Flexural Modes Research Articles

Structural Behaviour of Polystyrene Foam Lightweight Concrete Beams Strengthened with FRP Laminates

Lightweight concrete (LWC) is one of the most important building materials nowadays. Many research studies were focused on LWC produced using lightweight aggregates. However, limited work was cited for LWC produced using polystyrene beads. In this study, LWC beams strengthened with carbon fibre reinforced polymer (CFRP) and glass fibre reinforced polymer (GFRP) were experimentally tested to investigate the improvement in their flexural and shear behaviours. LWC in this investigation was achieved by partial replacement of normal aggregate by polystyrene beads and resulted in approximately 30% less weight compared to Normal weight concrete. Fourteen Reinforced Concrete (RC) LWC beams of 100 mm by 300 mm cross section having an overall length of 3250 mm were tested under four-point bending. These beams were designed, detailed, and tested to obtain flexural and shear mode of failure. These beams were divided into two groups based on the intended failure mode. In each group, six beams were strengthened using CFRP and GFRP laminates, while the remaining one beam was used as control. The tested parameters were the type of FRP, the width of the laminates used in shear strengthening, and the number of layers used in flexural strengthening. It was found that strengthening of LWC beams using CFRP and GFRP layers resulted in increasing the loading capacity and decreasing deflection as compared to control. The strengthening with CFRP and GFRP is also suitable in reducing the crack width and crack propagation which is more significant in LWC beams. The experimental results were also compared with the expressions in codes for forecasting the strength of LWC beams and it was that these expressions are compatible with the experimental results.

Flexural fatigue behavior of novel co-curing damping composite structures

In order to investigate the flexural fatigue performance of novel carbon fiber reinforced bismaleimide resin matrix damping sandwich composite structure prepared by co-curing process, three-point flexural fatigue tests were carried out on composite structure embedded with damping films of different thickness. The flexural fatigue failure mode, fatigue life and damage evolution law of sandwich beam were obtained, and different damage mechanisms of sandwich beam under flexural fatigue load were analyzed. The S-N curves of undamped composite were fitted by three-point flexural fatigue test. The fatigue characteristics of the undamped composite and damping composite were compared and analyzed. The results showed that the fatigue life of damping composite decreased with the increase of damping layer thickness under the same cyclic load. A numerical simulation model of three-point flexural fatigue performance of damping composite was established. The fatigue life variation trend of damping composite under different damping layer parameters (number of damping layers, location of damping layers, distribution of damping layers) was further simulated, which provided theoretical basis for the fatigue design of damping composite.

Experimental measurements of a prototype vibraphone bar with three-dimensional cutaway geometry.

This article discusses the fabrication and testing of two prototype vibraphone bars. Bar cutaway shapes vary along both the length and width of the bar, whereas previous examples in the literature vary only along the length. Bar shapes were designed using a method, previously published by the authors, that tunes both flexural and torsional modes. Fabrication issues prevented the first prototype from achieving its desired geometry. These issues were resolved in the second prototype, which accurately reflects its designed geometry and produces modal frequencies that agree well with design targets.

Control of low-frequency guided elastic wave modes in a hollow pipe using a meta-surface

A locally resonant meta-surface for preferential excitation of a guided mode in a hollow pipe can improve ultrasonic guided wave inspection of pipelines. The proposed meta-surface comprises a periodic arrangement of bonded prismatic rod-like resonators in the circumferential and axial directions of the pipe. We demonstrate the presence of bandgaps for the low-frequency axisymmetric longitudinal modes L(0,1) and L(0,2) and the torsional mode T(0,1). The generated bandgaps can be used to filter the higher harmonics associated with the system nonlinearity to improve nonlinear ultrasonic measurements on pipes. These bandgaps exist even for the non-axisymmetric flexural modes but with their hybridized dispersion curves exhibiting mode-coupling for higher circumferential orders. Moreover, a “partial” bandgap is obtained where preferential transmission of the L(0,2) mode over L(0,1) is possible. We discuss the potential advantages of this partial bandgap to improve pipeline inspections using the L(0,2) mode. Time-domain finite element analyses are used to validate the presence of these bandgaps under radial, circumferential, and axial excitation that mimics the excitation using a ring of piezoelectric transducers. Finally, we discuss the influence of resonator spacing, filling fraction, and the number of resonator rings on the bandgaps for an informed meta-surface design.

A Closed-Loop System for Resonant MEMS Sensors Subject to Blue-Sideband Excitation

This study reports a closed-loop system (CLS) for resonant micro-electromechanical systems (MEMS) sensors subject to blue-sideband excitation (BSE) for the first time. Compared with the conventional excitation scheme, which uses an AC signal with a frequency that is very close to or equal to that of the desired MEMS resonator mode, the BSE scheme applies an AC signal with a frequency equal to or near the sum of two resonant frequencies to excite the resonator. This requires a CLS to provide a sum-frequency excitation signal to serve as the resonator’s feedback driving signal for practical applications. The proposed CLS mainly consists of a digital lock-in amplifier (DLA), a phase-locked loop (PLL) and a BSE control module (BSE-CM), and is implemented using a field-programmable gate array (FPGA). Experiments showed that the system can track the combined frequency of two flexural modes of the resonator in real-time. In addition, a potential application of the CLS for resonant MEMS sensors subject to BSE is preliminarily demonstrated, showing that the sensitivity of a vacuum-packaged resonant MEMS accelerometer can be enhanced by 166%. This approach could also be applied to reduce the effects of the feedback phase, or to simultaneously monitor multiple parameters. This study represents critical progress for practical sensing using the BSE scheme.

Numerical Investigation of Shape-Memory Alloy–Reinforced Bridge Columns Subjected to Lateral Impact Loads

This paper numerically investigates the dynamic behavior of bridge piers reinforced with shape-memory alloy (SMA) rebar when subjected to lateral impact loads. Performance of SMA reinforced pier is compared with column reinforced by conventional steel rebar by performing finite-element (FE) simulations in LS-DYNA. The impact performance of the columns is evaluated by considering variations in different structural- and loading-related parameters including the type of SMA rebar, the length of SMA rebar (LSMA), the impact velocity (Vimp), and the axial load ratio (ALR). From the FE simulations, it is found that the use of SMA rebars at the plastic hinge regions and the impact loading height of the columns significantly enhances the impact resistance and the recoverability of the columns by reducing their damage levels and residual displacements. Also, the failure modes of the columns tend to govern by flexure by using SMA rebars, and the columns reinforced with Cu-based (Cu–Al–Mn) SMA rebars are more likely to fail in flexural modes compared to those reinforced with Ni-based (Ni–Ti) SMA rebars. However, the negative influences of SMA rebars on the impact resistance of the columns are found when LSMA exceeds 0.5 under impact loads with velocities greater than 15 m/s. In addition, an ALR greater than 0.1 considerably increases the impact resistance of the columns.

Experimental Research on Flexural Mechanical Properties of Ultrahigh Strength Concrete Filled Steel Tubes

Based on the project of the Guansheng Qujiang Bridge, the flexural mechanical properties of an ultrahigh strength concrete filled steel tube (UHSCFST) were discussed. A total of six UHSCFST beam specimens were tested, and the cube strength (fcu) of the core concrete reached 80.3–115.2 MPa. The effects of concrete strength on flexural bearing capacity, deformation characteristics, and failure modes of UHSCFST specimens were discussed. Test results showed that the bending failure modes of UHSCFST specimens were the same as those of ordinary ones. The failure of UHSCFST specimens was attributed to excessive deflection, and local buckling occurred in the compression zone. Moreover, the bending capacity of the specimens did not decrease, even if they had yielded. Although ultrahigh strength concrete was poured, all of the specimens displayed outstanding bending ductility. The main function of core concrete was to provide radial restraint for the steel tube to avoid premature buckling. When the steel content of the specimen section was constant, the strength increases of core concrete had a slight impact on the bending failure mode, bearing capacity and ductility of UHSCFST specimen. The research results can deepen the understanding of the mechanical behaviors of the UHSCFST composite truss structure.

Exceptional Points and Skin Modes in Non-Hermitian Metabeams

We present a non-Hermitian metabeam exhibiting an exceptional point (EP) induced by enforcing parity-time (PT) symmetry through applied external forces. The EP is formed by the hybridization of two flexural wave modes and its output displacement is enhanced by attaching two pillars on top of the beam. The introduction of a tiny mass perturbation that breaks the PT symmetry leads to a splitting of the eigenfrequencies at the EP with a square-root dependence on the perturbation mass. This effect manifests itself in a splitting of resonant peaks in the frequency response. The enhanced sensitivity of the EP paves the way to the detection of small perturbations such as tiny masses and cracks. Another property of the metabeam is the existence of skin modes whose energies are localized at one end of the beam and can be generated by implementing nonreciprocal feedback interactions between the pillars. We demonstrate that the skin modes are broadband and independent of the excitation positions. From a practical perspective, we show the great potential of skin modes in broadband energy harvesting. Our study proposes approaches to manipulate the non-Hermitian elastic wave phenomena, paving the way for the development of highly sensitive sensors, vibration control, and energy harvesting.

Linear and Nonlinear Optical Properties of a Doubly Clamped Suspended Monolayer Graphene Nanoribbon Nanoresonator

We studied the optical properties of a hybrid structure that was composed of a semiconductor quantum dot and a doubly clamped suspended graphene nanoribbon nanoresonator. We obtained analytical results for the linear and third-order optical susceptibilities of the hybrid system. The spectrum of the linear susceptibility exhibited a single resonance, and its position depended on the value of the on-resonance exciton energy and the exciton–nanoribbon resonator coupling strength coefficient; the amplitude of the resonance was independent of the values of these parameters. The third-order optical susceptibility spectrum exhibited a sharp resonance arising at low frequencies of the probe field, the position of which depended only on the frequency of the fundamental flexural phonon mode. It also presented a broader resonance arising at higher frequencies of the probe field, the position of which was determined both by the coupling strength coefficient and by the exciton frequency; its amplitude depended solely on the exciton–photon coupling strength.

A Study on the Applicability of the Impact-Echo Test Using Semi-Supervised Learning Based on Dynamic Preconditions.

The Impact-Echo (IE) test is an effective method for determining the presence, depth, and area of cracks in concrete as well as the dimensions of the sound concrete without defects. In addition, shallow delamination can be measured by confirming a flexural mode in the low-frequency region. Owing to the advancement of non-contact sensors and automated measurement equipment, the IE test can be measured at multiple points in a short period. To analyze and distinguish a large volume of data, applying supervised learning (SL) associated with various contemporary algorithms is necessary. However, SL has limitations due to the difficulty in accurate labeling for increased volumes of test data, and reflection of new specimen characteristics, and it is necessary to apply semi-supervised learning (SSL) to overcome them. This study analyzes the accuracy and evaluates the applicability of a model trained with SSL rather than SL using the data from the air-coupled IE test based on dynamic preconditions. For the detection of delamination defects, the dynamic behavior-based flexural mode was identified, and 21 features were extracted in the time and frequency domains. Three principal components (PCs) such as the real moment, real RMS, and imaginary moment were derived through principal component analysis (PCA). PCs were identical in slab, pavement, and deck. In the case of SSL considering a dynamic behavior, the accuracy increased by 7–8% compared with SL, and it could categorize good, fair, and poor status to a higher level for actual structures. The applicability of SSL to the IE test was confirmed, and because the crack progress varies under field conditions, other parameters must be considered in the future to reflect this.

Full-scale experimental investigation on the seismic performance of PC columns before and after repair of grouting defects

This research focused on investigating the influence of insufficient grouting on the seismic performance of precast concrete (PC) columns, connected using grouted sleeves, and validating the feasibility and reliability of the repair method for insufficient grouting. To realize these, five full-scale PC columns were tested under cyclic loads, including one specimen without grouting defects, two specimens with defect ratios of 45% and 60%, respectively, which were determined by previous cyclic test results of grouted sleeve connections (GSCs), and two repaired specimens which had initial defect ratios of 45% and 60%, respectively. The effects of defect ratios and repair actions were analyzed, and the test results indicated the following: 1) The bar slip dominated the failure of two specimens with defect ratios as expected, rather than the flexural failure mode for the specimen without defects. A rocking phenomenon was observed since the occurrence of bar slip, and the pinching phenomenon appeared for the corresponding hysteretic curves. The load-bearing, deformation and energy dissipation capacities were significantly lower than those of the specimens without defects. The increase in the defect ratio decreased the drift ratio associated with the bar-slip phenomenon, but the influence of the defect ratio on the seismic performance after the bar slip was negligible. 2) The bar-slip behavior was effectively prevented after the repair of insufficient grouting. Hence, the repaired specimens exhibited the expected flexural failure mode, and the load-bearing, deformation, and energy dissipation capacities were generally comparable with those of the specimen without defects. Rocking behavior and pinching phenomenon were not observed after repair. The negative influences of insufficient grouting were almost eliminated, thus validating the reliability of the repair method. The research outcome can serve as a reference for quality control of PC structures using GSCs.

Modulated flexural edge waves in a plate with its free edge structured by an array of grooves

A flexural edge wave (FEW) is a guided wave propagating along the free edge of a semi-infinite isotropic elastic thin plate. Here, we investigate the FEW in a plate with its free edge structured by an array of grooves, revealing the essence of a kind of modulated FEW. We analytically solve the dispersion relation of the modulated FEW by developing the coupled mode theory (usually used in diffraction optics and acoustics) that couples diffraction modes and high-order flexural waveguide modes, and discuss the propagation characteristics of the first- and second-order modulated FEWs (symmetric and antisymmetric modes, respectively). Based on the features of the dispersion curves corresponding to the unit cells of the plate with grooves of graded depths, we numerically and experimentally realize the rainbow trapping of the first-order modulated FEW and the mode conversion of the second-order modulated FEW to the bulk wave. Our work provides new ideas for the manipulation of flexural waves and has the potential to develop corresponding acoustic devices based on the FEW.

Influences of wrinkles induced by tows’ offset in automated fiber placement on the bending properties of composites

This paper studies the influence of wrinkles caused by tows’ offset on the bending performance of composite laminates during Automated Fiber Placement (AFP) manufacturing. In this paper, the different distances of tows’ offset are set to prepare laminates containing various wrinkles and obtain the characteristics of different wrinkles through the feature recognition algorithm. Then a three-point bending test is conducted to investigate the influences of different wrinkles on the flexural strength and failure mode of laminates. The results indicate that wrinkle defects reduce the flexural strength of the laminate by about 12% to 15%, and the flexural strength is positively correlated with the wrinkle smoothness S. As the wrinkles increase, the failure mode of the laminate gradually changes from local collapse under the punch to instantaneous shear failure in the wrinkle area, and the degree of warping and delamination increases. Therefore, avoiding wrinkle defects can effectively maintain flexural strength and reduce the extent of warping and delamination.

Observable responses of micro-cantilever array to dynamic acoustic forces at higher mode in the broadband frequency window

We develop a theoretical framework describing numerical approach to explore dynamic acoustic force sensitivity using micro-cantilever array in monomodal and bimodal operations. The excitation force at the second eigenmode frequency is supplied to the micro-cantilevers in monomodal operation. Since we focus on measurement sensitivity of acoustic forces at higher frequencies, deflections of micro-cantilevers at higher mode, second flexural mode, are obtained. In bimodal operations, external driving forces at the first and second eigenmode frequencies are applied simultaneously for the actuation of micro-cantilevers in an array. Depending on acoustic force strength, the application of driving force at higher eigenmode frequency in bimodal excitation scheme increases the phase sensitivity in measurement of acoustic forces within a particular frequency scope. For both excitation schemes, oscillation observables such as amplitude and phase shift are determined with respect to acoustic force frequencies for diverse acoustic force strengths. Simulation results suggest that wider high-sensitivity frequency band could be acquired, utilizing resonantly excited micro-cantilever array. For our case, we obtain the high-sensitivity frequency band of around 200–270 kHz and 440–570 kHz for the acoustic force strengths in the range of 126–1138.5 pN.

σh symmetry and electron-phonon interaction in two-dimensional crystalline systems

The coupling of electrons and phonons is governed wisely by the symmetry properties of the crystal structures. In particular, for two-dimensional (2D) systems, it has been suggested that the electrons do not couple to phonons with pure out-of-plane distortion, as long as there is a $\sigma_h$ symmetry. We show that such a statement is correct when constituents of the unit-cell layer are only located in the $\sigma_h$ symmetric plane; a prominent example of such a system is graphene. For those 2D crystals in which atoms are vertically located away from the horizontal symmetric plane (e.g., 1H transition metal dichalcogenides), acoustic flexural modes do not couple to the electrons up to linear order, while optical flexural phonons, which preserve $\sigma_h$ symmetry, do couple with the electrons. Our conclusions are supported by an analytic argument together with numerical calculations using density functional perturbation theory.

Piezoelectric patch vibration control unit connected to a self-tuning RL-shunt set to maximise electric power absorption

This paper presents a modular vibration control unit formed by a piezoelectric patch connected to a self-tuning RL-shunt, which can be bonded on thin structures to reduce the resonant response of a specific target low-order flexural mode due to a stationary stochastic excitation. The resistive and inductive components of the shunt are tuned online with an extremum seeking gradient search algorithm in such a way as to maximise the time-averaged electric power absorbed by the shunt from the resonant response of the target flexural mode of the structure. The tuning is thus implemented locally in the unit without the need of additional sensors to monitor the vibration of the structure. The paper presents both simulation and experimental results for a thin rectangular panel model structure, which is excited by a broadband stationary stochastic force and is equipped with five piezoelectric patches connected to the proposed self-tuning RL-shunts. To start with, the study shows that the resistance and inductance necessary to minimise the time-averaged resonant response of the target flexural mode closely match the values that would maximise the time-averaged electric power absorption by the shunt from the resonant response of the target flexural mode. Also, it shows that these two cost functions describe mirrored bell-surfaces with constant-inductance and constant-resistance principal axes. Hence, it proposes an independent inductance and resistance tuning sequence, which is based on an extremum seeking gradient search algorithm along the two principal directions of the electric power cost function. Finally, the online convergence to the optimal RL values of the proposed tuning algorithm is verified experimentally using a digital shunt.

Analytical Investigation on Behaviour of Cold Formed Deep Joist Channel Section

The application of cold formed steel elements in construction is becoming very popular due to several advantages like Speedy construction, higher strength to weight ratio, dimensional stability and recycled material. CFS is proposed to use as building components as beams, columns, Joists, wall panels etc. The load carrying capacity of cold-formed steel (CFS) joists can be enhanced by employing optimization techniques. Recent research studies have mainly focused on optimizing the bending capacity of conventional channel with and without lips that are used as joists. The objective of the study is to examine the flexural strength, failure mode and load-deflection of the cold formed steel double furred channel section with and without web openings under flexure.

Comparison of flexural behaviors between plain and steel-fiber-reinforced concrete beams with hybrid GFRP and steel bars

This study investigates the flexural behavior of steel-fiber-reinforced concrete (SC) beams with hybrid glass fiber reinforced polymer (GFRP) and steel bars. The experimental results of current SC beams are compared with those of the plain concrete (PC) beams conducted in our previous research. Taking account of the differences in nominal reinforcement ratio and reinforcement layout of seven tested SC beams, the test results including cracking load, ultimate load, failure mode, crack spacing and width, and mid-span deflection were firstly discussed. Then, a comprehensive comparison of flexural behaviors between SC beams and PC beams with same reinforcements was conducted in this paper. Especially, the crucial effects of type and strength of concrete on flexural capacity and failure mode of test beams were analyzed in detail. Finally, for concrete beams reinforced with hybrid (GFRP and steel) bars, the optimization of two balanced nominal reinforcement ratios was proposed to ensure the beam’s flexural failure in an appropriate-reinforced mode without rupture of GFRP bars.

Torsional Fracture Resistance of Niti Rotary Glide Path Files under Flexural Stress

This study aimed to evaluate the effects of flexural stress on the torsional fracture resistance of NiTi glide path files. PathFile #16/02, RaCe #15/04, RaCe Evo #15/04, HyFlex EDM #15/03, TruNatomy Glider #17/02, and V Taper 2H #17/04 were examined by scanning electron microscopy (SEM) (n = 3/brand) and subjected to differential scanning calorimetry (n = 2/brand). Torsional fracture resistance testing was performed in straight (ISO 3630-1) and flexural modes (n = 15/brand/mode). Flexural mode testing involved instruments rotating within a stainless-steel artificial double-curved canal. Ultimate strength and distortion angle until failure were recorded, and fractured instruments were examined by SEM. Statistical analyses involved independent sample t-test and one-way analysis of variance with Games–Howell pots hoc test. Austenitic transformation- finishing temperatures of heat-treated files were above body temperature. For RaCe Evo, HyFlex EDM, TruNatomy Glider, and V Taper 2H, the flexural mode resulted in a significantly higher distortion angle compared to the straight mode (p < 0.05). The maximum torque of RaCe Evo, HyFlex EDM increased with the flexural stress (p < 0.05). V taper 2H showed the highest distortion angle and ultimate strength. SEM showed typical patterns of torsional fracture for all tested files. The flexural stress positively affected distortion angle of heat-treated NiTi glide path files.

Adobe mixtures reinforced with fibrillated polypropylene fibers: Physical/mechanical/fracture/durability performance and its limits due to fiber clustering

This study assesses the feasibility of the incorporation of fibrillated polypropylene fibers (FPFs), an engineered multidimensional and multifilament fiber mostly used to reinforce concrete mixtures, into adobe mixtures (AMs), a traditional and manually-made material used to produce adobe blocks. The incorporation of FPFs was assessed using increasing dosages (0%, 0.25%, 0.5%, and 1% in wt% of clay soil) of FPFs. These fibers were gradually added and mixed with the clayey soil prior to incorporation of water to promote uniform mixtures with adequate fiber distribution to reduce the formation of fiber clusters. The impact of FPFs was evaluated in terms of its effects on the bulk density (physical), compressive and flexural strength (mechanical), flexural toughness indices (fracture) and water erosion resistance (durability) of AMs. Results indicate that increasing dosages of FPFs monotonically reduce average values of bulk density, as well as compressive and flexural strength of AMs. On the other hand, these increasing dosages of FPFs monotonically increase average values of water erosion resistance as well as flexural toughness indices, varying the flexural failure mode from brittle (unreinforced AM) to ductile (reinforced AMs) because of the adequate bonding and FPF-bridging effect after the crack generation as confirmed by instrumentation as well as digital image correlation evaluations implemented in this study. The significant reductions of bulk densities and compressive and flexural strengths obtained for fiber-reinforced AMs were related to the increasing number of fiber clusters found for increasing dosages of FPFs within the fiber-reinforced mixtures, which was evaluated using scanning electron microscopy analyses. For example, positively the AM incorporating 1% of FPFs increased, on average, the flexural toughness by 674% and reduced the bulk density and water erosion depth by, on average, 9% and 64%, respectively, when compared to the unreinforced AM. However, this large dosage of FPFs also generated a significant reduction of the compressive strength (60% on average) and the flexural strength (43% on average) when compared to the plain mixture. On the other hand, a small dosage of FPFs (0.25%) generated less significant improvements in terms of flexural toughness, bulk density, and water erosion (on average, increment of 58% and reductions of 2% and of 38%, respectively, when compared to the unreinforced AM). Yet, the latter mixture presented reductions, on average, of compressive and flexural strengths of 24% and 16%, respectively, when compared to the plain mixture, and these reductions were significantly smaller than the reductions obtained by the largest FPF dosage, due to the significantly smaller number of fiber clusters presented by the 0.25% dosage when compared to the 1% dosage. Finally, the mechanical performance limitations exhibited by the incorporation of FPFs, especially in large dosages, are related to generated fiber clusters due to the inherent morphology of these FPFs as well as the traditional manual confection process of AMs. Therefore, this study recommends the implementation of FPFs in AMs, but in small dosages and/or suggests the implementation of a mechanical mixing/compaction process that guarantee a more uniform fiber distribution that reduces the generation of fiber clusters.