Plate Modes Research Articles

Effect of lamination sequence and warhead shape on impact resistance of fiber‐metal laminates

AbstractIn this work, the failure mode and ballistic protection capability of the carbon fiber aluminum alloy laminated target plate under the impact of high‐speed projectile body were studied by ballistic impact test. The effects of the lamination sequence and warhead shape difference on the impact resistance of the laminated aluminum alloy and carbon fiber laminates were analyzed. Two kinds of projectile bodies, flat and oval head, were used to carry out multiple high‐speed impact experiments on four groups of targets with different stacking sequences. By analyzing the result, it is found that the lamination sequence of the target plate has a significant effect on the anti‐impact performance only when the flat head projectile impacts, while the ovoid projectile has almost no effect. In the fiber‐metal composite configuration, the aluminum plate placed in front of the carbon fiber plate showed the best resistance to flat head bullet impact, the ballistic limit speed reached 135 m/s, and the overall impact resistance improved by up to 26% compared with other configurations. Unlike the shear failure caused by flat head projectile, ovoid projectile impact can cause serious tensile and tear damage. Based on the experimental results, it is clear that the laminated structure has better penetration resistance against the flat head projectile, and the placement of aluminum plate on the impact surface can change the failure mode of carbon fiber laminates and improve the energy absorption level of composite plates.Highlights Unlike traditional fiber‐metal laminates, the target plate used in this experiment does not use adhesive, which makes the deformation of the two materials will not affect each other, which is conducive to the study of its own impact resistance. The mechanical behavior and damage failure mode of the target plate under high speed impact load were studied. The impact of ovoid projectile changes the damage failure mode of the target plate. For the configuration of fiber‐metal laminates, the ballistic limit value is as low as 100 m/s, and the energy absorption value fluctuates in the range of 145–190 J with the change of impact velocity. Compared with ovoid projectile, laminated material has stronger impact resistance to flat head projectile. The metal plate arranged on the impact surface can change the damage mode from shear failure to tensile failure, thus greatly improving the ballistic limit and impact resistance, overall impact resistance can be improved by up to 26%.

ZK61m magnesium alloy plate thickness effect on the impact characteristics of blunt projectiles experimental and numerical simulation studies

To study the impact resistance of ZK61m magnesium alloy plate, firstly, impact experiments were conducted on magnesium alloy plates of different thicknesses using a one-stage gas gun system to obtain the ballistic limit velocity (BLV) and failure mode of the target plate. In addition, the velocity of the punch plug was analyzed by the squeeze chisel block velocity model. Finally, the corresponding numerical simulations were carried out using the Lode parameter-independent MJC fracture criterion and the Lode parameter-dependent MMC fracture criterion, and the influence mechanism of the Lode parameter on the numerical simulation results was analyzed. The results show that under the impact of the blunt projectile, different thicknesses of target plates mainly occur shear plug failure, the BLV first tends to flatten and then increases sharply with the increase of its thickness. Besides, in the same velocity interval, the plugging velocity decreases with the increase of the target plate thickness; the Lode parameter has an obvious influence on the simulation results, which the MMC fracture criterion is more consistent with the experimental results. However, with the increase of the target plate thickness, both MMC and MJC fracture criteria show the phenomenon of overestimation of the material ductility.

Identification of guided Lamb wave modes in thin metal plates using water path corrected frequency – wavenumber [f-k] analysis

Acoustic microscopy is widely used for the material characterization of thin plates having thicknesses <100μm. For thin plate material characterization, the acoustic microscopy-based approach utilizes the guided Lamb wave modes generated in the plates by defocusing a single high-frequency focused transducer. Identification of the guided wave modes is vital in material characterization. Frequency-wavenumber analysis using 2D-FFT is commonly used to identify guided wave modes. In PVDF-based focused transducers used in acoustic microscopy, edge waves originating from the transducer rim influence the generation of guided waves, making the conventional frequency-wavenumber analysis erroneous. This study proposes a new water path corrected frequency-wavenumber (f-k) analysis using 2D-FFT to overcome the challenges imparted by the edge waves. In this approach, the water path of the Lamb wave modes is calculated and removed from the waveforms before performing 2D-FFT. The proposed approach has been demonstrated on thin metal plates of Aluminum, Copper and Brass having thicknesses of 45μm, 52μm and 52μm, respectively. A good correlation is obtained between theoretical and experimental results.

Experimental study on the impact response of the polyurea-coated 3D auxetic lattice sandwich panels subjected to air explosion

A series of air explosion experiments were carried out on the 3D polyurea-coated auxetic lattice sandwich panels in order to combine the advantages of auxetic materials and polyurea. The deformation, dynamic strain, and acceleration of the front and back plate were obtained. The results show that the dynamic response of the 3D polyurea-coated auxetic lattice sandwich panel could be divided into four stages: the shock wave action stage, the auxetic effect stage, the overall deformation stage, and the oscillation stage. The “N” type displacement time history of the back plate center due to the auxetic effect is found through the experiments. It is also found that the concave “hat-shaped” deformation mode of the back plate is opposite to the impact direction. This anomalous deformation mode is of great significance for impact protection. Finally, three dynamic response mode of the 3D polyurea-coated auxetic lattice sandwich panel subjected to air explosion is revealed. This study could provide a reference for the shock resistance design of structures.

Hybrid wave/current energy harvesting with a flexible piezoelectric plate

We investigate the dynamics and energy production capability of a flexible piezoelectric plate submerged close to the free surface and exposed to incident head gravity waves and current. A theoretical model is derived in which the flag and its wake are represented with a vortex line while the body of the fluid is considered to be inviscid. The model is employed to describe the hydrodynamic interactions between a flexible plate, its wake, gravity incident waves and the current. The model reveals two distinct vibration states of a piezoelectric device corresponding to almost similar optimal energy production levels. The first is associated with the cantilever fluttering mode of the plate, with limited dependency on the plate's flexibility across different Froude numbers and incoming wave frequencies. The other resembles the flow-induced flapping mode in more flexible plates, with the energy output showing a higher dependency on plate flexibility. The concurrent existence of these two energetic modes allows adjustment of the plate length to consistently achieve the maximum energy production level across different flow conditions. The role of the Froude number of the system's responses is explored and correlated to the appearance of gravity wave groups on the surface, each propagating with a different wavenumber. It is shown that a submergence depth of less than half of the body length is required to reach a high energetic condition in subcritical and critical flows. Finally, the optimal inductive and resistive values are related to proper matching between flow, mechanical and electrical time scales.

Research on Lateral Performance of Corrugated Steel Plate Shear Walls Connected with Beams Only under Horizontal Loads

This paper investigates the lateral performance of corrugated steel plate shear walls with corrugation laid vertically connected with beams only (CboSPSW). A numerical model for the CboSPSW was developed, and verified by a laboratory test. Based on the verified numerical model, extensive parametric analyses were carried out to investigate the key parameters’ effects on the shear performance of CboSPSWs, including the height ratio, aspect ratio, opening rate, and surrounding frame stiffness. In these parametric analyses, strength and lateral stiffness losses of the corrugated steel plate (CSP), buckling, and failure modes of the shear walls were investigated. In addition to these, a simplified model for the CboSPSW was developed to predict the shear performance of the shear wall. The results show that the CboSPSWs exhibit large strength, initial stiffness, and good displacement ductility. Compared with the corrugated steel plate shear walls with vertical corrugated steel plates connected with beams and columns (CbcSPSW), the strength of the CSPs decreased 15–28% in the CboSPSWs. The free edges of the CSPs in the CboSPSWs should be strengthened by adding stiffeners on one side or two sides of the CSPs in practical projects. The aspect ratio and opening rate of the CSPs should be controlled for strength decreases of the CSPs. The modified strip model can be used to predict shear performance of the CboSPSW with a reasonable accuracy.

Free Vibration Analysis of Trapezoidal Bi-Stable Laminates Supported at the Elastic Midpoint of the Median Line

This study investigates the natural vibration of trapezoidal bi-stable laminates (TBL) with elastic supports at the midpoints of the median lines. Configuration of the midplane of the TBL is expressed by a polynomial with 17 parameters. Then, the first order shear deformation theory, curing temperature, and nonlinear strain displacement relations combining energy principles are applied to obtain the bi-stable shapes numerically. Three translational springs and two rotational springs are added at the midpoint of the median line in the trapezoidal bi-stable laminate to acquire elastic point supports. And, by varying the stiffness of the springs, arbitrary elastic point support boundary conditions can be achieved. Chebyshev polynomials are applied to characterize the mode shape function of the TBL. The vibration mode functions of the TBL are mapped to a square area under the new coordinate system by using the coordinate mapping method. Furthermore, the effects of geometry, layup sequence, and spring stiffness on the natural vibrations of the TBL are analyzed, which provides a reference for research in this field. The innovation and highlights lie in the following: (1) the natural frequencies and modes of trapezoidal bi-stable plates are solved; (2) arbitrary elastic support is achieved by a set of artificial springs; (3) the influences of spring stiffness, layer sequence, and trapezoidal base angle on the natural vibration of a trapezoidal bi-stable plate are studied.

Wave Propagation in a LRPC Composite Double Panel Structure with Periodically Attached Pillars and Etched Holes

The locally resonant phononic crystal (LRPC) composite double panel structure (DPS) made of a two-dimensional periodic array of a two-component cylindrical LR pillar connected between the upper and lower composite plates is proposed. The plates are composed of two kinds of materials and periodically etched holes. In order to reveal the bandgap properties of structure theoretically, the band structures, displacement fields of eigenmodes and transmission power spectrums of corresponding 8 × 8 finite structure are calculated and displayed by using finite element method (FEM). Numerical results and further analysis demonstrate that if the excitation and response points are picked on different sides of the structure, a wide band gap with low starting frequency is opened, which can be treated as the coupling between dominant vibrations of pillars and plate modes. In addition, the influences of filled-in rubber, etched hole and viscidity of soft material on band gap are studied and understood with the help of “base-spring-mass” simplified model.

Novel design method of screwed connections of cold-formed steel built-up plates

The ultimate capacity and failure modes of composite plates have been widely investigated, especially those assembled by using self-drilling screws. The cold-formed steel (CFS) built-up plate connected by self-drilling screws is the research object in this paper. The screw built-up plate (SBP) is taken from the built-up flanges of the CFS built-up double-limbs closed column. In conjunction with the author's previous experiment, a theoretical model for the critical buckling stress of the SBP is presented. The innovation lies in considering the influence of the shear slip effect in the theoretical model. The kinematic relations between single plates of the SBP are given according to the energy method, and the stress calculation equation of the SBP is proposed through theoretical derivation. In this equation, a thickness reduction coefficient of the SBP is proposed. Subsequently, the influence of key parameters on the proposed equation is studied by finite element analysis. It indicates that the proposed equation of the critical buckling stress in this paper can truly reflect the true loading of SBP through comparative analysis of multiple parameters. Additionally, the study in this paper lays the foundation for the calculation of the bearing capacity of the CFS double-limbs closed built-up columns.

Experimental Investigation on Flexural Behavior of U-Shaped Steel–Concrete Composite Beams with Bolt Connections under a Negative Bending Moment

Because U-shaped steel beams filled with concrete have the advantages of reduced construction period and superior structural performance, they have been widely used as structural elements. In this study, the flexural behavior of newly developed bolt-connected U-shaped steel and concrete composite beams under a negative bending moment was experimentally evaluated. The main test variables were bolt spacing in bottom steel plates and types of U-shaped steel sections. Test results showed that the flexural behavior of the composite beams is determined by the plate-buckling mode of bolt-connected bottom steel plates. Composite beams with a greater bolt spacing than that in the standard AISI S100-16 experienced early plate buckling of the bottom steel plates, resulting in reduction of flexural stiffness and maximum flexural strength. Thus, the buckling mode of bolt-connected bottom plates should be considered for bolt-connected U-shaped composite beams under a negative bending moment. The longitudinal lips of U-shaped steel sections can increase the flexural performance of composite beams due to anchorage performance of the steel sections with lips.

Scale-up of Co–Ni cathodes produced from spent Ni–Cd batteries for hydrogen production in an oxy-hydrogen gas cell

Ni(II) and Co(II) ions are recovered from real leached positive electrodes of spent Ni–Cd batteries, and subsequently co-deposited on A36 carbon steel using direct and pulsed currents. The idea is to evaluate how variations in texture and composition of recycled coatings affect their catalytic activities for H2 production at microelectrolysis levels, and using an oxy-hydrogen gas (HHO) cell. The most active Ni–Co electrocatalyst in 0.1 M HClO4 or KOH towards hydrogen evolution reaction (HER) is formed using pulsed current at −50 mA cm−2, according to electrochemical measurements and gas chromatography (GC). This plating mode favors grain size refinement and pH rise during metal deposition, to prevent the formation of oxides/hydroxides with low catalytic activity arising in direct current. In the HHO cell, the most active Co–Ni coating produces 21.63 mL min−1 H2, while A36 carbon and 304 stainless steels present lower generations of 7.30 and 7.55 mL min−1, respectively.

Directivity of quasi-SH0 modes in cubic anisotropic media

We studied the zeroth order shear horizontal modes (SH0 modes) and the quasi-SH0 modes in cubic-anisotropic plates and proposed a formula to describe the scattering directivity of these guided wave modes in arbitrary directions. The quasi-SH0 waves has many unique advantages. However, their velocity and amplitude are influenced by the material anisotropy and change with incidence orientation. In our finding, when the guided wave incidence orientation coincides with the material symmetry plane, the quasi-SH0 modes’ amplitudes generated by a uniform force are approximately equal. Otherwise, the amplitudes are significantly smaller. The formula derived by reciprocity consideration explains this phenomenon. We applied the formula to monocrystalline silicon. The results also show that the quasi-SH0 mode is both velocity non-dispersive and directivity non-dispersive in low-fd (frequency thickness product) state. We established an experimental system based on EMATs and verified the theoretical predictions. This paper completes the theoretical basis for damage reconstruction and acoustic imaging by guided waves in complex structures with cubic anisotropy.

Study on welding buckling evaluation method based on inherent strain theory and eigenvalue buckling analysis

Welding buckling deformation is one of the foremost failure modes of thin plate welded structures. It is important to estimate welding buckling for structural design and process optimization. Inherent strain-based welding buckling evaluation methods have been proved to be valid, but the existing methods have low efficiency due to requiring multiple inherent forces. In this study, a novel welding buckling evaluation method based on longitudinal shrinkage force was established. The effectiveness of the proposed method was validated using a butt welded joint. In addition, this method was applied in a large-scale thin plate structure for evaluating the structural stability, the effects of heat input, welding manner, and external constraints on welding deformation and buckling were also discussed. The results reveal that the proposed inherent strain-based welding buckling evaluation method can be used to judge whether welded structures are buckled. The reduction of welding heat input and the use of single-sided welding can mitigate welding deformation. Increasing external constraints can not only reduce the welding deformation, but also improve the welding critical buckling load for preventing welding buckling.

Active Control Topological Valley Modes in Metamaterial Plates

Phononic crystals and metamaterials have a unique band structure that allows for the existence of topologically protected surface states. The topologically protected edge states can guide elastic waves without significant scattering or loss of energy. One of the most promising applications of topological insulators in wave guiding is in the field of acoustics, where they can be used to design highly efficient and robust acoustic wave guides. However, the high efficiency, precision, reconfigurability, and robustness of elastic waves remains challenging. The topological insulators provide a feasible method to design high-efficiency, robust, and low-backscattering waveguides. In this work, a novel design of hexagonal metamaterial plates composed of a base plate and piezoelectric patches is proposed. The hexagonal metamaterial plate can generate robust topologically protected edge waves via active control. The paths of the topologically protected edge waves can be tuned by adjusting the control parameters. The robustness and efficiency of the proposed hexagonal metamaterial plate are testified to by the numerical examples. These findings provide systematic theoretical guidelines for designing reconfigurable wave guides, elastic wave splitters, and novel elastic wave devices and hold great promise for the development of high-performance and versatile wave guide technologies with potential applications in a wide range of fields.

The role of blocking dynamics and current on wave scattering due to finite floating elastic plate

The role of wave blocking on flexural gravity wave motion with oblique incidence and current is discussed. The oblique wave incidence due to a finite floating elastic plate is investigated using the eigenfunction expansion method. The role of different wave propagating modes on reflection coefficient is discussed. The reflection and transmission coefficients, the surface elevation, and plate deflection in the presence of current are derived. The effects of flexural rigidity and the uniform current speed on reflection and transmission coefficients are analyzed. The resonating nature of reflection coefficient for some fixed values of plate length is observed. Significant effects of different combinations of wave propagating modes of plate covered regions and open water regions on the reflection and transmission coefficients are observed. The wave energy propagation from reflection coefficient decreases whenever the Froude number increases. It has been found that the amplitude of the plate deflection increases as the value of the Froude number increases. The amplitude and wavelength of the reflection coefficient are higher for the combination of the first propagating mode of the plate covered region and the second propagating mode of the open water region. Moreover, it is found that zero reflection and full transmission occurs periodically. Co-propagating waves are found to transmit more energy while counter-propagating waves reflect more energy. Higher values of flexural rigidity result in reduced wave energy transmission.

Axial Compressive Behavior of Cross-Shaped CFST Stub Columns with Steel Bar Truss Stiffening.

Concrete-filled steel tube (CFST) columns have been widely used in residential buildings due to their high bearing capacity, good ductility, and reliable seismic performance. However, conventional circular, square, or rectangular CFST columns may protrude from the adjacent walls, resulting in inconvenience in terms of the arrangement of furniture in a room. In order to solve the problem, special-shaped CFST columns, such as cross-shaped, L-shaped, and T-shaped columns, have been suggested and adopted in engineering practice. These special-shaped CFST columns have limbs with the same width as the adjacent walls. However, compared with conventional CFST columns, the special-shaped steel tube provides weaker confinement to the infilled concrete under axial compressive load, especially at concave corners. The parting at concave corners is the key factor affecting the bearing capacity and ductility of the members. Therefore, a cross-shaped CFST column with steel bar truss stiffening is suggested. In this paper, 12 cross-shaped CFST stub columns were designed and tested under axial compression loading. The effects of steel bar truss node spacing and column-steel ratio on the failure mode, bearing capacity, and ductility were discussed in detail. The results indicate that the columns with steel bar truss stiffening can change the final deformation mode of the steel plate from single-wave buckling to multiple-wave buckling, and the failure modes of columns also subsequently change from single-section concrete crushing failure to multiple-section concrete crushing failure. The steel bar truss stiffening shows no obvious effect on the axial bearing capacity of the member but significantly improves the ductility. The columns with a steel bar truss node spacing of 140 mm can only increase the bearing capacity by 6.8% while nearly doubling the ductility coefficient from 2.31 to 4.40. The experimental results are compared with those of six design codes worldwide. The results show that the Eurocode 4 (2004) and the Chinese code CECS159-2018 can be safely used to predict the axial bearing capacity of cross-shaped CFST stub columns with steel bar truss stiffening.

Defect identification in variable thickness waveguides using SH0 guided wave

Guided waves, especially Lamb waves, propagating in plate-like structures with constant thicknesses have been investigated intensively in the past decades in the context of structural health monitoring (SHM) and non-destructive testing (NDT). However, structures with variable thicknesses are also very common in practice, such as ship hulls whose thickness varies for satisfying various load conditions, and defect identification for such structures is also of importance. In this paper, we compare the propagation characteristics of both Lamb modes and SH0 mode in variable thickness plates and propose to use the SH0 mode for defect identification in such waveguides because of its non-dispersive property. First, the non-dispersive property of the SH0 mode in waveguides with variable thickness is demonstrated in theory. Then, a wave prediction method is adopted to illustrate the differences between the Lamb modes and the SH0 mode when propagating in waveguides with constant or variable thickness. Finally, experiments are conducted on a variable thickness plate to verify the non-dispersive property of the SH0 mode and further compare the results with those of the Lamb modes. Recently developed thickness-poled omnidirectional shear horizontal piezoelectric transducers (OSH-PTs) are used to produce pure SH0 waves. It is observed that the velocity of the Lamb modes may change significantly and the group velocity of the S0 mode even decreases by 55.1% during propagation, which hampers Lamb modes from defect identification in variable thickness plates. By contrast, the SH0 mode is non-dispersive thus promising for damage detection, and its effectiveness for defect localization in such structures is validated experimentally.

Spurious Modes in Laterally Excited Bulk Acoustic Resonators (XBARs): Analysis and Suppression

Laterally excited bulk acoustic resonators (XBARs) are plate mode resonators in which one of the higher-order plate modes transforms into the bulk acoustic wave (BAW) due to the very thin plates used in these devices. The propagation of the primary mode is usually accompanied by numerous spurious modes, which deteriorate resonator performances and restrict potential XBARs' applications. This article suggests a combination of different methods for insight into the nature of the spurious modes and their suppression. Analysis of the BAW slowness surface provides optimization of XBARs for single-mode performance in the filter passband and around it. The rigorous simulation of admittance functions in the optimal structures allows for further optimization of electrode thickness and duty factor. Finally, the nature of different plate modes generated in a wide frequency range is clarified via simulation of dispersion curves, which characterize acoustic mode propagation in a thin plate under the periodic metal grating, and visualization of displacements accompanying wave propagation. Application of this analysis to lithium niobate (LN)-based XBARs demonstrated that in LN cuts with Euler angles (0°, 4°-15°, 90°) and plate thickness dependent on orientation and varying between 0.05 and 0.1 wavelengths, the spurious-free response could be achieved. Due to tangential velocities of 18-37 km/s combined with the coupling of 15%-17% and feasible duty factor a/p = 0.5, the found XBAR structures can be applied in high-performance 3-6 GHz filters.

Ballistic performance of spherical fragments penetrating PCrNi3MoV target plates

PCrNi3MoV steel is a medium-carbon, low-alloy quenched and tempered steel that finds its applications in military gun barrels due to the high wear resistance and ablation resistance. To study the penetration and failure modes of PCrNi3MoV plates impacted by tungsten spheres, tungsten spheres of various diameters (5 mm, 8 mm, and 10 mm) were used to impact PCrNi3MoV steel plates with thicknesses of 6 mm, 9 mm, and 14 mm. The penetration performance of the spheres was analyzed for different velocities, and the ultimate penetration velocity of the plate was obtained. It was found that the primary failure modes of the PCrNi3MoV plate were compression pitting failure and shear failure. Using the dimensional analysis method, a relationship between the bulge height of the steel plate and the fragment velocity, an equation for the ultimate penetration velocity, and a relationship between the target penetration energy and the fragment velocity were obtained. Then, a projectile–target action index was proposed to describe the process of tungsten spheres with different velocities impacting target plates. The results suggested that under the same thickness of the target plate, a larger-diameter fragment required more kinetic energy to obtain the same ultimate penetration effect as a smaller-diameter fragment. The equations obtained through dimensional analysis predicted values that agreed well with experimental values, indicating that these equations can be applied to engineering applications.

Axial compressive behavior of PBL-stiffened double-skin composite walls considering local buckling: Experimental and theoretical investigation

Double-skin composite walls (DSCWs) stiffened with perforated ribs (perfobond leiste in German, abbreviated as PBL) has gained popularity in large-scale structures due to their industrial construction potential. This study aims to explore the axial compressive behavior of PBL-stiffened DSCWs, considering the post-local buckling effect of the faceplates. Six PBL-stiffened DSCWs underwent an experimental investigation under axial compressive loads to evaluate their failure mode, load-axial behavior, ductility, and local buckling behavior. The study also examined the effect of the spacing of transverse and longitudinal PBLs and the introduction of headed studs on the axial compressive behavior of DSCWs. Results reveal that decreasing the spacing of transverse PBLs enhances the confining effect on the infilled concrete, increasing the axial compressive resistance of DSCWs. The introduction of studs delays local buckling and results in strain-hardening of the faceplates, improving the axial compressive resistance of DSCWs. However, increasing the longitudinal PBL spacing weakens the out-of-plane restraint of the faceplates, decreasing both local buckling load and compressive resistance. Assuming the longitudinal PBLs as out-of-plane continuous elastic supports, the elastic critical local buckling coefficient of PBL-stiffened plates with unilateral restraints was derived using the Ritz method. Based on this, the critical relative stiffness of the PBL can be determined, which helps in identifying the local buckling mode of the PBL-stiffened plates. To estimate the post-local buckling behavior of PBL-stiffened plates with unilateral restraints, an effective area method was proposed. Finally, a formula was proposed to predict the axial compressive resistance of PBL-stiffened DSCWs, considering the post-buckling effect. A suggested design procedure for PBL-stiffened DSCWs was also provided.