An Efficient Damage Quantification Method for Cylindrical Structures Enhanced by a Dry-Point-Contact Torsional-Wave Transducer

Quantification of damage sizes in cylindrical structures such as pipes and rods is of paramount importance in various industries. This work proposes an efficient damage quantification method by using a dry-point-contact (DPC) transducer based on the non-dispersive torsional waves in the low-frequency range. Theoretical analyses are first carried out to investigate the torsional wave interaction with different sizes of defects in cylindrical structures. A damage quantification algorithm is designed based on the wave reflections from the defect and end. Capitalizing on multiple excitations at different frequencies, the proposed algorithm constructs a damage image that identifies the geometric parameters of the defects. Numerical simulations are conducted to validate the characteristics of the theoretically-predicted wave-damage interaction analyses as well as the feasibility of the designed damage quantification method. Using the DPC transducer, experiments are efficiently carried out with a simple physical system. The captured responses are first assessed to confirm the capability of the DPC transducer for generating and sensing torsional waves. The sizes of the defects in two representative steel rods are then quantified with the proposed method. Both numerical and experimental results demonstrate the efficacy of the proposed damage quantification method. The understandings of the wave-damage interaction and the concept of the damage quantification algorithm lay out the foundation for engineering applications.

Torsional waves with force-free magnetic fields in solar plasma structures

ABSTRACT The aim here is to model torsional waves in homogeneous and expanding twisted flux tubes of solar coronal magnetic plasma structures. For the sake of simplicity, a force-free condition applicable to solar magnetic structures is presented to determine the existing three-dimensional equilibrium magnetic fields. The determined magnetic field is implemented to study the effects of the magnetic twist parameter on the eigenvalues and eigenfunctions of torsional waves. Solenoidal and force-free conditions are applied to find the three-dimensional components of the magnetic field with respect to the numerical flux function. The obtained differential equation is linear where the technique of the separation of variables is implemented in order to solve it. The equilibrium magnetic field components and appropriate vector potential are extracted. Using the provided components in the magnetohydrodynamic theory, a differential equation that governs the frequency dependence of the torsional wave is obtained, whereby the differential transform method is solved. Both eigenvalues and eigenfunctions of torsional waves are calculated numerically. The obtained values for the frequency of the fundamental mode and its first harmonic, together with appropriate functions, exhibit a fine consistency with observations, with regards to the ratio of ω2/ω1, which is estimated to be around 2. At a fixed distance from the tube axis, the ratio increases with the increase of the twist parameter. The higher the applied twist parameter, the more variations of the ω2/ω1 ratio are observed. We cannot find significant variations of the eigenfunctions of torsional waves due to the twist parameter. The consistency between analytical results and observations proves adequate for implementing a force-free equilibrium magnetic field subject to conditions in solar plasma structures regarding torsional wave propagation.