach shows a better agreement with FEM for strongly anisotropic materials in comparison with other published methods

Modeling and design of robotic systems having spring-damper actuators

The role of inherent dynamics for the improvement of control strategies of robotic systems is studied. A mathematical formulation of the optimal control problem that is suitable for this investigation is proposed. In solving this problem closed-form expressions have been obtained for the optimal control strategies for n degrees-of-freedom robotic systems with passive (unpowered) drives and no restrictions upon their controlling stimuli, and with non-linear viscoelastic spring-damper actuators. The obtained results can be used in designing optimal spring-damper-like passive drives for robotic systems

Modelling of guided wave propagation for detecting delamination in large composite structures

The aim of this study is to identify the challenges in computational modelling of guided wave (GW) propagation in large composite structures and propose approaches to overcome them. Firstly, effects of using shell elements and a stiffness reduction approach to model delamination in composite laminates and sandwich structures are investigated. Secondly, the obtained methods and conclusions are used to model GW propagation in a wind turbine blade with the aim of delamination detection. Results show that low frequency GW can be used as a potentially efficient tool for structural health monitoring of composite wind turbine blades

Optimization of control laws of the bipedal locomotion systems

The mathematical statement of the problem of energy-optimal control for a bipedal locomotion system is given. The proposed statement of the problem is characterized by broad utilization of experimental data of normal human locomotion. It is done mainly by means of the mathematical formulation of the constraints imposed both on the phase coordinates and on the controlling stimuli of a system. A numerical method for the solution of the optimal control problems for highly nonlinear and complex bipedal locomotion systems is proposed. The method is based on a special procedure of converting the initial optimal control problem into a standard nonlinear programming problem. This is made by an approximation of the independent variable functions using smoothing cubic splines and by the solution of an inverse dynamics problem. The key features of the method are its high numerical effectiveness and the possibility to satisfy a lot of restrictions imposed on the phase coordinates of the system automatically and accurately. The proposed method is illustrated by computer simulation of the energy-optimal anthropomorphic motion of the bipedal walking robot over a horizontal surface

Energy-optimal control of bipedal locomtion systems

The mathematical statement of the problem of energy-optimal control for a bipedal locomotion system is given. The proposed statement of the problem is characterized by broad utilization of experimental data of normal human locomotion. It is done mainly by means of the mathematical formulation of the constraints imposed both on the phase coordinates and on the controlling stimuli of a system. A numerical method for the solution of optimal control problems for highly nonlinear and complex bipedal locomotion systems is proposed. The method is based on a special procedure of converting the initial optimal control problem into a standard nonlinear programming problem. This is made by an approximation of the independent variable functions using smoothing cubic splines and by the solution of inverse dynamics problem. The key features of the method are its high numerical effectiveness and the possibility to satisfy a lot of restrictions imposed on the phase coordinates of the system automatically and accurately. The proposed method is illustrated by computer simulation of the energy-optimal anthropomorphic motion of the bipedal walking robot over a horizontal surface

EFFECTS OF DELAMINATION ON GUIDED WAVE PROPAGATION IN LAMINATED COMPOSITE BEAMS – NUMERICAL SIMULATION

In this study, three methods are used to model guided wave propagation in composite laminate including delamination. First, the model is created using 3D solid elements and delamination is applied between the plies. Next, composite laminate is modelled by homogenizing the material properties into a single layer with 3D shell elements. Delamination is applied using duplicate node method (DNM) and stiffness reduction method (SRM). The three models are compared by comparing the wave pattern, time signal and wave velocity. Results show SRM can be used as the most efficient method with reasonable accuracy to model wave propagation in large and complicated structures