Energy Velocity Of Waves Research Articles

Effect of pressurization on helical guided wave energy velocity in fluid-filled pipes

The effect of pressurization stresses on helical guided waves in a thin-walled fluid-filled pipe is studied by modeling leaky Lamb waves in a stressed plate bordered by fluid. Fluid pressurization produces hoop and longitudinal stresses in a thin-walled pipe, which corresponds to biaxial in-plane stress in a plate waveguide model. The effect of stress on guided wave propagation is accounted for through nonlinear elasticity and finite deformation theory. Emphasis is placed on the stress dependence of the energy velocity of the guided wave modes. For this purpose, an expression for the energy velocity of leaky Lamb waves in a stressed plate is derived. Theoretical results are presented for the mode, frequency, and directional dependent variations in energy velocity with respect to stress. An experimental setup is designed for measuring variations in helical wave energy velocity in a thin-walled water-filled steel pipe at different levels of pressure. Good agreement is achieved between the experimental variations in energy velocity for the helical guided waves and the theoretical leaky Lamb wave solutions.

Propagation of electromagnetic energy through a dispersive and absorptive medium

The quasi-static energy density and corresponding energy velocity of electromagnetic waves in dielectrics and metamaterials consisting of arrays of wires and split-ring resonators (SRRs) were approximated by functions of the (effective) constitutive parameters. Using the Poynting theorem for a quasimonochromatic electromagnetic wave concurrently interacting with electric and magnetic dipoles, exact formulas for the average total energy density and energy velocity of the wave in a dispersive medium with losses are derived as functions of the refractive index . The energy velocity satisfies relativistic causality in the passive dispersive medium and generalizes notions of the group and energy velocities. Calculation of the energy density of the magnetic field in a medium with the non-Lorentz permeability is also clarified in the Appendix.

Guided waves dispersion analysis for prestressed viscoelastic waveguides by means of the SAFE method

The work focuses on the effect of a general state of initial stress on the dispersion behavior of guided waves in viscoelastic waveguides. To this purpose, an extension of the Semi Analytical Finite Element (SAFE) method is proposed to formulate the wave equation and to extract the waves modal properties in viscoelastic prestressed waveguides. The wave equation is derived in linearized incremental form within an updated Lagrangian framework, where the prestressed configuration is considered to be slightly deviated from the corresponding unstressed one. Next, by using the SAFE method and the Boltzmann superposition principle, a linear algebraic system of equations is obtained in the complex wavenumber-frequency domain. Dispersive guided waves wavelengths, phase velocity, group velocity and attenuation, are extracted by solving a polynomial eigenvalue problem. A modal formula for the wave energy velocity calculation, that exploits the wave equation SAFE matrices only, is proposed. Such formula is based on the linearized incremental form of the Poynting theorem obtained by manipulating the energy balance principle expressed in material description.Numerical examples on a hysteretic 113A standard rail profile and on an ASME 1-1/2 Schedule 160 steel pipe, considering various states of initial stress and applied loadings, are presented to show the effect of prestress on the dispersive properties of mechanical waves in viscoelastic waveguides.

Guided Wave Nondestructive Inspection of Grouted Rock Bolts: Experiment and Numerical Simulation

The properties of a longitudinal guided wave with central frequency 5kHz propagating in partially grouted rock bolts were studied by experimental and numerical simulation methods. The guided wave was excited by the impact–echo method on the free end of the bolt, and the excited wave measured in the experiments was used as excitation input in the numerical simulation. The numerical results match well with the experimental ones. Two empirical formulas were obtained for when the reflected waves from the upper interface and from the embedded end of the bolt could be distinguishably detected. Conclusion is drawn from the simulation results that the guided wave energy velocity in the embedded section of the bolt increases with the increase of elastic modulus of the grout media. A new method was proposed for anchorage quality testing and its effectiveness was proved by a testing example.

Testing nonlinear electrodynamics in waveguides: the effect of magnetostatic fields on the transmitted power

In Born–Infeld theory and other nonlinear electrodynamics, the presence of a magnetostatic field modifies the dispersion relation and the energy velocity of waves propagating in a hollow waveguide. As a consequence, the transmitted power along a waveguide suffers slight changes when a magnetostatic field is switched on and off. This tiny effect could be better tested by operating the waveguide at a frequency close to the cutoff frequency.

The Poynting vector applied to the complex refractive index in a hot plasma near the electron cyclotron frequency and to the cyclotron resonance observed on topside ionograms

The electron cyclotron resonance is the only fundamental resonance observed on topside ionograms that, up to the present, has not been understood. There is a solution to the hot plasma dispersion equations for the wave frequency f near the cyclotron frequency fH when the wave number k makes a small angle to the Earth's magnetic induction B. For this case, the magnitude of the imaginary part of k is more than half the real part. This means that the group velocity, dω/dk, where ω = 2πf, is complex. The real part of dω/dk is too large to explain the cyclotron resonance observations. In addition to the wave number, the dispersion relations for a hot magnetoplasma can be used to obtain the electric and magnetic fields of the cyclotron wave and hence the Poynting vector. Dividing the Poynting energy flux by the energy density of the wavefield, where the energy density is the sum of the electric, magnetic, and electron energy densities, gives the Poynting velocity VP, which is a good approximation to the actual wave energy velocity for f near fH. Cyclotron waves are strongly damped but can exist several milliseconds as observed. The waves radiate from the plane containing B and the dipole antenna L. The waves with f > fH beat with those with f < fH to produce the beat frequency observed on fixed‐frequency ionograms.

Characteristic Velocities for Higher-Order Stokes Waves in Deep Water

The accuracy of asymptotic expressions for phase, wave energy, and wave action velocities for steady, plane gravity waves progressing in deep water and with no ambient currents is investigated. The calculations are to a large extent based on Fenton's fifth-order Stokes wave theory. Using the dispersion relation correct to sixth order for arbitrary water depth, the phase velocity is calculated to fourth order in wave steepness for infinitely deep water; this is in accordance with a number of previously found results. Potential and kinetic energy is calculated, which leads to the energy density correct to sixth order. Comparison with previous findings showed one discrepancy, which can however be explained. Also, the energy flux is found correct to sixth order, leading to a fourth-order expression for the wave energy velocity. From sixth-order action and action flux results, the wave action velocity is finally calculated correct to fourth order. Agreement with more accurate numerical results is excellent for all three velocities except near the wave of maximum steepness. Practical asymptotic formulas are introduced, enabling one to calculate the characteristic velocities explicitly from given wave height and period. Two new exact relations between integral properties for deep water with no current are presented.

Propagation of surface waves in anisotropic solids: theoretical calculation and experiment

This paper utilizes the Stroh-Barnett's integral formalism of surface waves in anisotropic solids to calculate the variation of surface wave speeds of a unidirectional fibre-reinforced composite in an efficient way. The decaying pattenr of the displacements and tractions along the depth were also calculated using the determined surface wave speeds. To study the propagations of surface waves in the fibre-reinforced composite plate experimentally, point-source/point-receiver (PS/PR) experiments were conducted. A pulsed laser was utilized to generate a point disturbance in the composite plate and the transient waves were recorded by a PZT transducer with an acting diameter of about 1.5 mm. The slowness curves of the surface wave energy velocity were determined from the experimental data and the results were in accordance with those calculated theoretically.