Bending Stiffness Research Articles

Evaluating physico-mechanical properties of NaOH-treated natural fibres: Effects of polyolefin

The bottle gourd plant fibres (BGPF) and okra fibres were processed and refined (w/w 6 % NaOH) before being incorporated with polyolefin (polypropylene) for composite fabrication using a blending technique. The polyolefin matrix is used to develop composites with 5 % okra fibres and varying percentages (25, 30, 35 and 40 %) of BGPF. The results indicated that the "35 % BGPF +5 % okra +60 % polypropylene" composition achieved remarkable mechanical properties with tensile strength (26.95 MPa), tensile modulus (3.16 GPa), decreased elongation at break (1.71 %), bending strength (52.53 MPa), bending modulus (3.45 GPa), impact strength (14.25 kJ/m2), and hardness (69 D-shore). Moreover, these composites absorbed minimal water when a specific portion was submerged. The scanning electron microscopy (SEM) test on the composites revealed good fibre adhesion and adherence content between BGPF and okra fibres. Additionally, the thermo-gravimetric analysis and differential scanning calorimetry exhibited weight loss of composites during maximum cellulose degradation (80 %) at 483 °C. In the composites of the fibre-PP matrix, two distinct physical changes were observed indicating glass transition and degradation. However, the mechanical properties decreased after soil degradation. Thus, remarkable properties were achieved for the fibres-fibres and fibres-polyolefin (polypropylene) interfacial interactions.

Insert-injection moulding and post-thermal treatment of hybrid continuous and discontinuous glass-fibre-reinforced polyamide composite products

Insert-injection moulding enables direct interfacial bonding of hybrid continuous and discontinuous fibre-reinforced thermoplastic products and simultaneously influences dimension stability and mechanical performance. This study investigates the insert-injection moulding of short-glass-fibre-reinforced polyamide 6 (SGF-PA6) bonded with 8 wt% unidirectional continuous-glass-fibre-reinforced polyamide 6 (CGF-PA6), focusing on the dimensional and mechanical properties of the hybrid CGF-SGF-PA6 products, which are essential for engineering applications. Orthogonal experiments revealed that injection melt temperature and pack pressure significantly impact warping deformation and bending properties. The study found strong correlations between dimensional stability and mechanical strength, with interfacial bonding influencing mechanical strength only. Optimised injection moulding reduced warpage to below 0.1 mm, while increasing bending strength and modulus to 400 MPa and 10 GPa, respectively. Post-thermal treatment further enhanced mechanical properties but led to increased warpage. These findings highlight an integrative control strategy for dimensional and mechanical properties of insert-injection moulded hybrid continuous and discontinuous fibre-reinforced thermoplastic products.

An Analysis of the Flexural Stiffness and Horizontal Bearing Capacity of CFRP Composite Pipe Piles in Marine Environments

Carbon-fiber-reinforced polymer (CFRP) is a composite material consisting of a resin matrix reinforced with carbon fibers. This study focuses on CFRP composite pipe piles as the subject of investigation, exploring the impact of substituting steel bars with CFRP bars on the bending performance of pipe piles through rigorous three-point bending tests. The attenuation of flexural stiffness in CFRP pipe piles under a chloride salt environment was anticipated. The lateral bearing capacity of CFRP pipe piles was calculated by introducing a stiffness degradation coefficient for the piles and utilizing the finite difference method. The findings of the analysis suggest that as the CFRP reinforcement replacement rate increases, the initial bending stiffness of the composite pipe pile experiences a corresponding decrease. After serving for 28.15 years, the steel reinforcement within the pipe pile commences rusting, resulting in a nonlinear decline in the bending stiffness of the composite pipe pile. As the service time of pipe piles increases, a higher replacement rate of CFRP reinforcement results in a slower attenuation of pile stiffness. Consequently, both the horizontal displacement at the top of the pile and the bending moment along the body of the composite pipe pile gradually increase over time. During the same service period, the higher the rate of CFRP reinforcement, the less noticeable the attenuation in the horizontal bearing capacity of the pile shaft.

Shear performance of glued and screwed timber-steel composite connections for composite timber-steel beams

Mid- to high-rise mass timber buildings gained popularity in the last decade. Yet, engineered wood products (EWPs) used to erect these buildings have structural limitations. EWPs present brittle failure modes, particularly in bending, shear and tension, and have a low modulus of elasticity resulting in shorted spans and deeper beams relative to those in the steel and reinforced concrete counterparts. Timber-steel hybrid beams represent a potential sustainable solution to overcome these limitations by taking advantages of the high strength, stiffness and ductility of steel, and the high capacity to weight ratio of timber. However, for this solution to be structurally performant, it is essential to create effective composite action between the two materials. This study therefore compares the structural efficiency of various bonding techniques between the steel and the timber materials. Two sets of assembly solutions, representing four connection types, were proposed and experimentally investigated: (1) connecting an embedded steel plate into the timber elements by using either polyurethane (PUR) structural adhesive with two manufacturing variations or 14 G×75 mm heavy duty screws, and (2) connecting a steel plate on the surface of the timber element using either PUR structural adhesive with self-tapping M4×40 mm screws or only self-tapping screws. Softwood Laminated Veneer Lumbers (LVL) and Grade 350 steel plates were used in the experimental tests. All bonding techniques were tested in shear. The shear capacity, the slip stiffness and the failure mode were evaluated. Additionally, the efficiency of the proposed manufacturing solutions was quantified by analytically evaluate the effective bending stiffness of a timber-steel composite beam manufactured with different bonding techniques being investigated. Results indicated that the glued connections allowed a significantly more efficient composite action, with failure occurring in the timber instead of at the composite interface and near-full composite action was reached, than the screwed connections. To achieve high composite action with the screwed solutions, a large number of screws was needed which may incur high manufacturing costs.

New four-point bending test protocol for the strength grading of timber: relationship between local and global modulus of elasticity (MOE) of maritime pine

ABSTRACT This study focuses on the characterisation of maritime pine according to standards EN408 and EN384 required for timber grading. A comparison of the EN408 bending test setup is performed with a new four-point bending protocol, reducing as much as possible, the effects of the shear force in the span where the deflection is measured. The study highlights difficulties to estimate accurately, the elasticity modulus of wood by using EN408 bending test setup. This is probably due to inaccuracies in the measurements of small curvatures and due to the local heterogeneities of wood. An original four-point bending test is proposed with 75% of the span of the wood beams in pure bending. This configuration clearly exhibits the convergence of measurements, in comparison to EN408 setup. The deformations generated by this new loading protocol allow a better evaluation of the bending modulus E 0. Moreover, the study reveals that the proposed setup supplies an increase of elasticity modulus close to 20%. In addition, dynamic tests are also performed to characterise the Young’s modulus. The experimental results reveal a better agreement between static test, using the new four-point bending configuration and dynamic method, than considering EN408 as a reference.

Fabrication of PBAT/lignin composite foam materials with excellent foaming performance and mechanical properties via grafting esterification and twin-screw melting free radical polymerization

As one of the mainstream biodegradable materials, poly(butylene adipate-co-terephthalate) (PBAT) foams offer a sustainable alternative to traditional plastic foams, effectively reducing environmental pollution. However, the high cost and poor mechanical performance of PBAT foams impede their practical application. Herein, the glycidyl methacrylate-grafted biomass lignin (GML) was used to produce a PBAT/GML composite foam with good foaming performance and mechanical properties at high lignin-filling amounts by twin-screw melting free radical polymerization and supercritical CO2 foaming process. The compatibility of GML in the PBAT matrix was improved due to the formation of ester bonds in modified lignin, endowing the PBAT/GML (PGML) composite foam with exceptional foaming performance. Additionally, the mechanical properties of PGML composite foam were remarkably enhanced due to the introduction of the abundant aromatic structures of GML and the construction of a stable covalent crosslinking network. The compressive strengths and compression modulus of the PGML foam were improved by 2.53 times and 2.47 times, while its bending strength and bending modulus were improved by 1.27 times and 3.92 times compared to the neat PBAT. This research affords a new strategy for developing low-cost biodegradable biomass PBAT/lignin composite foam materials with good foaming performance and mechanical properties.Graphical abstract

Preparation and characterization of functional dual network hydrogel for motion monitoring in smart bra

The smart bra is a kind of sports underwear with providing health monitoring and comfort protection for women breast in sports. Developing smart sensing materials that combine comfort and functionality for sensing breast condition remains a challenge. Here, natural polysaccharide sodium alginate (SA), acrylamide (AM) monomer and chitosan (CS) and polypyrrole (PPy) in-situ polymerized from pyrole (Py) monomer were used as raw materials to successfully synthesize double network conductive hydrogel by two-step method. The results show that in the hydrogels, the entanglement and interpenetration of macromolecules produce toughness (tensile/compressive strength is ∼0.248 MPa/∼2.836 MPa), elasticity (tensile/compression elastic recovery rate is∼94.06 %/∼98.41 %) and durability (after 30 tensile/compression cycles conducting at 25 %, 50 % and 100 % constant strain keep at high recovery rate). The rich moisture content provides its adhesion (adhesion strength ∼4.7557 kPa) and flexibility (bending stiffness 1.0843 cN cm∼), presenting sufficient adhesion reliability and robustness to different substrates. The addition of PPy enables the hydrogel to have conductivity (6.77 × 10−2 S cm−1) and sensing performance (tensile/compression sensitivity is ∼1.94/∼1.43). The conductive hydrogel, as a flexible strain sensor, shows good adhesion, flexibility, elasticity and sensitivity in application of sports smart bra, can detect both the tensile behavior of skin and the compression state of tissue through its mechano-electricity, and accurately sense the changes of physiological parameters during movement. The conductive hydrogel with high elasticity and strength has broad application prospects in smart bra.

The effect of cycling shoe sole stiffness on sprint power output

Competitive and recreational cyclists use stiff-soled shoes that firmly attach to ‘clipless’ pedals. When compared to very flexible running shoes, very stiff cycling shoes with clipless pedals enhance power output during sprint cycling. However, a recent study showed no difference in power output or sprint performance between commercially available cycling shoes that span a range of longitudinal bending stiffnesses (∼200 to 500 N·m/rad). Thus, we sought to identify the likely range of sole stiffnesses below 200 N·m/rad over which reduced cycling shoe sole stiffness begins to decrease maximal power output. We measured the mechanical power outputs of 25 road cyclists during maximal sprints wearing shoes with identical uppers but with three different sole stiffnesses. Each participant completed nine 50 m sprints (three trials for each shoe) on a road with a steady, uphill grade of 9.1%. The three shoe sole conditions were: injected nylon (longitudinal bending stiffness 194 N·m/rad), moderate stiffness thermoplastic polyurethane (medium TPU) (43 N·m/rad), and low stiffness TPU (soft TPU) (9 N·m/rad) all ridden with the same clipless pedals. Stiffness was quantified using a simple testing apparatus. Power output decreased below the sole stiffness of ∼200 N·m/rad but only moderately. Maximal 1 s crank power (Pmax1) decreased −3.1% (ES = −0.59, p = 0.020) from Nylon to medium TPU and then further decreased −2.4% (ES 16 = −0.50, p = 0.054) from medium TPU to soft TPU. Interpolating our results suggests just a ∼1% loss in Pmax1 at a sole stiffness of 100 N·m/rad. Within reasonable limits, cycling shoe sole stiffness has only a small effect on power output.

IMST-based identification of time-varying cable forces in cable-supported bridges: Numerical, experimental, and field test validation

Accurately assessing the structural integrity of cable-supported bridges hinges upon the precise determination of time-varying cable forces. In this study, a novel method is proposed for identifying these forces, even with the challenge of having only a single accelerometer available. Leveraging an improved Multisynchrosqueezing Transform (IMST) with an efficient ridge extraction algorithm, this method offers a robust solution. The IMST is employed to construct a clearer time-frequency spectrum based on the monitored acceleration response of a cable. Subsequently, the time-frequency ridge extraction algorithm enables the derivation of the cable's instantaneous frequency. Ultimately, the time-varying cable forces are computed by using the axially loaded beam theory and considering the influence of bending stiffness. Validations through a numerical benchmark model and a scaled cable testing confirm the efficacy of this approach. Result indicates that the average error in identifying cable forces is less than 2.50% in the numerical simulation. Moreover, the method is successfully applied to a real-world bridge scenario, demonstrating its ability to accurately evaluate cable forces despite having access to only a single-point noisy acceleration response.

Thermal modification of fast-growing Firmiana simplex wood using tin alloy: Evaluation of physical and mechanical properties

Wood is an important structural material, but some undesirable properties limit its application in construction. This study investigated the effect of tin alloy thermal modification (TTM) on selected physical and mechanical properties of Firmiana simplex (Chinese bottletree) wood. Tin alloy thermal modification of F. simplex was performed in a tin alloy bath at two different temperatures (150 oC and 210 oC for 2 h and 8 h). Physical properties such as swelling, water absorption and density and mechanical properties like modulus of elasticity, modulus of rupture, impact bending, compression strength and Brinell hardness of tin alloy thermal modified and control samples were evaluated. The results showed that tin alloy thermal modification decreased the swelling of the wood to 4,85 %, 1,45 % and 6,99 % along the tangential, radial and volumetric coefficient and water absorption and density decreased to 53,10 % and 290 kg/m3 respectively compared to the control. Modulus of elasticity, modulus of rupture, impact bending, compression strength and Brinell hardness of tin alloy thermal modified F. simplex at 210 °C for 8 h decreased to 6366,1 MPa, 54,9 MPa, 2,7 MPa, 29,4 MPa and 1113,5 MPa respectively compared to the control. In conclusion, the tin alloy thermal modified wood at 210 oC significantly affected the physical and mechanical properties of the wood.

Identification of damage in timber I-beams using continuous wavelet transform of deflection measured with digital image correlation

The article presents a method for detecting damage in timber I-beams based on the continuous wavelet transform (CWT) of their static deflection, measured using the ARAMIS digital image correlation (DIC) system. So far, no detailed uncertainty analysis for this type of identification has been carried out. Filling this gap was the main motivation for the authors to conduct this research. For this purpose, analytical and experimental static deflection CWT analyses were performed for the timber I-beams with softwood flanges and oriented strand board webs, in which local cross-sectional weakenings were artificially introduced for verification purposes. A detailed analysis of the CWT uncertainty resulting from measurement errors and numerical data processing allowed its expression as a function of the beam axis position and the scale parameter. Based on the research, a new methodology was formulated for the diagnostic defect identification in timber beams related to bending stiffness reduction.

Analysis and mitigation of uncertainties in damage identification by modal-curvature based methods

The objective of this paper is to address and reduce the uncertainties associated with measurement noise and discretization in damage identification methods based on modal curvature analysis. The experimental case study considers the local reduction in the bending stiffness of a slender beam under free-free and simply supported boundary conditions. First, the analysis of error sources and their propagation is theoretically set up. Second, the mitigation of uncertainties in damage localization is pursued using a two-stage approach based on multiple hypothesis testing relative to the normalized indices and the definition of a combined macro-index. Finally, the Monte Carlo method is exploited to obtain the statistical error distribution of the experimental damage position and severity predictions by randomizing the numerical displacement mode shapes with the identified noise. The present analysis allows us to find the optimal number of sensors that minimizes the combination of bias and truncation errors, to highlight how sensor spacing and data noise affect damage localization, and to determine the uncertainty bounds of the predicted damage severity. The two-stage approach, enhanced by selecting thresholds related to real noise levels and tuned on SHM objectives, appears to improve identification accuracy compared to the separate use of damage indices based on absolute confidence levels.

Spatial and frequency identification of the dynamic properties of thin plates with the Frequency-Adapted Virtual Fields Method

Vibroacoustic inverse methods use the measured response of a vibrating structure to identify a structural parameter or a dynamic load. Two inverse methods are considered, the Force Analysis Technique (FAT) and the Virtual Fields Method (VFM). The Corrected Force Analysis Technique (CFAT) is a variant of FAT that corrects its singularity. This correction allows the method to be applied in the high-frequency domain, when the number of measurement points per flexural wavelength becomes small. In this study, the proposed novelty is the development of a Frequency-Adapted VFM (FA VFM) to the case of a Love–Kirchhoff plate. Thanks to this method, the VFM can now be applied to identify the equivalent bending stiffness and structural damping of a thin plate when the number of measurement points per wavelength is small. The method has previously been developed for an Euler–Bernoulli beam. An experimental identification of the complex bending stiffness of an locally damped aluminium plate using Laser Doppler Velocimetry (LDV) data and the developed method is performed. The experimental study shows for the first time that the FA VFM can be used to map the equivalent bending stiffness and structural damping as a function of position on a plate and identify these parameters as a function of frequency over a large frequency band. The results of the Frequency-Adapted VFM are compared with those of CFAT and the classical VFM approach. FA VFM results are more accurate than those of classical VFM and similar to those of CFAT.

Structure and properties of homogeneous toughened poly(vinyl alcohol) blended membrane and exploration of application in membrane separation

Polyvinyl alcohol (PVA) has excellent physical and chemical properties; however, its rigidity easily leads to brittleness and breakage during use. Additionally, due to intramolecular hydrogen bonding, the dense structure of the film limits its application. This research used a self-toughening approach by homogeneously blending PVA 0588 and PVA 0499 with different molecular weights to enhance the toughness of PVA and create a porous structure for broader application in membrane separation. Porous PVA membranes were then produced through mechanical stretching. Rheological testing, differential scanning calorimetry, and dynamic thermomechanical analysis confirmed that the blend system is partially compatible. Mechanical characterization revealed that adding PVA 0499 decreased the tensile modulus, strength, and bending modulus of the blended film but increased the elongation at break, reaching a maximum of 179 %. This result indicates that homogeneous blending effectively achieved PVA self-toughening. After this, the PVA blended membrane underwent mechanical stretching. Results showed that the stretched membrane developed a porous structure with a PVA 0588 content of 60 wt%, yielding a pure water flux of 70.3 L m−2 h−1 MPa−1 and a glucan rejection rate of 91.07 %. The molecular weight cut-off test demonstrated that the resulting porous membrane was suitable for water treatment, effectively filtering substances with a molecular weight of ≥70 kDa. The membrane also exhibited notable antifouling properties. The hydrophilicity and high roughness of the porous membrane facilitated the formation of additional hydrogen bonds between the membrane surface and water molecules, thereby reducing direct contact between pollutants and the membrane surface. This study provides preliminary theoretical and experimental insights into enhancing PVA toughness and expanding its applications in membrane separation. Furthermore, homogeneous blending opens new avenues for improving the mechanical performance of polymers.

Research on the development and performance of flexible protective fabrics with knitted structure

Personal protective textiles (PPTs) protect humans from sharp objects. However, PPTs are designed primarily for protective performance, and their stiff material and single function make them unsuitable for long-term wear. In this study, we developed flexible protective textiles using advanced flat knitting technology. These textiles offer excellent cut resistance, good abrasion resistance, high flexibility, and warmth-retention properties. A flexible protective fabric (FPF) with knitted structure was designed with an outer layer that provides cut and abrasion resistance, an intermediate layer, and an inner layer for heat storage. The study examined the cut resistance, abrasion resistance, flexibility, thermal management, breathability and stability of the developed fabrics. FPF has excellent abrasion and cut resistance. The cut resistance of the fabric was tested in three directions. The warp cutting load was 2145 gf, while the weft cutting load was 2347 gf. The diagonal cutting load was the largest at 2364 gf, resulting in an A5 cutting grade for high cutting hazards. Compared with other protective fabrics available on the market, FPF stands out due to its softness and the smallest bending stiffness in both the warp and weft directions. Additionally, it has excellent thermal management performance and breathability, providing 53% insulation and 146 mm/s breathability. Stability tests have shown that FPF has excellent color fastness to perspiration, good cleaning stability and aging stability for cut resistance, flexibility, warmth-retention properties and breathability.

Design optimization of automotive carbon fiber composite material floor laminate based on PSO-BFO algorithm

In response to the current challenges of low precision and efficiency in the optimization of composite material layups, the insufficient lightweight of automotive body floors, and the high cost of carbon fiber composites, this study introduces an optimized design method for carbon fiber composite flooring layups. Based on implicit parametric technology, a hybrid PSO-BFO (Particle Swarm Optimization-Bacterial Foraging Optimization) algorithm is employed. This approach achieves an integrated optimization of materials, processes, and structures, thereby balancing and reducing costs. The SFE-CONCEPT is utilized to establish an implicit parameterization model for the body floor, which is validated through experiments and finite element simulation analysis. Concept design and modeling of the carbon fiber composite material floor laminate are performed. Continuous variable optimization is employed to determine the thickness, tile shape, and number of layers for the front, middle, and rear floors. A continuous variable discretization rounding strategy is used to obtain the discrete layer numbers for each laminate orientation of the composite material floor. The continuous fiber lamination strategy is applied to create different shared lamination regions. The PSO-BFO hybrid optimization method is proposed to optimize the lamination sequence as a multi-objective optimization, addressing the challenges of discrete lamination sequence, explosive combinations, and multiple variables in the optimization design of carbon fiber composite material floor laminates. The optimization results demonstrate improvements of 34.4% in floor quality M, 6.0% in static bending stiffness BS, and 5.3% in lightweight coefficient QLX using the proposed PSO-BFO method. PSO-BFO and PSO-GA (Particle Swarm Optimization-Genetic Algorithm) methods are more capable of obtaining global optimal solutions for complex optimization problems than single optimization algorithms. Still, the results obtained by the PSO-BFO method are more balanced.

Three-Dimensional Printing Limitations of Polymers Reinforced with Continuous Stainless Steel Fibres and Curvature Stiffness

This study investigates the printability limitations of 3D-printed continuous 316L stainless steel fibre-reinforced polymer composites obtained using the Materials Extrusion (MEX) technique. The objective was to better understand the geometric printing limitations of composites fabricated using continuous steel fibres, based on a combination of bending stiffness testing and piezoresistive property studies. The 0.5 mm composite filaments used in this study were obtained by co-extruding polylactic acid (PLA), with a 316 L stainless steel fibre (SSF) bundle. The composite printability limitations were evaluated by the printing of a series of ’teardrop’ shaped geometries with angles in the range from 5° to 90° and radii between 2 and 20 mm. The morphology and dimensional measurements of the resulting PLA-SSF prints were evaluated using μCT scanning, optical microscopy, and calliper measurements. Sample sets were compared and statistically examined to evaluate the repeatability, turning ability, and geometrical print limitations, along with dimensional fluctuations between designed and as-printed structures. Comparisons of the curvature bending stiffness were made with the PLA-only polymer and with 3D-printed nylon-reinforced short and long carbon fibre composites. It was demonstrated that the stainless steel composites exhibited an increase in bending stiffness at smaller radii. The change in piezoresistance response of the PLA-SSF with load applied during the curvature bending stiffness testing demonstrated that the 3D-printed composites may have the potential for use as structural health monitoring sensors.

Static Model of the Underwater Soft Bending Actuator Based on the Elliptic Integral Function

Underwater soft manipulators are increasingly used for grasping underwater organisms and cultural relics due to their compliance and ability to protect delicate objects. Unlike rigid manipulators, these soft manipulators feature underwater soft bending actuators that deform under external forces, making their shape and output force challenging to predict. Consequently, classical beam theory is no longer applicable. To address these issues, this article models the underwater soft bending actuator as a cantilever beam and establishes its shape and output force using elliptic integral functions. Additionally, this article proposes a method for determining the unknown parameters of the driver shape and output force model using optimization techniques and introduces a solution process based on the particle swarm optimization framework. Given the role of tensile and bending stiffness in the actuator’s performance, this paper employs a parameter identification method based on length and bending angle information. Tests demonstrate that the proposed method effectively estimates the deformation and output force of the underwater soft bending actuators, confirming its accuracy.

Advances in longitudinal equivalent bending stiffness analysis-novel nonlinear characteristics in the assembly process of prefabricated subway stations

The longitudinal bending stiffness of quasi-rectangular prefabricated subway stations plays a great important role in studying their mechanical behavior and conducting safety assessments. To address the issue of immature stress assumptions for existing prefabricated subway stations, three stress assumptions and five bending modes are proposed while considering the coupling effect between axial force and bending moment. The study investigates novel nonlinear characteristics in the longitudinal equivalent bending stiffness and the influencing factors during the assembly of an existing subway station. An effective method for identifying the longitudinal bending modes suitable for the prefabricated subway station is established, the proposed solution has a good agreement with measured longitudinal bending stiffness efficiency. The study demonstrates that the longitudinal bending mode of the prefabricated subway station shifts from "upward convex" to "downward concave" due to the stepwise assembly method. The longitudinal bending stiffness efficiency displays a significant hysteresis curve, eventually stabilizing at approximately 1 %. Upon completion of the monitoring ring assembly, the concrete bears both longitudinal tensile and compressive stress. When assembling 10 rings from the monitoring ring, the longitudinal reinforcing bars bear tensile stress. The longitudinal bending stiffness of the prefabricated subway station exhibits significant time-variable characteristics throughout the assembly process. The research findings can provide effective references for the analysis of longitudinal mechanics and bending performance during the assembly process.

Experimental identification of the bending stiffness and damping of plates using the frequency-adapted virtual fields Method

Inverse vibroacoustic methods can be used to identify the complex bending stiffness of a plate from its vibratory response. This work focuses on the Virtual Fields Method (VFM) and the Force Analysis Technique (FAT). The VFM uses functions called virtual fields to solve the Principle of Virtual Work, a weak form of equilibrium, and identifies complex bending stiffness. Here, the virtual fields are defined as piecewise functions over a surface smaller than the plate (virtual window). FAT uses a finite-difference scheme to discretize the fourth-order spatial derivatives of the displacement in the local equilibrium of the plate and thus estimates the bending stiffness. The application of a finite-difference scheme creates a bias in the identified stiffness, which increases with frequency. The Corrected Force Analysis Technique (CFAT) corrects this bias in the high-frequency domain. In this study, it is proposed to apply the CFAT principles to the VFM to adapt the method, using the virtual window size, so it can be applied it in the high-frequency domain. FAT, CFAT, the VFM and the Frequency-Adapted VFM will be presented. The method was tested on experimental data to identify the complex bending stiffness of an aluminium plate partially covered with a damping material.