Stress Wave Field Research Articles

Determination of Strength Characteristics of Basalt Composite in COMSOL Multiphysics

Some strength characteristics of basalt melt, and basalt fiber are considered. The analysis of micromechanics and stress analysis is carried out on the example of composite cylindrical reinforcement based on multilayer and equivalent single-layer theory. The distributions of the stress wave field of three different values of natural frequencies and mode shapes in three samples of objects from the melt of basalt and basalt fiber are studied using the COMSOL Multiphysics software package. It has been established that three parameters of basalt fiber and basalt melt mainly influence the natural frequency and shape of the modes: these are the volume fraction, the density of the basalt fiber and the density of the basalt melt. It has also been found that the concentration of basalt melt, and basalt fiber affect the strength of the composite material.

Feasibility of Stress Wave-Based Debond Defect Detection for RCFSTs Considering the Influence of Randomly Distributed Circular Aggregates with Mesoscale Homogenization Methodology.

In order to efficiently investigate the effect of the mesoscale heterogeneity of a concrete core and the randomness of circular coarse aggregate distribution on the stress wave propagation procedure and the response of PZT sensors in traditional coupling mesoscale finite element models (CMFEMs), firstly, a mesoscale homogenization approach is introduced to establish coupling homogenization finite element models (CHFEMs) with circular coarse aggregates. CHFEMs of rectangular concrete-filled steel tube (RCFST) members include a surface-mounted piezoelectric lead zirconate titanate (PZT) actuator, PZT sensors at different measurement distances, a concrete core with mesoscale homogeneity. Secondly, the computation efficiency and accuracy of the proposed CHFEMs and the size effect of representative area elements (RAEs) on the stress wave field simulation results are investigated. The stress wave field simulation results indicate that the size of an RAE limitedly affects the stress wave fields. Thirdly, the responses of PZT sensors at different measurement distances of the CHFEMs under both sinusoidal and modulated signals are studied and compared with those of the corresponding CMFEMs. Finally, the effect of the mesoscale heterogeneity of a concrete core and the randomness of circular coarse aggregate distribution on the responses of PZT sensors in the time domain of the CHFEMs with and without debond defects is further investigated. The results show that the mesoscale heterogeneity of a concrete core and randomness of circular coarse aggregate distribution only have a certain influence on the response of PZT sensors that are close to the PZT actuator. Instead, the interface debond defects dominantly affect the response of each PZT sensor regardless of the measurement distance. This finding supports the feasibility of stress wave-based debond detection for RCFSTs where the concrete core is a heterogeneous material.

Stress tensor double dot product imaging condition for elastic reverse time migration

AbstractAs one of wavefield separation methods in elastic reverse time migration, the decoupled wave equation succeeds to separate the particle velocity of P‐ and S‐wave without mode crosstalk. However, it fails to decouple the stress of P‐ and S‐wave which encounters with the problem of crosstalk. To overcome the crosstalk, the paper has proposed the quasi‐stress equations to decouple the stress tensor wavefields of P‐ and S‐wave based on the decoupled stress–strain relationship. Because P‐ and S‐wave stress wavefields are second‐order tensors, different from the imaging method of vector decoupled particle velocity wavefields, a double dot product imaging condition is proposed to obtain scalar images. Based on the total source‐stress tensor wavefields and separated receiver‐stress tensor wavefields, we obtain the scalar images of quasi‐PP and quasi‐PS from the stress information by the double dot product imaging condition. Several numerical examples are evaluated to demonstrate the effectiveness of the separation of P‐ and S‐wave stress and advantage of the proposed imaging condition from the second‐order stress tensor wavefields.

Interface debonding detection of grouted connection based on Lamb wave energy leakage

Grouted connections (GCs) are transitional elements that have been extensively employed in offshore wind turbine support structure to transfer loads from superstructure to foundation. However, interface debonding defects between steel tube and grout layer have an adverse effect on the durability and fatigue resistance of the GC. An effective interface debonding defects detection approach for GC is necessary. In this study, interface debonding defects detection approach based on Lamb wave energy leakage was proposed and validated numerically and experimentally. Numerical studies on Lamb wave energy leakage models and the GC models were performed to study mechanism of detection approach. Lamb wave is excited on the surface, and stress wave fields and time-history response of models were extracted and compared. Experimental investigations were carried out to verify the applicability of the proposed approach in practice. A scaled GC specimen was constructed and Lamb wave was excited by the PZT patches mounted on the surface of GC specimen. The output voltage of surface-mounted PZT sensors under different axial loads were compared. Both numerical and experimental results show that the proposed approach is effective to the detection of interface debonding defects. The damage evolution index (DEI) based on wavelet packet energy is defined and it can be adopted to qualitatively determine the initiation and evolution of the damage.

ДИСПЕРСІЙНИЙ АНАЛІЗ ПОЗДОВЖНІХ ІМПУЛЬСІВ ДЕФОРМАЦІЙ У КАНАТАХ МІНІМАЛЬНОЇ МАСИ ВАНТАЖОПІДЙОМНИХ МЕХАНІЗМІВ КРАНІВ

Dispersion analysis of longitudinal deformation pulses in minimum mass ropes of cranes load lifting mechanisms (which satisfy the conditions of equal strength in each specific cross section) is carried out in the article. The phase and group waveform velocities occurring in the ropes of this type are determined. The impulse dispersion by the method of lifting the load "with the pickup"/"from the base" ("from the ground") was investigated using the stationary phase method. Such methods are used in this work as: 1) classic methods of mathematical physics; 2) complex Fourier transform over time; 3) stationary phase method for the calculation of the integral which characterizes the deformations in the remote field during its asymptotic schedule. It is shown that the asymptotic schedule reduces the analysis of stress and deformation wave fields arising in the rope to the using of the Airy function with a complex argument. The sign of this argument is determined by the sign of the third derivative of the frequency by the wave vector for mentioned above fields near stationary points of the group velocity of wave formations (hear, in accordance, the second derivative is equal to zero). It is substantiated that Airy function is responsible for reproducing the nature of perturbations before and after the wave front moving inside the rope system. The phase velocity with which the constant phase plane of the exponential multiplier is carried in the rope is determined. This multiplier the spatial-temporal dependence of the emerging waveform describes. Near the pulse front (load/deformation of the rope), its duration increases, but the amplitude decreases in proportion to the cubic root of the distance to the observation point. The formula is established, according to which the asymptotic of this problem solution should be built, in the case of the curve extreme of waveform propagation group velocity in the rope. A similar approach gives the possibility to explore the main patterns of no stationary wave fields generated in the ropes of cranes load lifting mechanisms. The results obtained in the work can be used for establishing cranes rope systems loads and deformations quantities estimates under the condition of their transience. Such loads/deformations usually cause of the above systems overstrain when lifting or lowering loads with different types cranes (particularly, bridge, gantry, portal), which work in operation modes (real operation mode) and can lead to emergencies (for example, breaks in rope systems).

Method of theoretically calculating spherical stress wave field in linear-hardening materials under impact load

Based on the linear hardening plastic constitutive model, the theoretical solution of the elastic-plastic spherical stress wave field under impact load is established. Firstly, the influence of the impact load unloading rate on the propagation of the spherical stress wave is analyzed, and three different types of propagation images are obtained. On this basis, the method of theoretically calculating the spherical wave equation in elastic stage, plastic loading stage and unloading stage is established separately, and the calculation scheme of particle displacement, particle velocity, stress and strain is given. Compared with the existing theoretical methods, this method takes into account the different propagation patterns of the stress waves under different unloading rates, and shows how to calculate the stress wave parameters in unloading stage, which is more applicable. This method is used to calculate the elastic-plastic spherical stress wave field under constant shock load and exponential attenuation shock load. The calculated results are in good agreement with those from the existing theoretical method and numerical simulation results in the elastic stage and also in the plastic loading stage. In the unloading stage, the existing theoretical method is no longer applicable, while the results obtained in this paper are in good agreement with the numerical simulation results, which verifies the correctness of the theoretical method.

Mesoscale numerical analysis and test on the effect of debonding defect of rectangular CFSTs on wave propagation with a homogenization method

In this paper, in order to distinguish the influence of both interface debonding defect and the mesoscale structure of concrete core on the stress wave field and the response of an embedded Piezoelectric-lead-zirconate-titanate (PZT) sensor in rectangular concrete filled steel tube (RCFST) members efficiently, a two dimensional (2D) mesoscale numerical concrete homogenization approach for concrete core considering the random distribution of circular, elliptical and irregular polygonal aggregates is proposed firstly. Then, mesoscale simulation on stress wave fields within the cross-section of RCFST members with and without interface debonding defects using both mesoscale models and their homogenization models are carried out, respectively. The effect of both mesoscale structure of concrete core and the interface debonding defects on the stress wave field of each member is discussed and the efficiency of the homogenization approach is illustrated. Therefore, the time-domain response of an PZT sensor embedded in the concrete core of RCFST members coupled with PZT patches under sweep frequency excitation signal is determined with multi-physics field simulation and compared when both mesoscale models and their homogenization models are used. Then, the sensitivity of the wavelet packet energy of the embedded PZT sensor response on the variation of both mesoscale structure of concrete core and the dimension of interface debonding defects is investigated in details. Finally, in order to illustrate the difference in the significance of the effect of interface debonding defect and the mesoscale structure of concrete core on stress wave propagation, comparative test with a set of RCFST members without and with interface debonding defects is carried out. Test results also show that the influence of interface debonding defects on embedded PZT sensor response and the stress wave fields is dominant. The detectability of interface debonding detection approach using stress wave measurement is illustrated efficiently with the proposed equivalent homogenization mesoscale modelling approach even the mesoscale structure of the concrete core is considered.

A Study on the Theoretical Calculation Method for Spherical Stress Wave Field in Linear Hardening Materials under Impact Load

基于线性硬化塑性本构模型，建立了冲击载荷作用下弹塑性球面应力波场的理论求解方法。首先，分析了冲击载荷卸载速率对球面应力波传播的影响，得到了三种不同类型的应力波传播图像；在此基础上，建立了弹性阶段、塑性加载阶段以及卸载阶段球面波动方程的理论求解方法，给出了质点位移、质点速度、应力和应变等物理量的计算方案。与已有理论方法相比，该方法考虑了不同载荷卸载速率条件下应力波的不同传播情况，并且给出了卸载阶段应力波参量计算方法，具有更广的适用范围。利用上述方法计算了恒定冲击载荷和不同指数衰减冲击载荷作用下弹塑性球面应力波场参量，在弹性阶段和塑性加载阶段，理论计算得到的物理量与已有理论方法和数值模拟结果基本吻合，在卸载阶段，已有理论方法不再适用，而本文理论计算得到的物理量与数值模拟结果基本吻合，验证了该理论方法的正确性。

Time Reverse Modeling of Damage Detection in Underwater Concrete Beams Using Piezoelectric Intelligent Modules.

Underwater cracks in concrete structures are often difficult to detect due to their complexity of the service environment. With numerical and experimental analysis of concrete beams immersed in water, an active monitoring system, based on a cement-based piezoelectric intelligent module array (CPIMA), was developed to locate and quantify the underwater cracks. Time reversal (TR) of the stress wave field is accomplished to focus on the crack area through the concrete beam specimen by the system. First, a piezoelectric actuator is applied to emit the initial propagating wave, which can be reflected, attenuated, and diffracted by the crack, transmitted through water filled in the crack, as well as diffracted by the coarse aggregates. To extract the damage waveforms associated with the crack and analyze the robust time-reversal invariance under the high-order multiple scattering effect, a pair of homogeneous and heterogeneous forward finite element (FE) models is established. Then, the damage waveforms are time-reversed and re-propagated in the inverse numerical model, where an optimal refocusing is achieved on the crack that behaves as an acoustic source. Finally, the damage area is obtained in the form of the stacked energy distribution of each time step. The focus results are represented by cloud images and compared with root-mean-square deviation (RMSD) values. Numerical simulation and experiments show that this method can identify and quantify underwater cracks effectively.

Use of numerical methods for identifying the number of wire breaks in prestressed concrete cylinder pipe by piezoelectric sensing technology

With theincreasing demand for long-distance transfer of water, prestressed concrete cylinder pipe (PCCP)has become the main pipe type due toits advantages among the pressure pipes. Detection for wire breaks is essential to prevent burst caused by a build-up of broken wires. After research on previous detection techniques, an innovative method based on piezoelectric sensing technology was proposed in this study. Multi-physics field prestressed concrete cylinder pipe (PCCP)-piezoelectric lead zirconate titanate (PZT) coupling finite element models containing actuators and sensors were established accordingly and taken on the linearity measurement to validate the model feasibility. A varying number of wire breaks were simulated in PCCP specimens with a diameter of 4 m to investigate their sensitivity to low-frequency sinusoidal and pulse signals. The stress wave field diagrams compare the healthy specimens versus the specimens with wire breaks at various time points to determine why the output voltage signals on the sensors change. Two types of damage indices, relative percentage deviation based on energy (RPDE) and amplitude (RPDA), were adopted to estimate the status of the wire breaks. The computation results indicated a linear correlation between the excitation and output voltages. Both the sinusoidal and pulse voltage signals were sensitive to the wire breaks, and the output voltage amplitudes changed with different low frequencies and numbers of wire breaks. However, there were some differences between the changing trends. Diffraction and reflection caused by wire breaks in stress wave propagation were the immediate causes of the energy loss and the time delay of primary wave. Furthermore, some other wave dissemination phenomena occurred, such as penetration, scattering, and reflection. The results coincide with the approximate experimental study regarding debonding detection of a concrete-filled steel tube and prove that the proposed approach is effective in identifying wire breaks. The damage index RPDE is suitable for determining whether there are broken wires and RPDA is fit for identifying the number of wire breaks for the 4 m-diameter PCCP specimens.

Vector-based elastic reverse time migration based on scalar imaging condition

The scalar images (PP, PS, SP, and SS) of elastic reverse time migration (ERTM) can be generated by applying an imaging condition as crosscorrelation of pure wave modes. In conventional ERTM, Helmholtz decomposition is commonly applied in wavefield separation, which leads to a polarity reversal problem in converted-wave images because of the opposite polarity distributions of the S-wavefields. Polarity reversal of the converted-wave image will cause destructive interference when stacking over multiple shots. Besides, in the 3D case, the curl calculation generates a vector S-wave, which makes it impossible to produce scalar PS, SP, and SS images with the crosscorrelation imaging condition. We evaluate a vector-based ERTM (VB-ERTM) method to address these problems. In VB-ERTM, an amplitude-preserved wavefield separation method based on decoupled elastic wave equation is exploited to obtain the pure wave modes. The output separated wavefields are both vectorial. To obtain the scalar images, the scalar imaging condition in which the scalar product of two vector wavefields with source-normalized illumination is exploited to produce scalar images instead of correlating Cartesian components or magnitude of the vector P- and S-wave modes. Compared with alternative methods for correcting the polarity reversal of PS and SP images, our ERTM solution is more stable and simple. Besides these four scalar images, the VB-ERTM method generates another PP-mode image by using the auxiliary stress wavefields. Several 2D and 3D numerical examples are evaluated to demonstrate the potential of our ERTM method.

Wave propagation simulation and its wavelet package analysis for debonding detection of circular CFST members

In order to investigate the interface debonding defects detection mechanism between steel tube and concrete core of concrete-filled steel tubes (CFSTs), multi-physical fields coupling finite element models constituted of a surface mounted Piezoceramic Lead Zirconate Titanate (PZT) actuator, an embedded PZT sensor and a circular cross section of CFST column are established. The stress wave initiation and propagation induced by the PZT actuator under sinusoidal and sweep frequency excitations are simulated with a two dimensional (2D) plain strain analysis and the difference of stress wave fields close to the interface debonding defect and within the cross section of the CFST members without and with debonding defects are compared in time domain. The linearity and stability of the embedded PZT response under sinusoidal signals with different frequencies and amplitudes are validated. The relationship between the amplitudes of stress wave and the measurement distances in a healthy CFST cross section is also studied. Meanwhile, the responses of PZT sensor under both sinusoidal and sweep frequency excitations are compared and the influence of debonding defect depth and length on the output voltage is also illustrated. The results show the output voltage signal amplitude and head wave arriving time are affected significantly by debonding defects. Moreover, the measurement of PZT sensor is sensitive to the initiation of interface debonding defects. Furthermore, wavelet packet analysis on the voltage signal under sweep frequency excitations is carried out and a normalized wavelet packet energy index (NWPEI) is defined to identify the interfacial debonding. The value of NWPEI attenuates with the increase in the dimension of debonding defects. The results help understand the debonding defects detection mechanism for circular CFST members with PZT technique.

Numerical study on the mechanism of active interfacial debonding detection for rectangular CFSTs based on wavelet packet analysis with piezoceramics

In recent years, Piezoelectric Lead Zirconate Titanate (PZT) based active interfacial debonding defect detection approach for concrete-filled steel tubular (CFST) columns has been proposed and validated experimentally. In order to investigate the mechanism of the PZT based interfacial debonding detection approach, a multi-physics coupling finite element model (FEM) composed of surface-mounted PZT actuator, embedded PZT sensor and a rectangular CFST column is constructed to numerically simulate the stress wave propagation induced by the surface-mounted PZT actuator under different excitation signals with different frequency and amplitude. The measurements of the embedded PZT sensor in concrete core of the CFST columns with different interfacial debonding defect lengths and depths are determined numerically with transient dynamic analysis. The linearity between the PZT response and the input amplitude, the effect of different frequency and measurement distance are discussed and the stress wave fields of CFST members without and with interface debonding defects are compared. Then, the response of the embedded PZT in concrete core is analyzed with wavelet packet analysis. The root mean square deviation (RMSD) of wavelet packet energy spectrum of the PZT measurement is employed as an evaluation index for the interfacial debonding detection. The results showed that the defined index under continuous sinusoidal and sweep frequency signals changes with the interfacial defects length and depth and is capable of effectively identifying the interfacial debonding defect between the concrete core and the steel tubular. Moreover, the index under sweep frequency signal is more sensitive to the interfacial debonding. The simulation results indicate that the interfacial debonding defect leads to the changes in the propagation path, travel time and the magnitude of stress waves. The simulation results meet the findings from the previous experimental study by the authors and help understand the mechanism of interfacial debonding defect detection for CFSTs using PZT technology.

Dynamic response of a solid with multiple inclusions under anti-plane strain conditions by the BEM

In this work, a 2D problem in elastodynamics that involves the finite elastic solid containing multiple cylindrical and elliptical inclusions and/or cavities of arbitrary size, number, material properties and geometrical configuration is solved. More specifically, anti-plane strain conditions are assumed to hold and all external loads have a time harmonic variation. The numerical method used for this purpose is the direct, displacement-based boundary element method (BEM) with sub-structuring capabilities. The BEM employs frequency-dependent fundamental solutions for a point load in the unbounded continuum, and requires discretization of all external and internal surfaces and interfaces only. The method is well suited for the computation of stress concentration factors, while solution at points inside the domain of interest can be expressed directly in terms of boundary data without recourse to domain discretization. Thus, an effective numerical scheme is developed, verified and subsequently used for extensive parametric studies. The numerical results obtained here show a marked dependence of the stress and displacement wave fields on the shape of the inclusions, their material properties, number and position, as well as their mutual interaction with the incoming horizontally polarized shear (SH) waves. The potential of the BEM to efficiently produce accurate results for the dynamic response of both finite and semi-infinite solids that are strengthened and/or weakened by multiple inclusions, as compared to other domain-type methods, makes it a valuable computational tool for solving certain categories of engineering problems. These range from fields as diverse as material science and non-destructive testing evaluation, to seismology and exploratory geophysics.

Stress imparted by the great 2004 Sumatra earthquake shut down transforms and activated rifts up to 400 km away in the Andaman Sea

The origin and prevalence of triggered seismicity and remote aftershocks are under debate. As a result, they have been excluded from probabilistic seismic hazard assessment and aftershock hazard notices. The 2004 M = 9.2 Sumatra earthquake altered seismicity in the Andaman backarc rift-transform system. Here we show that over a 300-km-long largely transform section of the backarc, M≥4.5 earthquakes stopped for five years, and over a 750-km-long backarc section, the rate of transform events dropped by two-thirds, while the rate of rift events increased eightfold. We compute the propagating dynamic stress wavefield and find the peak dynamic Coulomb stress is similar on the rifts and transforms. Long-period dynamic stress amplitudes, which are thought to promote dynamic failure, are higher on the transforms than on the rifts, opposite to the observations. In contrast to the dynamic stress, we calculate that the mainshock brought the transform segments approximately 0.2 bar (0.02 MPa) farther from static Coulomb failure and the rift segments approximately 0.2 bar closer to static failure, consistent with the seismic observations. This accord means that changes in seismicity rate are sufficiently predictable to be included in post-mainshock hazard evaluations.

The steady-state oscillations of the elastic infinite cone loaded at a vertex by a concentrated force

In the proposed paper, a new problem on the steady-state oscillations of an elastic infinite cone is solved for the point oscillating force enclosed to a cone’s vertex. On a cone’s conic surface, the stresses are given. The auxiliary problem for a cone truncated by a spherical surface is formulated with the aim to obtain the solution of the initial problem. The solution is constructed with the help of the integral transformation method and the method of Green’s function. The limiting transition in the solution’s formulas is carried out to obtain the exact solution of the initial problem. The calculation of the displacements and the stress wave field of the cone is performed.

Analysis of Geometric Effects on Stress Wave Propagation in Epoxy Resins of Plate-Like Structure by Dynamic Photoelasticity Combined with Strain Gauge

Experimental studies have been conducted using the dynamic photoelastic technique combined with a strain gauge to investigate geometric effects on stress wave propagation in axially impacted epoxy resins of plate-like structure. Dynamic photoelasticity provides a means of visualizing the stress wave field inside a solid. A device that triggers the generation of stress waves by direct projectile impact is used to conduct high-speed photoelasticity and strain gauge measurements. This triggering is achieved by an electrical connection between projectile and sample. The geometric effects of the width-to-wavelength ratio on the propagation speed and attenuation coefficient of stress waves were analyzed for isotropic rectangular rods of different width-to-thickness ratios, the thickness being the same in each case. The experimental results for stress wave speed as a function of width-to-wavelength ratio are in reasonable agreement with theoretical predictions based on a modified Love's equation involving the geometric effects due to lateral inertia.

Cone model for two surface foundations on layered soil

In this paper, the cone model is applied to the vibration analysis of two foundations on a layered soil half space. In the analysis, the total stress field in the subsoil is divided into the free-field and the scattering field. Seed’s simplified method is adopted for the free-field analysis, while the cone model is proposed for analyzing the dynamic scattering stress wave field. The shear stress field and the compressive stress field in the layered stratum with two scattering sources are calculated by shear cone and compressive cone, respectively. Furthermore, the stress fields in the subsoil with two foundations are divided into six zones, and the P wave and S wave are analyzed in each zone. Numerical results are provided to illustrate features of the added stress field for two surface foundations under vertical and horizontal sinusoidal force excitation. The proposed cone model may be useful in handling some of the complex problems associated with multi-scattering sources.

Photoelastic simulation of the stress wave field around a tunnel in an anisotropic rock mass subject to shock load

The stress wave field around a tunnel in an anisotropic medium subject to shock load is analyzed using the dynamic photoelastic method. The influence of various factors on the distribution and magnitude of boundary stresses around the tunnel are studied by simulating the deformation process. The time dependence of the dynamic stress concentration factor on the tunnel walls is established

Stress wave fields in plates weakened by curvilinear holes with edge cracks

The dynamic fracture of plates weakened by holes with edge cracks and subjected to impulsive loading is studied using the dynamic photoelastic method. The time dependences of the stress intensity factors and the crack growth rate are examined for three models of plates with circular holes and edge cracks