We model elastic waves in bearing raceways to detect defects and friction. By treating raceways as hollow cylinders, we derive 4×4 systems for vibrational modes, enabling forward and inverse problem solving. Using roller count and speed as priors reduces sensor requirements. Examples show recovery of contact traction and detection of elastic emissions.
A large variety of engineering and biological materials have a non-zero internal stress distribution, even in the absence of applied forces. These stresses can arise from thermal expansion or volumetric growth, for example, in the production of the …
We resolve the challenge of relating effective wave properties to measurable reflection and transmission coefficients in acoustic measurements of dense particulates by deriving a systematic extension of the quasi-crystalline approximation for halfspace materials with random particulates.
When waves scatter through dense particle arrangements, they bounce multiple times between particles—a process called multiple scattering. This is critical for applications like ultrasound imaging of composites. We solve the wave scattering problem for particles arranged in a cylinder, a case that hasn't been solved before. Using ensemble averaging, we derive an effective T-matrix describing the cylinder's total scattering behavior. For simple scatterers, this reduces to a homogeneous cylinder with an effective wavenumber. Monte Carlo simulations confirm our theoretical predictions are accurate across a wide range of frequencies.
Mechanical stress in tissue is important but hard to measure. The angled shear wave identity (ASWI) estimates stress from shear-wave speeds without needing a constitutive model. This work extends ASWI to viscous and anisotropic tissues, deriving the relevant dispersion relations and showing that stress recovery in viscous media requires measuring both wave speed and attenuation. The extension to materials with memory is also discussed.
Mechanical stress in tissue is important but hard to measure. The angled shear wave identity (ASWI) estimates stress from shear-wave speeds without needing a constitutive model. This work extends ASWI to viscous and anisotropic tissues, deriving the …
There has not been a satisfying numerical validation of the theory of effective waves in random particulate materials. Validation has been challenging because the theoretical methods for effective waves have been limited to random particulate media in infinite slabs or half-spaces, which require a very large number of particles to perform accurate numerical simulations. This paper offers a solution by providing, from first principles, a method to calculate effective waves for a sphere filled with particles for a spherically symmetric incident wave. We show that this case can excite exactly the same effective wavenumbers, which are the most important feature to validate for effective waves. To check correctness, we also deduce an integral equation method which does not assume the effective wave solution. Our methods are, in principal, valid for any frequency, particle volume fraction and disordered pair-correlation. With the methods we provide, it is now possible to validate, with a heavier Monte Carlo simulation, the predictions from effective wave theory..
Mechanical stresses across different length scales play a fundamental role in understanding biological systems' functions and engineering soft machines and devices. However, it is challenging to noninvasively probe local mechanical stresses in situ, particularly when the mechanical properties are unknown. We propose an acoustoelastic imaging-based method to infer the local stresses in soft materials by measuring the speeds of shear waves induced by custom-programmed acoustic radiation force.
Real-world solids, such as rocks, soft tissues and engineering materials, are often under some form of stress. Most real materials are also, to some degree, anisotropic due to their microstructure, a characteristic often called the ‘texture anisotropy’. This anisotropy can stem from preferential grain alignment in polycrystalline materials, aligned micro-cracks or structural reinforcement, such as collagen bundles in biological tissues, steel rods in pre-stressed concrete and reinforcing fibres in composites. Here, we establish a framework for initially stressed solids with transverse texture anisotropy.
We present a framework for linear wave propagation in thermo-visco-elastic materials. The framework includes classical cases, but its main advantage is to simplify how to model interactions between solids and fluids, and everything in between. In general there are two types of compressional waves (one pressure dominated and another thermal dominated) and a shear wave in free-space. We provide simplified approximations for all these waves valid for most all materials and frequency ranges commonly used.