Stress Wave Attenuation Research Articles

Flapwise Vibration of Rotating Functionally Graded Beam

Functionally Graded materials have been widely used in engineering applications due to the advantage of smooth and continuous variation in material properties, better fatigue life, less stress concentration, lower thermal stresses and attenuation of stress waves. By intelligently designing material constitutions and gradient distributions of FGMs, structures made of them can have excellent dynamic and thermodynamic characteristics. In the present study Flapwise vibration of rotating functionally graded beam is studied. The effective material properties are determined using Mori Tanaka Method. The natural frequencies are obtained using differential transform method (DTM). The effect of rotating speed, gradient index and hub radius on natural frequency are discussed.

Simulation of stress wave attenuation in plain weave fabric composites during in-plane ballistic impact

An analytical method is presented for the simulation of longitudinal stress wave attenuation in typical plain weave fabric composites made of E-glass/epoxy and T300 carbon/epoxy under in-plane ballistic impact. The stress wave propagation/attenuation simulation studies are carried out for the case of in-plane impact of projectiles on composite beam targets. Geometrical modeling of plain weave fabric composites and an algorithm for stress wave propagation/attenuation are presented. Studies are carried out for both free edge and rigid boundary conditions for different beams. Based on the analytical simulation, for typical plain weave E-glass/epoxy composite beams studied, it is observed that the stress intensity is about 5% of the incident value when the longitudinal stress wave reaches a distance of 110mm from the point of in-plane impact at the representative section.

Protein viscosity, mineral fraction and staggered architecture cooperatively enable the fastest stress wave decay in load-bearing biological materials

One of the key functions of load-bearing biological materials, such as bone, dentin and sea shell, is to protect their inside fragile organs by effectively damping dynamic impact. How those materials achieve this remarkable function remains largely unknown. Using systematic finite element analyses, we study the stress wave propagation and attenuation in cortical bone at the nanoscale as a model material to examine the effects of protein viscosity, mineral fraction and staggered architecture on the elastic wave decay. It is found that the staggered arrangement, protein viscosity and mineral fraction work cooperatively to effectively attenuate the stress wave. For a typical mineral volume fraction and protein viscosity, an optimal staggered nanostructure with specific feature sizes and layouts is able to give rise to the fastest stress wave decay, and the optimal aspect ratio and thickness of mineral platelets are in excellent agreement with experimental measurements. In contrary, as the mineral volume fraction or the protein viscosity goes much higher, the structural arrangement is seen having trivial effect on the stress wave decay, suggesting that the damping properties of the composites go into the structure-insensitive regime from the structure-sensitive regime. These findings not only significantly add to our understanding of the structure-function relationship of load-bearing biological materials, and but also provide useful guidelines for the design of bio-inspired materials with superior resistance to impact loading.

Stress Wave Attenuation in Noncollinear Structures Subjected to Impulsive Transient Loadings

AbstractThis paper presents an exploration of noncollinear Timoshenko beam structures for attenuating the stress waves generated from impulsive transient loadings. Due to the existence of the noncollinear segments, flexural waves are generated in addition to the longitudinal waves. Furthermore, the resulting waves are dispersive and thus provide higher potential for the attenuation of the stress waves. Symmetric patterns are found to be more appropriate for increasing the stress-wave attenuation capacity, as these patterns can eliminate bending stress effects at the boundary of the structures. More generally, an adaptive optimization methodology is developed to find the most efficient layout of the noncollinear stress-wave attenuators (NSWAs). This methodology uses genetic algorithms (GA), coupled with an explicit finite-element (FE) method for analyzing the wave-propagation behavior of the structures. The developed methodology is capable of updating the FE model of each trial solution, as the geometric c...

Study of the bottom-hole rock stress field under water jet impact

ABSTRACTOn the basis of analysis of the bottom-hole rock stress field under water jet impact, there are three types of coupling, which include the coupling of pore fluid and water jet, the coupling of pore fluid and rock matrix, and the coupling of water jet and rock matrix. The fluid-solid coupling model with the four main factors of three-dimensional in-situ stress, fluid column pressure, pore pressure, and water jet velocity is established and calculated by the finite element method and the finite volume method. The results show that the maximum principal stress of the bottom-hole increases with the increase of bottom-hole differential pressure. The maximum jet impact force is proportional to the square of the jet velocity; the pore pressures on the impact surface and along impact axis decrease in the form of cubic parabola with the increase of the distance. The local effect is obvious under water jet impact; the main affected area of the water jet is 2 times jet radius on the impact surface and 2.5 to 3.5 times jet radius along the impact axis when water jet velocity increases from 50 to 250 m/s, which is consistent with the stress wave attenuation theory. Study of the bottom-hole rock stress field under water jet impact provides a numerical research method for study of the water jet rock breaking mechanism under actual drilling conditions and the theoretical basis for faster and more efficient drilling.

Mixed convolved action principles in linear continuum dynamics

The paper begins with an overview of several of the classical integral formulations of elastodynamics, which highlights the natural appearance of temporal convolutions in the reciprocal theorem for such problems. This leads first to the formulation of a principle of virtual convolved action, as an extension of the principle of virtual work to dynamical problems. Then, to overcome the key shortcomings of Hamilton’s principle, the concept of mixed convolved action is developed for linear dynamical problems within the context of continuum solid mechanics. This new approach is broadly applicable to both reversible and irreversible phenomena without the need for special treatments, such as the artificial definition of Rayleigh dissipation functionals. The focus here is on linear elastic and viscoelastic media, which in the latter case is represented by classical Kelvin–Voigt and Maxwell models. Remarkably, for each problem type, the stationarity of the mixed convolved action provides not only the governing partial differential equations, but also the specified boundary and initial conditions, as its Euler–Lagrange equations. Thus, the entire initial/boundary value problem definition is encapsulated in a scalar mixed convolved action functional written in terms of displacements and stress impulses. The resulting formulations possess an elegant structure that provides a versatile framework for the development of novel computational methods, involving finite element representations in both space and time. We present perhaps the simplest approach by employing linear three-node triangular elements for two-dimensional analysis, along with linear shape functions over the temporal domain. Numerical examples are included to verify the formulation and to explore concepts of stress wave attenuation.

Interface profile optimization for planar stress wave attenuation in bi-layered plates

Stress waves scatter upon entering a new medium. This occurs due to the reflection and transmission of the waves, which depends on the impedance mismatch between the two materials and the angle of incidence. For a bi-layered structure with finite dimensions and constant impedance ratio, the scattering and intensity of the stress waves may be varied by changing the interface profile between the two layers. In this paper, a methodology is proposed for optimizing the interface profile between the layers of a finite bi-layered plate for the objective of planar stress wave attenuation. The bi-layered plates are subjected at one end to highly impulsive loadings with various durations, and the geometry of the internal interface is optimized for the purpose of minimizing the amplitude of the maximum reaction force at the opposite fixed end. The optimization methodology is based on a genetic algorithm, which is coupled with a finite element method for analyzing the wave propagation behavior of the plates. It is observed that the interface profile and the amount of stress wave attenuation depend on the duration of the applied impulsive loading, with higher amounts of attenuation obtained when the wavelength associated with the impulsive load is small compared to the dimensions of the bi-layered plates.

Phononic layered composites for stress-wave attenuation

The aim is to design a layered metamaterial with high attenuation coefficient and high in-plane stiffness-to-density ratio using homogenization to calculate and optimize the dynamic effective stiffness and mass density of layered periodic composites (phononic layers) over a broad frequency band. This is achieved by: (1) minimizing the frequency range of the first pass band, (2) maximizing the frequency range of the stop band, and (3) creating local resonance over the second pass band. To verify the theoretical calculation, laboratory samples were fabricated and their attenuation coefficient were measured and compared with the theoretical results. It is observed that over 4–20kHz frequency range the attenuation per unit length in the optimally designed composite can exceed 500dB/m; which increases with increasing frequency. A dynamic Ashby chart, depicting attenuation coefficient vs. in-plane stiffness-to-density ratio, is presented for various engineering materials and is compared with the fabricated metamaterial to show the significance of our design. This method can be used in variety of applications for stress wave management, e.g., in addition to match the impedance of the resulting composite to that of its surrounding medium to minimize (or essentially eliminate) stress wave reflection.

A novel fabrication approach for impact resistance laminated ceramics

Abstract A novel approach via tape casting and reactive hot pressing was presented to fabricate impact resistance laminated ceramics, and the designability of soft and hard interbedded microstructure, the controllability of in-situ interfaces and the dynamic performance potentials of the laminated ceramics were investigated. Laminated ZrO–Zr 2 CN/Si 3 N 4 ceramics with designable microstructure and controllable in-situ interfaces were fabricated by synergistically designing the thickness of the matrix and controlling the heating rate. The dynamic compressive responses of the laminated ceramic were tested with a range of high strain rates from 1.1 × 10 3 s −1 to 3.3 × 10 3 s −1 , and the results showed that the laminated ceramics obtain excellent dynamic compressive performance with high dynamic strength of 1.1–2.6 GPa, large pseudoplastic strain of 7.7–12.2% and good energy absorptivity of 23.34–34.59%. Multi-reflection and attenuation of stress wave at interfaces were the main reason of excellent comprehensive performance.

Analysis of the Stress Wave Effect During Rock Breakage by Pulsating Jets

Formation, propagation and attenuation of stress waves during rock breakage by pulsating jets are simulated by introducing the Johnson–Holmquist-Concrete nonlinear constitutive model, and using the smoothed particle hydrodynamics approach. The curve of stress over time at different locations of the rock surface under the action of high-velocity pulsating jets is obtained, as well as relationship curve between amplitude of stress wave and distance to jet action spot. Based on the computational results, breakage behavior of rocks under stress wave effect, and impacts of jet velocity and rock properties on stress wave effect are analyzed. The results show that the stress wave effect of pulsating jets is rather strongly localized, and the amplitude of stress wave decreases sharply with increasing distance to jet action spot. The intensity and effect range of stress wave are in direct proportion to jet velocity; besides, there is a threshold velocity regarding macroscopic failure of rocks. Rocks of different lithologies have somewhat different failure modes under stress wave action of pulsating jets; failure mode of low strength rocks like sandstone is mainly crack propagation under tensile stress during rock loading and unloading processes, whereas the failure mode of hard brittle rocks such as limestone and granite is mainly longitudinal failure caused by stress concentration.

Experimental investigation of the stress wave propagation inside a granular column impacted by a shock wave

A simple experimental technique, based on pressure transducers, capable of measuring the stress wave that propagates along the solid phase of a granular column after being hit head-on by a plane shock wave is presented. The technique is based on installing couples of gauges at different cross-sections along the granular column in such a way that one transducer measures the overall pressure acting on it while the other measures only the pressure exerted on it by the gaseous phase of the granular column. By means of the presented experimental technique the time histories of the stresses normal to the shock tube walls and data on the stress wave attenuation as it propagates downstream towards the shock tube end wall were obtained.

Planar stress wave attenuation in plates with circular voids and inclusions

This paper addresses planar stress wave attenuation in finite rectangular aluminum plates with circular voids and two types of inclusions; namely, high-density polyethylene (HDPE) and steel. The voids and inclusions act as a source of impedance mismatch and scatter the waves within the plates. The plates studied here have multiple numbers of circular voids and inclusions with different dimensions and positions, and are subjected to short duration transient loadings. To find the most efficient layout and dimensions of the circular voids and inclusions within these plates, a heuristic optimization methodology is developed based on Genetic Algorithms (GA). This methodology is coupled with the Finite Element (FE) method to analyze the wave propagation behavior of the plates under elastic response. The developed optimization methodology is capable of updating the FE model of each candidate design during the optimization procedure, as each in general has different geometric characteristics. The results show that the attenuation capacity of the plates with circular voids and inclusions is a complex function of the dimensions of the plates and the wavelength associated with the transient loading, as well as, the type, positions and dimensions of the voids and inclusions. It is observed that significant amounts of planar stress wave attenuation can be achieved, if the dimensions and positions of the circular voids and inclusions are selected appropriately.

On the relationship between the dynamic behavior and nanoscale staggered structure of the bone

Bone, a typical load-bearing biological material, composed of ordinary base materials such as organic protein and inorganic mineral arranged in a hierarchical architecture, exhibits extraordinary mechanical properties. Up to now, most of previous studies focused on its mechanical properties under static loading. However, failure of the bone occurs often under dynamic loading. An interesting question is: Are the structural sizes and layouts of the bone related or even adapted to the functionalities demanded by its dynamic performance? In the present work, systematic finite element analysis was performed on the dynamic response of nanoscale bone structures under dynamic loading. It was found that for a fixed mineral volume fraction and unit cell area, there exists a nanoscale staggered structure at some specific feature size and layout which exhibits the fastest attenuation of stress waves. Remarkably, these specific feature sizes and layouts are in excellent agreement with those experimentally observed in the bone at the same scale, indicating that the structural size and layout of the bone at the nanoscale are evolutionarily adapted to its dynamic behavior. The present work points out the importance of dynamic effect on the biological evolution of load-bearing biological materials.

Research on the Law of Propagation and Attenuation of the Explosive Stress Wave in Surrounding Rocks at Different Levels

By using nonlinear finite element analysis software-ANSYS/LS-DYNA, a numerical model was carried out to simulate the explosive stress wave generated from a single-hole coupling continuous charge blasting which varies with time at different levels of rock. Meanwhile, the propagation and attenuation law of the explosive stress wave at different rock levels was analyzed to gain an in-depth knowledge of rock explosion. The result shows that the explosive stress wave in rock is in the trend of exponential decay and presents three forms: shock wave, stess wave and seismic wave. It illustrates that numerical simulation can objectively reflect the failure law of rock blasting and provide theoretical and technical guidance for the corresponding practical engineering.

Study on Dynamic Behavior and Tensile Strength of Concrete Using 1D Wave Propagation Characteristics

Concrete structures are usually fractured under dynamic loadings, so it is important to have a clear knowledge of their dynamic behavior and tensile strength. First, the principle of one-dimensional (1D) stress wave reflection and superposition at free surface is briefed, and the spalling test method based on the Hopkinson bar is presented. Then, the attenuation law of stress wave is explored and the dynamic tensile/compressive moduli of concrete are evaluated according to the wave propagation experiment. Lastly, the influences of strain rate on the spalling tensile strength and failure patterns of concrete are further analyzed. The testing results demonstrate that the attenuation of stress wave accords with an exponential law when propagating in the concrete bar. The difference between the dynamic elastic moduli of concrete in tension and in compression is minor. Spalling tensile strength is sensitive to strain rate, and there is an obvious linear correlation between dynamic increase factor (DIF) and strain rate in a log-log plot for strain rate above 1.0/s; a single fracture occurs at low strain rate, while multiple fractures are detected with increasing strain rate.

Propagation of torsional waves in a thin circular plate of generalized phononic crystals

By introducing periodicity in the direction of variable vectors, the concept of existing phononic crystals (PCs) is expanded to generalized phononic crystals (GPCs), and a one-dimensional thin circular plate of GPCs (GPC plate) consisting of two alternating homogeneous materials is constructed. To show the characteristics of a torsional stress wave propagating along the radial direction, a transfer matrix is derived based on the basic torsional wave equation of the thin circular plate in cylindrical coordinates. A localization factor is introduced to evaluate the average attenuation of torsional stress waves in the structure, thus the band gaps are calculated. The inherent relationships between wave attenuation band, wave front and periodicity are discussed in detail. Finite element method simulations, numerical analyses and the insertion loss method are combined to investigate the effects of the main parameters on the torsional stress wave band in GPC plate. The results show that there are significant band gaps of the torsional stress waves caused by the periodicity of GPC plate, which are similar to those of existing PCs, and the localization factor can be used for the wave analysis of GPCs. In addition, structural and material parameters have a great influence on the wave attenuation band of the GPC plate.

Stress Attenuation Mechanism of Foam Core Sandwich Panels Subjected to Close-Range Blast Loading

A series of experiments have been conducted to investigate the stress wave attenuation mechanism and the response of sandwich panels made of steel face sheets with foam cores under blast loading in close range. Quantitative results including shock wave pressure and face sheet deflection were obtained and the deformation/failure modes of specimens were identified and discussed systematically. Results show that the face sheet deflection was reduced by adopting a higher density core, however, performance of sandwich panels in blast wave attenuation degrade. Cell collapse type of the central region of the foam core is dominated by brittle crushing under close-range blasting loading. All front face sheets produce localized failure at the focal area and global deformation in the peripheral region.

Stress wave micro–macro attenuation in ceramic plates made of tiles during ballistic impact

Abstract Stress wave attenuation studies during ballistic impact are presented for longitudinal tensile waves propagating along the planar direction within a ceramic plate made of hexagonal tiles bonded with an adhesive. When a stress wave reaches an interface between the ceramic tile and the adhesive layer, reflection and transmission of the incident stress wave takes place leading to attenuation of the wave. This is because of impedance mismatch at the ceramic–adhesive and adhesive–ceramic interfaces. This phenomenon is referred to as macro attenuation. Reflection and transmission of the impact induced stress waves would also take place at the interfaces between grains and grain boundaries within the ceramic plate. This would also lead to attenuation of stress waves, and is referred to as micro attenuation. Micro attenuation is modeled using the stress wave attenuation coefficient. Stress wave attenuation studies are carried out based on both micro and macro attenuation. An algorithm is presented for tracking impact induced planar stress waves and predicting their intensities and extent of attenuation. It is observed that stress wave attenuation is significant as the waves propagate within the ceramic plate. A combination of micro and macro attenuation would give the correct estimate of planar stress distribution around the point of impact.

Revisiting Kolsky bar data evaluation method

Conventional Kolsky bar data evaluation method is based on the assumption of stress equilibrium within the specimen during testing. When the objective is to generate stress–strain diagrams up to failure, damage initiation and evolution within the specimen should be taken into account. In that case, stress wave attenuation would take place and the assumption of stress equilibrium would not be valid. In this study, the data evaluation method is revisited and analytical expressions considering possible damage are presented. The revisited method gives higher specimen strain rate and strain compared with the conventional method. Both methods give the same specimen stress.

Microstructural design studies for locally dissipative acoustic metamaterials

Stress wave attenuation performance of locally dissipative acoustic metamaterials with various damped oscillator microstructures is studied using mechanical lattice models. The presence of damping is represented by a complex effective mass. Analytical solutions and numerical verifications of transmissibility are obtained for Kelvin-Voigt-type (KVO), Maxwell-type, and Zener-type (ZO) oscillators with viscous damping. Although peak attenuation at resonance is diminished, dissipative microstructures can provide broad spectrum attenuation without increasing mass ratio, obviating the bandgap width limitation of locally resonant microstructures. KVO gives the best broad spectrum performance akin to a low-pass filter for excitation frequencies above a cut-off value for a prescribed transmissibility criterion. For ZO, by tailoring the damping and stiffness, the frequency range of appreciable attenuation can at least span the bandgap widths of two limiting locally resonant cases. Static and frequency-dependent measures of optimal damping that maximize the attenuation characteristics are proposed. A transitional value for the excitation frequency is identified within the locally resonant bandgap, above which there always exists an optimal amount of damping that renders the attenuation for the dissipative metamaterial greater than that for the locally resonant case. Further microstructures with hysteretic damping depict a frequency-independent scaling in the effective mass and attenuation factor, but the bandgap width remains nearly the same as that for the corresponding viscously damped microstructures. This study demonstrates that dissipative microstructures, which are to some extent unavoidable in practical designs, when tuned, provide a means to substantially enhance the attenuation bandwidth of locally resonant acoustic metamaterials while also enabling the removal of the energy sequestered by the oscillators from the system.