Experimental wavelet analysis of flexural waves in beams

The wavelet transform (WT) is applied to the time-frequency analysis of flexural waves in beams. The WT with the Gabor wavelet decomposes a dispersive wave into each frequency component in the time domain, which enables one to determine the traveling time of a wave along the beam at each frequency. By utilizing this fact, a method is developed to identify the dispersion relation and impact site of beams.     

The region of nonlinear effects for intensive sound pulses in the ocean

The formation of a stationary shock wave is studied in media with an arbitrary power dependence of the damping coefficient on the frequency. The conditions for existence of a stationary shock wave are defined and it is shown that when acoustic signals propagate in the ocean the region of nonlinear effects is limited. For acoustic waves generated by explosive sources a calculation is given of the location of the transition point of the nonlinear wave into a linear one, and the dependence of this point on the charge weight is defined.     

Acoustic waves in a cylindrical duct with periodically varying cross section

The null field approach is used to study the propagation of acoustic waves in a rotationally symmetric hard-walled duct with a periodically varying cross section. For a radius that varies sinusoidally along the axial distance, numerical computations give the axial wave number and the passbands and stopbands of the modes of the duct. In particular, small passbands are seen to exist even for very large variations in radius, and probably all the way to the point where the duct is cut off. We also present some plots which show the pressure pattern inside the duct.     

Design and analysis of nonlinear-transformation-based broadband cloaking for acoustic wave propagation

A coordinate-transformation method can be used to design invisibility cloaks for many types of waves, including acoustic waves. The traditional method for designing a cloak depends on a transformation from a virtual space to a physical space. Previous acoustic cloaks that are mainly designed with linear-transformation-based acoustics have drawbacks that acoustic wave trajectories in the cloaks cannot be controlled and tuned. This work uses a nonlinear mapping from a ray trajectory perspective to construct acoustic cloaks with tunable non-singular material properties. Use of a ray trajectory equation is a straightforward and alternate way to study propagation characteristics of different types of waves, which allows more flexibility in controlling the waves. A broadband cylindrical cloak for acoustic waves in an inviscid fluid is realized with layered non-singular, homogeneous, and isotropic materials based on a nonlinear transformation. Some advantages and improvements of the invisibility nonlinear-transformation cloak over a traditional linear-transformation cloak are analyzed. The invisibility capability of the nonlinear-transformation cloak can be tuned by adjusting a design parameter that is shown to have influence on the acoustic wave energy flowing into the region inside the cloak. Numerical examples show that the nonlinear-transformation cloak is more effective for making a domain undetectable by acoustic waves in an inviscid fluid and shielding acoustic waves from outside the cloak than the linear-transformation cloak in a broad frequency range. The methodology developed here can be used to design nonlinear-transformation cloaks for other types of waves.     

Determination of the optimal Gabor wavelet shape for the best time-frequency localization using the entropy concept

The continuous Gabor wavelet transform (GWT) has been utilized as an effective and powerful time-frequency analysis tool for identifying the rapidly-varying characteristics of some dispersive wave signals. The effectiveness of the GWT is strongly influenced by the wavelet shape that controls the time-frequency localization property. Therefore, it is very important to choose the right Gabor wavelet shape for given signals. Because the characteristics of signals are rarely known in advance, the determination of the optimal shape is usually difficult. Based on this observation, we aim at developing a systematic method to determine the signal-dependent shape of the Gabor wavelet for the best time-frequency localization. To find the optimal Gabor wavelet shape, we employ the notion of the Shannon entropy that measures the extent of signal energy concentration in the time-frequency plane. To verify the validity of the present approach, we analyze a set of elastic bending wave signals generated by an impact in a solid cylinder.     

Holographic interferometry measurements of transient bending waves in tubes and rings

Propagating bending waves are studied in a tube of steel and in a ring of aluminum. The waves are generated by the impact of a ballistic pendulum. Holographic interferometry, with a double-pulsed ruby laser as light source, is used to record the waves. A conical mirror is placed axially inside the tube. Axial illumination and axial observation directions, make it possible to view all sides of the tube simultaneously with a high sensitivity to radial deformation. The interferograms, which have an unusual perspective, are captured with a CCD-camera and then spatially transformed into an unwrapped strip of the tube wall. This makes the interpretation of the measurements simpler. The geometry of the tube causes the wave pattern to propagate with different speed and amplitude along and across the tube, even when the material itself is isotropic. A finite-element simulation of the impact is compared to the corresponding experiment. An impact on a ring with a defect is performed in order to study the effect on the wave pattern. The proposed method could be used in nondestructive testing of pipes.     

Numerical simulation of laser ultrasonic detection of the surface microdefects on laser powder bed fusion additive manufactured 316L stainless steel

A numerical model is presented in this article to investigate the interactions between laser generated ultrasonic and the microdefects (0.01 to 0.1 mm), which are on the surface of the laser powder bed fusion additive manufactured 316L stainless steel. Firstly, the influence of the transient sound field and detection positions on Rayleigh wave signals are investigated. The interactions between the varied microdefects and the laser ultrasonic are studied. It is shown that arrival time of reflected Rayleigh (RR) waves wave is only related to the location of defects. The depth can be checked from the feature point Q, the displacement amplitude and time delay of converted transverse (RS) wave, while the width information can be evaluated from the RS wave time delay. With the aid of fitting curves, it is found to be linearly related. This simulation study provides a theoretical basis for quantitative detection of surface microdefects of additive manufactured 316L stainless steel components.     

双层碳纳米管中的周向导波

考虑双层碳纳米管的层间范德华力,采用连续介质力学的波动理论,建立了双层碳纳米管中周向导波传播模型,研究周向导波的频散现象.通过与单层碳纳米管结果的比较表明,双层碳纳米管中周向导波的传播表现出更为明显的频散特性,出现更多的模态干涉现象,并发现在某些特殊频率处出现成对模态的消失与新启现象.     

Non-homogeneous radiation and outflow boundary conditions simulating incoming acoustic and vorticity waves for exterior computational aeroacoustics problems

A set of non-homogeneous radiation and outflow boundary conditions which automatically generate prescribed incoming acoustic or vorticity waves and, at the same time, are almost transparent to outgoing sound waves produced internally in a finite computation domain is proposed. This type of boundary condition is needed for the numerical solution of many exterior aeroacoustics problems. In computational aeroacoustics, the computation scheme must be as non-dispersive and non-dissipative as possible. It must also support waves with wave speeds which are nearly the same as those of the original linearized Euler equations. To meet these requirements, a high-order/large-stencil scheme is often necessary. The proposed non-homogeneous radiation and outflow boundary conditions are designed primarily for use in conjunction with such high-order/large-stencil finite difference schemes. © 1998 John Wiley & Sons, Ltd.     

Wave propagation in transversely isotropic porous piezoelectric materials

Wave propagation in porous piezoelectric material (PPM), having crystal symmetry 6 mm, is studied analytically. Christoffel equation is derived for the propagation of plane harmonic waves in such a medium. The roots of this equation give four complex wave velocities which can propagate in such materials. The phase velocities of propagation and the attenuation quality factors of all these waves are described in terms of complex wave velocities. Phase velocities and attenuation of the waves in PPM depend on the phase direction. Numerical results are computed for the PPM BaTiO₃. The variation of phase velocity and attenuation quality factor with phase direction, porosity and the wave frequency is studied. The effects of anisotropy and piezoelectric coupling are also studied. The phase velocities of two quasi dilatational waves and one quasi shear waves get affected due to piezoelectric coupling while that of type 2 quasi shear wave remain unaffected. The phase velocities of all the four waves show non-dispersive behavior after certain critical high frequency. The phase velocity of all waves decreases with porosity while attenuation of respective waves increases with porosity of the medium. The characteristic curves, including slowness curves, velocity curves, and the attenuation curves, are also studied in this paper.     

Acoustic diode: Wave non-reciprocity in nonlinearly coupled waveguides

The paper describes a passive time-independent setting for non-reciprocal wave transmission in mechanical and acoustic systems with strong nonlinearities. In the proposed system vibro-impact elements with pre-defined clearances are used to couple two non-dispersive waveguides. The asymmetry necessary for the non-reciprocal behavior is realized through unequal grounding springs of the vibro-impact elements. We show that, for appropriate selection of the parameters, the proposed system acts as a mechanical diode, allowing the transmission of acoustic waves in one direction and completely preventing reverse transmission. Two different designs of the coupling elements are suggested, with the possibility of single-sided or double-sided impacts. A unique feature of the proposed non-reciprocal acoustic system is that minimal distortion of the harmonic content of the transmitted wave occurs, in contrast to current designs where nonlinear non-reciprocity is achieved at the expense of a rather strong distortion of the transmitted signals. For both designs, we derive exact solutions for propagation and reflection of the harmonic waves, and demonstrate the possibility for strong non-reciprocity. Stability properties of the observed solutions in the space of parameters are also explored.     

Sound wave scattering by circular cylindrical shells

The symmetric (S₀) and antisymmetric (A₀) Lamb-type waves generated in a thin elastic cylindrical shell by normal incidence of an acoustic wave have been considered. The typical frequency dependencies (FD) of the backscattered acoustic pressure at on observetion point in the far field are presented. The spectra of the S₀ and A₀ waves are marked on them. It was found that if the A₀ wave is excited in the shell, then its phase velocity is greater than the sound velocity in the fluid surrounding the shell. The parameter which defines the center of the strong bending domain (SBD) is defined. It is shown that in this domain the A₀ wave is practically non-dispersive. Phase velocity data for the A₀ wave are given. Spectra and dispersion curves of the S₀ wave for shells which have different relative thickness s and which are made of different materials have been examined.     

The axisymmetric Rayleigh waves in a semi-infinite elastic solid

It is well-known that Rayleigh wave, also known as surface acoustic wave(SAW), solutions in semiinfinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the depth. Applications of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation. A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical coordinates. It is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius, confirming the existence of surface acoustic waves is irrelevant to coordinate system. On the other hand, the solutions can be treated as plane waves in regions far away from the source. Furthermore, the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.     

Effect of impinging plate geometry on the self-excitation of subsonic impinging jets

In the generation of discrete tones by subsonic impinging jets, there exists a difference of opinion as how the feedback is achieved, i.e., the path of the feedback acoustic waves is whether inside the jet or outside the jet? The only available model (Tam and Ahuja model) for the prediction of an average subsonic jet impingement tone frequency assumes that the upstream part of the feedback loop is closed by an upstream propagating neutral wave of the jet. But, there is no information about the plate geometry in the model. The present study aims at understanding the effect of the plate geometry (size and co-axial hole in the plate) on the self-excitation process of subsonic impinging jets and the path of the acoustic feedback to the nozzle exit. The present results show that there is no effect of plate diameter on the frequency of the self-excitation. A new type of tones is generated for plates with co-axial hole (hole diameter is equal to nozzle exit diameter) for Mach numbers 0.9 and 0.95, in addition to the axisymmetric and helical mode tones observed for plates without co-axial hole. The stability results show that the Strouhal number of the least dispersive upstream propagating neutral waves match with the average Strouhal number of the new tones observed in the present experiments. The present study extends the validity of the model of Tam and Ahuja to a plate with co-axial hole (annular plate) and by doing so, we indirectly confirmed that the major acoustic feedback path to the nozzle exit is inside the jet.     

Propagation of guided waves in pressure vessel

Pressure vessels usually operate under extremes of high/low temperatures and high pressures. Defect, such as crack and corrosion, can result in leakage or rupture failures, even catastrophic incidents. Guided wave-based structural health monitoring (SHM) technology is one of the most prominent options in non-destructive evaluation and testing (NDE/NDT) techniques. Propagation of guided waves in a typical pressure vessel is systematically investigated in this study for the application of guided wave-based SHM. Shape of the pressure vessel is a cylinder with two end caps. Because of geometric similarity, theory of guided wave propagation in the cylinderical structure is analyzed to study dispersive features of guided waves in the pressure vessel. Dispersion curves of three different types of guided wave modes, viz. the longitudinal, torsional and flexural modes, are calculated using theoretical method. Based on the analyses and experimental wave signals, central frequency and wave parameters of incident wave are optimized. Effect of contained liquid on propagation of guided waves, especially the L(0, 2) mode, in the pressure vessel is further investigated to minimize energy leakage of the wave to the contained liquid. The analytical method, finite element analysis (FEA) and experiments are applied to study propagation characteristics of guided waves in the pressure vessel, so as to demonstrate the feasibility of guided wave-based non-destructive evaluation and testing (NDE/NDT) for such kind of complex structures.     

GUIDED CIRCUMFERENTIAL WAVES IN DOUBLE-WALLED CARBON NANOTUBES

A model of guided circumferential waves propagating in double-walled carbon nan- otubes is built by the theory of wave propagation in continuum mechanics,while the van der Waals force between the inner and outer nanotube has been taken into account in the model.The dispersion curves of the guided circumferential wave propagation are studied,and some dispersion characteristics are illustrated by comparing with those of single-walled carbon nanotubes.It is found that in double-walled carbon nanotubes,the guided circumferential waves will propagate in more dispersive ways.More interactions between neighboring wave modes may take place.In particular,it has been found that a couple of wave modes may disappear at a certain frequency and that,while a couple of wave modes disappear,another new couple of wave modes are excited at the same wave number.     

Destabilization of long-wavelength Love and Stoneley waves in slow sliding

Love waves are dispersive interfacial waves that are a mode of response for anti-plane motions of an elastic layer bonded to an elastic half-space. Similarly, Stoneley waves are interfacial waves in bonded contact of dissimilar elastic half-spaces, when the displacements are in the plane of the solids. It is shown that in slow sliding, long-wavelength Love and Stoneley waves are destabilized by friction. Friction is assumed to have a positive instantaneous logarithmic dependence on slip rate and a logarithmic rate weakening behavior at steady-state.Long-wavelength instabilities occur generically in sliding with rate- and state-dependent friction, even when an interfacial wave does not exist. For slip at low rates, such instabilities are quasi-static in nature, i.e., the phase velocity is negligibly small in comparison to a shear wave speed. The existence of an interfacial wave in bonded contact permits an instability to propagate with a speed of the order of a shear wave speed even in slow sliding, indicating that the quasi-static approximation is not valid in such problems.     

Scattering of electromagnetic waves by an acoustic disturbance in the atmosphere

Summary The variations in density associated with an acoustic wave are shown to influence the propagation of an electromagnetic wave. The variation in electric permittivity of the atmosphere caused by an acoustic wave is expressed by the power density of the wave. Under the assumption that the acoustic waves are spherical, the scattered field at large distances is given in terms of definite integrals which are evaluated by means of the method of Stationary Phase. The limiting case of plane acoustic waves is discussed, and two numerical examples are given.     

Short-wave modes for wave ducts in quasi-stratified media

Propagation of harmonic waves in three-dimensional ducts, with slowly varying properties in the horizontal directions, is treated. The wave length is assumed to be small in comparison with the width of the duct. A set of asymptotic solutions to the wave equation (generalisations of normal modes of horizontally homogeneous wave-guides) is constructed. The method extends the applicability region of the method of “vertical modes and horizontal rays” and gives a simple estimation of the latter. Oscillations bounded by the wave-guide's boundaries or by the caustics are treated, and a unified formal procedure for construction of appropriate asymptotic solutions is proposed. The vicinity of ‘horizontal caustics’ is investigated. The analysis is carried out for the examples of acoustic and internal gravitational waves in fluids.     

Exact and soliton solutions to nonlinear transmission line model

A nonlinear transmission line (NLTL) is comprised of a transmission line periodically loaded with varactors, where the capacitance nonlinearity arises from the variable depletion layer width, which depends both on the DC and AC voltages of the propagating wave. An equivalent circuit model of NLTL is discussed analytically, in this article, and different type of solutions are celebrated. The improved extended tanh-function method has been applied successfully to extract the solutions. The obtained solutions are solitary wave solutions, singular periodic solutions, singular soliton solutions, Jacobi elliptic doubly periodic type solutions and Weierstrass elliptic doubly periodic type solutions. It is a very convenient tool to study the propagation of electrical solitons which propagate in the form of voltage waves in nonlinear dispersive media.