Structural Stiffness Research Articles

Modal analysis and structural noise control of vehicle body frame

The structural noise inside the vehicle cabin is mainly low-frequency vibration, which is closely related to the modal characteristics of the vehicle frame. The finite element method was used to simulate and calculate the body frame under free modal conditions, and the first four effective modal shapes were obtained. The calculation error of the natural frequencies was verified through modal experiments. Taking structural stiffness into account, a sound-structure coupled model was established. The suspension connection point was selected as the excitation point, and a one-way dynamic load was applied to obtain the noise and vibration responses of the front and rear rows. Based on the modal analysis results, the top-roof reinforcement scheme was adopted to verify the noise suppression effect of the structure. The results show that the optimized structure can effectively suppress structural noise, which plays an important role in improving the NVH characteristics.

Seismic resistance analysis and optimization of gymnasium truss structure

The gymnasium is mainly composed of truss structure, with a large span, and requires high seismic performance. To ensure greater stability of the truss structure, modal analysis was conducted on the mechanical model, yielding the natural frequencies and modal shapes. In order to improve the seismic performance, BRB rods were added to the support points, and the frame structure was reinforced with diagonal braces. Through modal verification, it can be seen that the stiffness of the truss structure was significantly improved. The internal forces of the truss were simulated under the El Centro and Taft seismic wave conditions. The results show that the optimized structure can significantly reduce the internal forces and improve the overall seismic performance. The fundamental natural period of the reinforced structure is less than that of the unreinforced structure, and the stiffness of the reinforced steel structure increases, making it more sensitive to vertical seismic motion.

Local Stability Analysis of a Composite Corrugated Steel Plate Pipe-Arch in Soil

The straight part of the corrugated steel plate (CSP) pipe-arch structure in soil may cause local buckling instability due to insufficient load-bearing capacity. Recently, composite CSP pipe-arch has been widely utilized to enhance structural stability, and their stability needs to be thoroughly investigated. This paper studies the local buckling stability problem of the straight part of composite CSP pipe-arch in soil by simplifying the soil support and introducing the inter-layer bonding effect. Based on elastic stability theory, a theoretical mechanical model of composite CSP pipe-arch was proposed. The Rayleigh–Ritz method and the semi-combined composite structure stiffness approximation were used to derive the critical buckling conditions for the straight part of the composite CSP pipe-arch. Through numerical calculation and influencing factors analysis, it is concluded that the critical buckling load of the straight part of the composite CSP pipe-arch structure is affected by the elastic modulus, thickness, Poisson’s ratio, rotational restraint stiffness and side length of the straight part of the material. In particular, it is found that as the inter-layer bonding coefficient increases, the critical buckling load is improved, while the critical buckling wave number is mainly influenced by the width of the straight part, elastic modulus, and inter-layer bonding coefficient. Additionally, we discussed the coupling effect of several key parameters on the stability of the structure. The results of this study offer theoretical foundations and guidance for the application of composite CSP pipe-arch in soil engineering, such as culverts, tunnels, and pipeline transportation.

Effect of Vertical Aspect Ratio on Mass, Stiffness and Vertical Geometric Irregular Structures

Occurrence of earthquake will highly damage the structures which are not modelled and designed to resist such loads it may cause sometimes the collapse of structures leads to loss of human lives. The size of the building and slenderness ratio are the important factors for the efficient structural design. The aspect ratio of buildings is considerably effects under seismic loads. It is important to know the influence of aspect ratio on the irregular structures in high seismic zone areas. The research has been performed on the 15 storey building frames of five cases with mass, stiffness and vertical geometric irregularities. Each case comprises of four models having various vertical aspect ratios. The purpose of this study is to investigate the influence of vertical aspect ratio on mass, stiffness and vertical geometric irregular structures and how the structure will vary under seismic loads. The irregularities are incorporated in to the buildings by increasing the loads and column height in particular storeys and by eliminating the columns and beam sections compared to adjacent storeys. Linear dynamic analysis is performed. It is observed that with the decrease of vertical aspect ratio the structural response will increases the response of storey displacement, base shear, storey drift and over turning moment in the cases of mass and stiffness irregular structures. In the case of vertical geometric irregular structures with the decrease of vertical aspect ratio the storey displacement and storey drift values decrease for all the models, the base shear, overturning moment and stiffness increases with the decrease of vertical aspect ratio. Key words: Mass irregularity, Stiffness irregularity, Vertical geometric irregularity, Vertical aspect ratio, Linear dynamic analysis.

A quantitative classification criterion for beam-to-column rigid connections in steel braced frames

As the key part of the force-transfer path in a steel frame, a reasonable modeling method of beam-to-column connections in the structural analysis model is crucial. From the designer’s perspective, a rational and accurate classification of beam-to-column connections is an invaluable basis for improving modeling efficiency and design accuracy. Although some investigations led by Eurocode 3 (EC3) have provided a systematic and quantitative approach for classifying beam-to-column connections, it is not sufficiently developed for general steel braced frames. In this paper, based on a modified analytical model of the beam-to-column connection substructure that accounts for the effect of braces, the rotational stiffness demand of the beam-to-column rigid connection is derived from the perspectives of structural lateral stiffness and stability. The quantitative relationship is established between the rotational stiffness demand and the relative stiffness of the braces. The accuracy and reasonability of the proposed analytical model and stiffness demand are verified using finite element models (FEMs) at both the story and structure levels. Particularly, the effect of the non-linear behavior of beam-to-column connections on the structural response under high-intensity earthquakes is further comparatively analyzed in the context of seismic design. The results demonstrate that, a beam-to-column connection can be modeled as a continuous rigid connection in non-linear analysis only if it simultaneously satisfies the following requirements: the rotational stiffness meets the demand proposed in this study, and the bending capacity is designed to be overstrength compared to the beam cross-section.

A Study on the Effect of Structural Compliance Placing in Soft Contact/Collision Properties of Multirotor Micro Aerial Vehicles

Adding compliance (softness) has been introduced as an effective way to improve the physical collision resilience characteristics of multirotor micro aerial vehicles (MAVs). This article answers the question “Where is the best place to apply compliance in a multirotor MAV to make it more collision‐resilient?” by analyzing the output data of more than 1200 drone collision tests through two sets of accelerated and nonaccelerated collision experiments for four main configurations of micro‐quadcopters each possessing a unique softness layout of physical frame. It is shown that while applying compliance to the protective propeller guards (bumpers) of a micro‐quadcopter provides a more elastic collision, it does not improve its energy‐dissipation (impact damping) characteristics. On the other hand, enhancing the inner frame of the micro‐quadcopter with a softer structure results in higher rates of impact energy damping during the collisions and an increase in the impact time, which results in lower impact accelerations the MAV experiences during the crush. A mathematical model is developed representing the contact/collision interactions as nonlinear viscoelastic forces. Comparing the results of the simulations to the experiments suggests that this model can effectively mimic the impact behavior of contacting/colliding MAVs with different structural stiffness and damping.

Electrodeposition of Cu 3D structures suitable for CO2 reduction

Porous Cu foam electrodes, suitable for cathodic CO2 reduction, were deposited in an acidic sulphate solution with different additives to obtain structures with a high real surface area and an adequate mechanical stability. The influence of the electrodeposition time and solution composition on the porosity parameters, microstructure and stiffness of Cu 3D structures was evaluated. Neither ammonium acetate nor polyethylene glycol were found to be effective additives to the Cu sulphate electrolyte to achieve the main objectives. Only the presence of Cl– ions in the deposition solution resulted in a threefold increase in the real surface area and the achievement of a sufficient mechanical stability of the Cu 3D structure. The latter effect is related to the specific influence of Cl– ions during the electrodeposition process on the microstructural characteristics, such as the size of micropores in the walls of holes and crystallite aggregates that form dendritic branches. These structural changes, in contrast to the Cu samples deposited in a solution without additives, resulted in larger real surface areas, while the denser structures deposited in the presence of Cl– ions ensured the mechanical stability of the 3D structure.

Investigation on the Seismic Damage and Identification of Lateral Stiffness for Ancient Timber Structures

ABSTRACTThis paper investigates the seismic damage and identification of lateral stiffness for ancient timber structures. Based on the shaking table test of a palace‐style timber structure, the lateral displacement responses, interstory equivalent lateral stiffness (IELS), and sensitivity of lateral displacement to degradation of IELS were analyzed to investigate the degradation and identification of IELS. The state and observation equations of a simplified mechanical model of the timber frame considering the friction slipping of the column base were predicted. Considering the noise disturbance in the test, the IELS of the model was identified by the partial least squares–singular value decomposition (PLS‐SVD) and extended Kalman filter (EKF) method. Results shown that the ratio of the IELS of the column frame layer to Ru‐Fu layer decreased as the seismic damage increased, and the peak lateral displacement was more sensitive to the damage of the column frame layer than the Ru‐Fu layer. Under nondamage conditions, the identification error of the IELS was about 10%, while the error ranged from 15% to 20% under damage conditions. Through the identification of the equivalent lateral stiffness of the Xi'an bell tower, it was validated that the hybrid method is effective in monitoring the IELS of ancient timber structures.

Evaluation of Static Displacement Based on Ambient Vibration for Bridge Safety Management.

The evaluation of bridge safety is closely related to structural stiffness, with dynamic characteristics and displacement being key indicators. Displacement is a significant factor as it is a physical phenomenon that bridge users can directly perceive. However, accurately measuring displacement generally necessitates the installation of displacement meters within the bridge substructure and conducting load tests that require traffic closure, which can be cumbersome. This paper proposes a novel method that uses wireless accelerometers to measure ambient vibration data from bridges, extracts mode shapes and natural frequencies through the time domain decomposition (TDD) technique, and estimates static displacement under specific loads using the flexibility matrix. A field test on a 442.0 m cable-stayed bridge was conducted to verify the proposed method. The estimated displacement was compared with the actual displacement measured by a laser displacement sensor, resulting in an error rate of 3.58%. Additionally, an analysis of the accuracy of displacement estimation based on the number of measurement points indicated that securing at least seven measurement points keeps the error rate within 5%. This study could be effective for evaluating the safety of bridges in environments where load testing is difficult or for bridges that require periodic dynamic characteristics and displacement analysis due to repetitive vibrations, and it is expected to be applicable to various types of bridge structures.

Shaking table test and control effect analysis of structure with negative stiffness damped outrigger

A shaking table test was conducted on a negative stiffness damped outrigger (NSDO) structure, designed based on a real engineering project, to gain insights into the practical performance of the NSDO under earthquakes when equipped with nonlinear negative stiffness devices (NSD) and dampers. A low-friction NSD was designed, built, and verified by experiments to mitigate the potential issue adversely affecting its performance. The shaking table tests showed that NSD effectively increases the maximum deformation of the damper under moderate earthquakes. Nevertheless, the NSD had no influence on the initial and dynamic stiffness of the NSDO structure when the NSD was not activated due to low displacement. With the bell-shaped damping model to match modal damping ratios, a simplified fishbone numerical model was developed to simulate the response of the NSDO structure and to study the control effect of the NSDO through parametric analysis. The results revealed that the modal damping ratios were not uniform from mode to mode, and an inaccurate higher-mode damping ratio would significantly affect the response predictions during NSDO design. The initial tangential negative stiffness of the nonlinear NSD could be used to analyze the control effect under moderate earthquakes, while the secant stiffness was necessary for severe earthquakes. In addition, a combined seismic reduction curve was proposed for a two-level seismic mitigation analysis.

Structural Analysis Technique and Its Validation for Large Range Mirror Refocusing System for Spaceborne Deployable Telescopes

Large aperture deployable telescopes with numerous onboard instruments are popular in the space industry for astronomy. Scientific data in various wavelength bands, from 0.6µ to 28µ, is provided by these instruments and is crucial for deep space exploration. The deployment mechanisms handle the alignment and functionality at the telescope level only. At instrument level, there is always a need for a refocusing system which can cater individual need of instrument for focusing independent to other instruments nearby. In this paper, we present a structural analysis technique for such a type of large range mirror refocusing mechanism, similar to the Near Infrared Spectrograph (NIRSpec) payload of the James Webb Space Telescope (JWST). The method relies on geometric non-linearity for large deflection, in which the structure's stiffness matrix changes as a function of loading. We have designed, analyzed structurally, and tested a 4mm range slider crank based compliant mechanism. The outcomes of linear and non-linear static analysis, computed numerically, have been compared. There are noticeable significant variations in one direction between the two analyses' results. The results are validated using appropriately designed and realized test setups, like measurements of displacement, changes in focus and image position of the optical system.

Grid Optimization of Free-Form Spatial Structures Considering the Mechanical Properties

In recent years, the application of free-form surface spatial grid structures in large public buildings has become increasingly common. The layouts of grids are important factors that affect both the mechanical performance and aesthetic appeal of such structures. To achieve a triangular grid with good mechanical performance and uniformity on free-form surfaces, this study proposes a new method called the “strain energy gradient optimization method”. The grid topology is optimized to maximize the overall stiffness, by analyzing the sensitivity of nodal coordinates to the overall strain energy. The results indicate that the overall strain energy of the optimized grid has decreased, indicating an improvement in the structural stiffness. Specifically, compared to the initial grid, the optimized grid has a 30% decrease in strain energy and a 43.3% decrease in maximum nodal displacement. To optimize the smoothness of the grid, the study further applies the Laplacian grid smoothing method. Compared to the mechanically adjusted grid, the structural mechanical performance does not significantly change after smoothing, while the geometric indicators are noticeably improved, with smoother lines and regular shapes. On the other hand, compared to the initial grid, the smoothed grid has a 21.4% decrease in strain energy and a 28.3% decrease in maximum nodal displacement.

Unexpected self-healing acceleration within urethane networks: lignosulfonate mediation of ionic and hydrogen bonds for ultra-strong recyclable elastomers

Stiff structures are generally considered detrimental to the materials’ self-healing efficiency because of the rigid conformation and restricted motion of the molecular chains. However, in this study, an unexpected acceleration in self-healing was observed in a urethane network when lignosulfonate, a bio-based stiff structure with stiff benzene rings, was introduced into the polyurethane matrix. An extraordinary increase in mechanical properties was achieved with just 3 wt% lignosulfonate added to the pristine sample, including a strength increase from 16.24 MPa to 42.89 MPa and elongation at break from 390% to 602%. Importantly, this significant enhancement in mechanical properties was accompanied by a notable acceleration in healing time efficiency, which increased by up to 44% compared to the pristine sample. This unique behavior can be attributed to the mediation of lignosulfonate on the ionic bonds between lignosulfonate and the urethane segment, as well as the hydrogen bonds formed within the urethane segments. This mediation ensures ultra-high strength without compromising the self-healing capacity and opens a way for accelerating elastomers self-healing efficiency through lignosulfonate, a readily available biomass-derived material. In addition, the addition of lignosulfonates gives the elastomer some Anti-UV performance.

SSI‐induced seismic earth pressures on an integral abutment bridge model: Experimental measurements versus numerical simulations and code provisions

AbstractIntegral abutment bridges (IABs) generate strong soil–structure interaction (SSI) effects due to their high structural stiffness and transmission of inertial and thermal loads generated at the deck directly to the abutments. Despite an increasing number of experimental and numerical studies available in the literature, there is a lack of consolidated methodologies to model dynamic SSI phenomena for IABs, particularly in seismic regions where uncertainties associated with the induced ground motions render the problem harder to tackle. This study proposes an advanced strategy to model the seismic response of IABs, accounting for dynamic interaction between the structure, the abutment and the foundation, including piles and earth retaining walls. To this end, detailed finite‐element studies were carried out employing OpenSees to simulate a recent experimental campaign on a scaled IAB model in a soil container (SERENA) carried out at EQUALS Lab, University of Bristol, in the framework of SERA/H2020 project. An extensive dataset in terms of recorded accelerations, displacements, strains and settlements are available from these tests, including earth pressures which are back‐calculated from bending strain measurements. The objectives of this paper are threefold: firstly, the model parameters are explored and assessed critically by comparing the results from the numerical simulations against the experimental data; secondly, once the model is deemed sufficiently representative of the experiments, earth pressures are obtained numerically, as these are not directly measured in the tests; thirdly, the estimated static and dynamic earth pressures on the abutment wall are compared with the predictions of two simplified analytical procedures currently under consideration for inclusion in the new Eurocode 8. The results indicate that records and predictions match well for frequencies of up to 40 Hz at model scale (about 8 Hz in prototype scale) and confirm that the proposed modelling strategy can be used in practical applications. The quasi‐elastic model proposed in this study is shown to provide dependable predictions for cases involving moderate strains in real‐life applications.

Geometric mechanics of kiri-origami-based bifurcated mechanical metamaterials.

We explore a new design strategy of leveraging kinematic bifurcation in creating origami/kirigami-based three-dimensional (3D) hierarchical, reconfigurable, mechanical metamaterials with tunable mechanical responses. We start from constructing three basic, thick, panel-based structural units composed of 4, 6 and 8 rigidly rotatable cubes in close-looped connections. They are modelled, respectively, as 4R, 6R and 8R (R stands for revolute joint) spatial looped kinematic mechanisms, and are used to create a library of reconfigurable hierarchical building blocks that exhibit kinematic bifurcations. We analytically investigate their reconfiguration kinematics and predict the occurrence and locations of kinematic bifurcations through a trial-correction modelling method. These building blocks are tessellated in 3D to create various 3D bifurcated hierarchical mechanical metamaterials that preserve the kinematic bifurcations in their building blocks to reconfigure into different 3D architectures. By combining the kinematics and considering the elastic torsional energy stored in the folds, we develop the geometric mechanics to predict their tunable anisotropic Poisson's ratios and stiffnesses. We find that kinematic bifurcation can significantly effect mechanical responses, including changing the sign of Poisson's ratios from negative to positive beyond bifurcation, tuning the anisotropy, and overcoming the polarity of structural stiffness and enhancing the number of deformation paths with more reconfigured shapes.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Optimal design of vibration resistance of fiber-reinforced composite sandwich plates embedded in a viscoelastic square honeycomb core

This work focuses on investigating the optimal design of composite sandwich plates (FCSPs) with a viscoelastic square honeycomb core (VSHC). Firstly, using the cross-fill theory, the complex modulus technique, the first-order shear deformation theory, the minimum strain energy principle, and the Newmark-β method, a theoretical model of the VSHC-FCSPs under half-sine pulse excitation is formulated to calculate the inherent frequencies, the peak and vibration decay time of the transient response in time domain. The peak and vibration decay time are taken as the indexes of the anti-vibration performance. Considering an index of structural stiffness performance, the average value of the inherent frequencies is adopted to calculate the overall stiffness. After a set of literature validations and optimization validations, the multi-objective genetic algorithm is employed to study the optimization issue of VSHC-FCSPs. The optimization objectives are to minimize the three design variables of the transient response peak, vibration decay time, and reciprocal of overall stiffness. Then, the fiber laying angle of each layer, the core thickness ratio and the modulus ratio are assumed as optimization variables. Finally, the results with good vibration resistance and structural stiffness in the Pareto front are chosen as references, and these corresponding variations of the design variables and optimization objectives are obtained. The optimization results have revealed that the optimization variables corresponding to the intermediate points should be selected as references to improve the anti-vibration capacity and ensure the structural stiffness performance.

Static and stability analyses of multi-strut type aluminium alloy suspen-dome structure with large opening

By combining the advantages of the multi-strut concept in cable dome structures with aluminum alloy material, a new type of prestressed spatial structure—the multi-strut aluminum alloy suspen-dome with a large opening—has been developed by integrating a lower prestressed support system into an aluminum alloy reticulated shell. The optimal structural configuration was determined by comparing the static, stability, and economic performance of three types of upper chord mesh topologies for this structure. Subsequently, an analysis of the static performance and large-scale parameters affecting the structural stability of the optimal grid topology was conducted. The study explored the influence of structural prestressing, overall shape, and support stiffness—encompassing three categories and seven parameters—on structural stability and material consumption. Additionally, the effects of initial imperfections and load distribution forms on structural stiffness and stability were further examined. Finally, the static properties, stability, and economic indicators of the structure were compared with two other structural systems: the steel suspen-dome and the cable dome. The results indicate that the pentagonal grid topology provides the best structural performance and that the structure is sensitive to cooling effects. Optimal values for key design parameters, such as the rise-span ratio and thickness-span ratio, were identified. Moreover, the economic advantages of the aluminum alloy suspen-dome compensate for its mechanical performance shortcomings compared to the steel suspen-dome. These findings offer innovative solutions and a scientific basis for the selection and stability design of aluminum alloy suspen-dome structures.

A quadrilateral inverse plate element for real-time shape-sensing and structural health monitoring of thin plate structures

The inverse finite element method (iFEM) emerged as a powerful tool in shape-sensing and structural health monitoring (SHM) applications with distinct advantages over existing methodologies. In this study, a quadrilateral inverse-plate element is formulated via a sub-parametric approach using bi-linear and non-conforming cubic Hermite basis functions for engineering structures, which can be modeled as thin plates. Numerical validation involves dense and assumed sparse sensor arrangements for in-plane, out-of-plane, and mixed general loading conditions. iFEM analysis reveals efficient monotonic convergence to analytical and high-fidelity finite element reference solutions. After successful numerical validation, defect detection analysis is performed considering minute geometric discontinuities and structural stiffness reduction because of latent subsurface defects under tensile and transverse loading conditions. The inverse formulation successfully resolves the presence of simulated defects under a sparse sensor arrangement. The proposed inverse-plate element is accurate in the full-field reconstruction of shape-sensing profiles and reliable in defect identification and quantification in thin plate structures.

Age- and sex-specific biomechanics and extracellular matrix remodeling of the ascending aorta in a mouse model of severe Marfan syndrome.

Thoracic aortic aneurysm (TAA) is associated with Marfan syndrome (MFS), a connective tissue disorder caused by mutations in fibrillin-1. Sexual dimorphism has been recorded for TAA outcomes in MFS, but detailed studies on the differences in TAA progression in males and females and their relationships to outcomes have not been performed. The aims of this study were to determine sex differences in the diameter dilatation, mechanical properties, and extracellular matrix (ECM) remodeling over time in a severe mouse model (Fbn1mgR/mgR = MU) of MFS-associated TAA that has a shortened life span. Male and female MU and wildtype (WT) mice were used at 1-4 mo of age. Blood pressure and in vivo diameters of the ascending thoracic aorta were recorded using a tail-cuff system and ultrasound imaging, respectively. Ex vivo mechanics and ECM remodeling of the aorta were characterized using a biaxial test system and multiphoton imaging, respectively. We showed that mechanical properties, such as structural and material stiffness, and ECM remodeling, such as elastic and collagen fiber content, correlated with diameter dilatation during TAA progression. Male MU mice had accelerated rates of diameter dilatation, stiffening, and ECM remodeling compared with female MU mice which may have contributed to their decreased life span. The correlation of mechanical properties and ECM remodeling with diameter dilatation suggests that they may be useful biomarkers for TAA progression. The differences in diameter dilatation and life spans in male and female MU mice indicate that sex is an important consideration for managing thoracic aortic aneurysm in MFS. NEW & NOTEWORTHY Using a mouse model (Fbn1mgR/mgR = MU) of severe thoracic aortic aneurysm in Marfan syndrome (MFS), we found that male MU aorta had an accelerated time line and increased amounts of dilatation, stiffening, and extracellular matrix (ECM) remodeling compared with female MU aorta that may have contributed to an increased risk of fatigue failure with cyclic loading over time and a reduced life span. We suggest that aortic stiffness may provide useful information for clinical management of aneurysms in MFS.

Intelligent design of multi-layered variable stiffness composite structure based on transfer learning

Variable stiffness composite structures offer more flexible design space than thin-walled metal structures and have greater potential for vibration-resistant design. When faced with multiple new types of design problems, the complex modelling and analysis procedures frequently prove to be both time-consuming and costly in terms of optimization. In this study, an innovative multi-layered variable stiffness (MVS) composite structure with high design flexibility is proposed, with images representation for curvilinearly stiffened paths, non-uniform layouts, and fiber and layup angles. Moreover, an intelligent optimization method based on transfer learning is proposed for addressing a variety of factors affecting dynamic design, including boundary types, structural features, and dynamic responses. The objective of the transfer learning model is to facilitate the inheritance and sharing of variable stiffness features, thereby enabling the efficient design of new problems with limited datasets. The validation of different examples shows that the transfer learning can effectively acquire the structural features from the existing source domain datasets, thereby significantly reducing the data for some new target domains by approximately 50%. In comparison to the initial constant stiffness (CS) structures, the different optimized configurations indicate that the MVS composite structures are capable of effectively enhancing the dynamic responses by 10%∼146% for natural frequency and dynamic compliance. Furthermore, the MVS optimized configuration displays superior dynamic responses in some problems, when compared to the CS optimized configuration.