Non-uniform Stiffness Research Articles

Dynamics and energy harvesting of a flow-induced snapping sheet with nonuniform stiffness distribution

Energy harvesting through periodic snap-through of a buckled sheet has recently gained considerable attention because of its potential applications in energy harvesting in low incoming flow. Although the snapping dynamics of uniform buckled sheets has been extensively studied, the present work focuses on the energy harvesting and dynamics of a nonuniform snapping sheet with both of its ends clamped in a channel flow. The analysis reveals that the sheet undergoes periodic snap-through oscillations, with its rear half consistently serving as the main contributor to effective energy harvesting, and the potential energy contributing significantly more than the kinetic energy. Varying the stiffness difference ΔEI* shows that increasing the stiffness of the rear part and decreasing that of the fore part shifts the deformation wave toward upstream and enhances the snapping amplitude of the fore part, optimizing energy extraction. At a length compression ratio ΔL* = 0.3, the maximum potential energy is observed for ΔEI* = 1, and the total energy peaks at ΔEI* = 2. The study also identifies an optimal ΔL* = 0.4 that maximizes both total and potential energies, and triples the potential energy in comparison with ΔL* = 0.1. However, the enhancement of nonuniformity disappears at ΔL* > 0.3 for the total energy and ΔL* > 0.2 for the potential energy. These findings provide insights to aid optimization of the design and performance of snapping sheet energy harvesters.

Amplitude‐dependent modal viscous damping for distributed stick–slip systems

AbstractAn accurate damping model serves as the foundation for reliable structural analysis. One of the primary sources of structural damping is the stick–slip mechanism caused by interfacial friction. Structural damping is usually represented by the modal damping ratio, and the modal equivalent viscous damping ratio (EVDR) of a stick–slip system is crucial in structural dynamic modeling. To date, an accurate yet simple prediction method for modal amplitude‐dependent EVDR that considers the distribution characteristics of the stick–slip mechanism remains unavailable. In the present study, the modal EVDRs of a distributed stick–slip system (DSSS) extended from a single degree‐of‐freedom stick–slip system were calculated using the modal energy equivalence method. The correlation between the stick–slip parameters and the modal damping behavior was investigated at various amplitude levels on the basis of the assumption of equal stick–slip parameters. A two‐parameter damping model represented by a single stick–slip damping model was developed to capture the amplitude dependence of the frictional EVDR. Furthermore, a practical prediction method based on the stick–slip parameters was proposed for the modal EVDR of the fundamental and higher‐order modes. The seismic analysis of two illustrative structures with nonuniform and uniform interstory stiffness demonstrated the effectiveness and applicability of the proposed method in predicting the modal EVDR of the DSSS. The proposed equivalent linear viscous damping system is suitable for the quick prediction of structural dynamic responses.

Evaluation of ride quality in a passenger car with non-uniform tyre radial stiffness

This study is dedicated to examining the influence of varying radial stiffness along the circumference of tyres on a road vehicle ride quality and with a specific focus on aspects relevant to maintenance. Computer simulations employing a three-dimensional road-vehicle model, developed within commercial multi-body software, were conducted to explore the multifaceted factors influencing vehicle behaviour. These factors encompass road unevenness, driving speed, and the range of radial force variation resulting from harmonic changes in tire radial stiffness. Furthermore, simulation tests were carried out using a model of a diagnostic wheel balancing machine, which holds significance in vehicle maintenance practices. Measurements obtained from a passenger car equipped with standard tires with minimal non-uniformity, served as reference values for assessing the car's vibration levels. Additionally, selected scenarios were examined, involving vehicle with multiple wheels exhibiting non-uniform radial stiffness. The findings underscore that non-uniform radial stiffness can magnify the detrimental effects of road irregularities, potentially leading to amplified vibration levels and a heightened need for maintenance considerations.

Modeling and analysis of gradient metamaterials for broad fusion bandgaps

A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap. First, three local resonators with linearly increasing stiffness are periodically attached to the spring-mass chain to construct the gradient metamaterial. The dispersion relation is then derived based on Bloch’s theorem to reveal the fusion bandgap theoretically. The dynamic characteristic of the finite spring-mass chain is investigated to validate the fusion of multiple bandgaps. Finally, the effects of the design parameters on multiple bandgaps are discussed. The results show that the metamaterial with a non-uniform stiffness gradient pattern is capable of opening a broad fusion bandgap and effectively attenuating the longitudinal waves within a broad frequency region.

Dynamic Analysis of the Bolted Joint Structure with Interval Uncertainties

This paper investigates the dynamic influence of joint interfaces in bolted joint structures subjected to uncertain-but-bounded parameters. Firstly, applying the thin layer elements (TLE) represents the contact interfaces with nonuniform stiffness distribution. The stochastic model updating method is employed to identify the uncertain parameters of TLE. Secondly, the Legendre interval method (LIM) is applied to calculate the natural frequencies of bolted lap joints with uncertain parameters. By introducing the elastic modulus of TLE as interval vectors, relations between the natural frequencies and uncertain parameters could be analyzed using the LIM. Furthermore, the dependence of the dynamic response on TLE parameters can be established based on the modal superposition principle. Considering the influence of uncertain parameters, an uncertain acceleration frequency response surrogate function (UAFRSF) is proposed to predict the dynamic behavior and qualitatively analyze the parameter sensitivity of the bolted lap joints. The elastic modulus of TLE in different contact regions is selected as the interval variable. The acceleration frequency responses of the bolted lap joints under uncertain parameters are investigated. Compared with MCs simulations with 200 samples and Chebyshev interval method results, the effectiveness of the proposed method for solving the uncertain acceleration frequency response of bolted lap joints is verified. This research will provide theoretical support for improving the design of aero-engine joint structures.

An inelastic beam-like model for nonlinear dynamic analyses of multi-storey buildings

This paper presents an equivalent non-uniform inelastic beam-like model for the evaluation of the nonlinear behaviour of multi-storey buildings subjected to earthquake loadings. The proposed beam can be used to model buildings with non-uniform mass and stiffness distribution. The model is characterised by a number of degrees of freedom corresponding to the number of floors of the building and is conceived to predict its nonlinear dynamic response after a proper calibration based on the results of pushover analyses performed on a nonlinear FEM model. In spite of its simplicity, the proposed equivalent model provides, with a very low computational effort, an accurate representation of the nonlinear dynamic behaviour of the building comparable to that obtained through the more demanding nonlinear 3D FEM models. The effectiveness of the proposed simplified modelling approach is here validated by means of nonlinear dynamic analyses firstly performed on a benchmark known in the literature as SAC9 building, modelled as a plane steel frame structure and secondly on a three-dimensional reinforced concrete structure, designed according to old standard structural design rules. The very good agreement with the results obtained through accurate 3D FEM frame modelling, for different earthquake loadings, on the considered benchmarks provides a first validation of the proposed inelastic equivalent beam-like model and suggests its potential use for the seismic assessment of building structures. The low computational cost related to the beam-like model could be particularly advantageous for all the seismic vulnerability approaches requiring several nonlinear dynamic analyses, as those related to large scale applications, or those expressed in terms of probability of failure generally expressed in terms of fragility curves.

Research on the Impact of Non-Uniform and Frequency-Dependent Normal Contact Stiffness on the Vibrational Response of Plate Structures

Mechanical interfaces are prevalent in industries like aerospace and maritime, where the normal contact stiffness on these surfaces is a crucial component of the overall stiffness of mechanical structures. From the perspective of structural mechanics, normal contact stiffness significantly affects the dynamic response of mechanical structures and must be considered in mechanical design and simulation analysis. Essentially, the mechanical interface represents a typical type of nonlinear contact, characterized by both its non-uniform distribution and its frequency-dependent properties under external excitations. A plate structure was designed to study the distribution and frequency-dependent characteristics of normal contact stiffness on the mechanical interface. Experiments validated that the normal contact stiffness not only significantly increases the fundamental frequency of the plate but also alters its mode shapes. To replicate the experimental results in simulations, the BUSH elements were used to model the normal contact stiffness within the plate structure, arranging it non-uniformly and setting it to vary with frequency according to the plate’s mode shapes and frequency response. This method accurately replicated the plate’s mode shapes and response curves within the 0–1000 Hz range in simulations.

Lightweight multi-layer graded pyramid folded structure based on tucked kirigami for green manufacturing

Lightweight structures are extensively utilized in various applications that demand exceptional mechanical properties and low densities, such as aerospace, vehicles, and construction components. However, the production of lightweight structures often entails significant material consumption and the emission of pollutants during the pressing and welding processes. Additive manufacturing (AM) has been hailed as a green technology that offers superior flexibility, reduces material wastage, and enables personalized design compared to traditional approaches. In this study, we present a novel lightweight multi-layer graded pyramid folded structure (PFS) based on tucked kirigami, with a focus on green manufacturing principles. The PFSs consist of nested pyramid cells connected by flat triangular plates. By leveraging stereolithography and a two-stage curing process, we achieve AM of multi-layer PFSs with excellent mechanical properties and shaping quality. Experimental studies were conducted on two-dimensional and three-dimensional graded PFSs under lateral and vertical quasi-static compressive loading to investigate the influence of gradient types and values on the mechanical performance of 3D printed PFSs. Our findings reveal that length gradients parallel to the load induce buckling deviations from the center, negatively impacting the performance of single-layer PFSs. Conversely, a height gradient along the z-direction further enhances specific energy absorption (SEA) and compressive strength. The results of this study provide a novel and viable approach to the design and manufacturing of multi-layer graded PFSs with programmable non-uniform stiffness. These graded PFSs hold significant potential for environment-friendly lightweight engineering applications.

Decaf: Monocular Deformation Capture for Face and Hand Interactions

Existing methods for 3D tracking from monocular RGB videos predominantly consider articulated and rigid objects ( e.g. , two hands or humans interacting with rigid environments). Modelling dense non-rigid object deformations in this setting ( e.g. when hands are interacting with a face), remained largely unaddressed so far, although such effects can improve the realism of the downstream applications such as AR/VR, 3D virtual avatar communications, and character animations. This is due to the severe ill-posedness of the monocular view setting and the associated challenges ( e.g. , in acquiring a dataset for training and evaluation or obtaining the reasonable non-uniform stiffness of the deformable object). While it is possible to naïvely track multiple non-rigid objects independently using 3D templates or parametric 3D models, such an approach would suffer from multiple artefacts in the resulting 3D estimates such as depth ambiguity, unnatural intra-object collisions and missing or implausible deformations. Hence, this paper introduces the first method that addresses the fundamental challenges depicted above and that allows tracking human hands interacting with human faces in 3D from single monocular RGB videos. We model hands as articulated objects inducing non-rigid face deformations during an active interaction. Our method relies on a new hand-face motion and interaction capture dataset with realistic face deformations acquired with a markerless multi-view camera system. As a pivotal step in its creation, we process the reconstructed raw 3D shapes with position-based dynamics and an approach for non-uniform stiffness estimation of the head tissues, which results in plausible annotations of the surface deformations, hand-face contact regions and head-hand positions. At the core of our neural approach are a variational auto-encoder supplying the hand-face depth prior and modules that guide the 3D tracking by estimating the contacts and the deformations. Our final 3D hand and face reconstructions are realistic and more plausible compared to several baselines applicable in our setting, both quantitatively and qualitatively. https://vcai.mpi-inf.mpg.de/projects/Decaf

Analysis of Concrete Pavement Slab resting on Non-uniform Elastic Foundation using the Finite Element Method

During the rigid pavement design, the concrete slab working on the base/subbase and subgrade is usually modeled as the slab on the elastic foundation. However, the non-uniform distribution of materials in the base or subgrade layers naturally exists in real conditions and should be considered. In this paper, a finite element method for calculating concrete pavement slabs on an elastic foundation with non-uniform stiffness distribution is developed. This study applies 4-node finite elements and Mindlin plate theory to formulate the finite element equations. The results predicted by the proposed approach are verified analytically. Calculation examples are conducted with the practical settings to investigate the influence of slab and foundation stiffness parameters on the slab displacement.

Issues of Developing Equal-Strength Two-Layer Spherical Rubber-Metal Hinges

Development of equal-strength two-layer spherical rubber­metal hinges (RMH), described in the paper, is associated with the problem that with an equal thickness of the layers of rubber bushings and an equal opening angle, there is a significant difference in their radial stiffness and relative deformation of the rubber. With hinge dimensions corresponding to those of the hinges used in the undercarriage of locomotives, there is a difference in relative deformation of inner and outer bushings by about 1,5 times. As a result, it is proposed to determine the load capacity of spherical two-layer RMH by the value of relative deformation of the rubber of the most loaded bushing. Also, studies have been carried out on the possibilities of creating a uniformly deformable design of a spherical two-layer RMH.To determine the characteristics of a spherical rubber-metal hinge, applied digital computer modelling based on the finite element method. A proposed parametrised geometric model of a spherical two-layer RMH and a finite element model of an elastic bushing offer the ratio of radial stiffnesses of outer and inner bushings, which is close to the preliminarily determined one, based on the equations of the theory of elasticity in displacements in a spherical coordinate system.It has been established that to achieve uniform elasticity by changing the opening angle, the opening angle of the outer reinforcement of RMH should be approximately 1,5 times less than the opening angle of the inner one. This makes it possible to reduce the width of outer reinforcement of RMH by 25 % but raises the problem of strength and rigidity of outer edges of intermediate reinforcement. Also, equal elasticity of hinge bushings can be achieved due to their different thicknesses, while to achieve non-uniform stiffness of bushings within ± 5 %, it is required to ensure that deviation of the intermediate cage diameter during hinge manufacture is less than ± 0,1 %.The obtained research results prove the practical possibility of creating an equally strong (with equal bushing rigidity) spherical two-layer RMH. The issue of searching for a compromise design of RMS, acceptable from the point of view of loading of the intermediate cage and of the requirements for manufacturing accuracy, requires further study.

Modeling and analysis of assembly variation with non-uniform stiffness condensation for large thin-walled structures

The increase of thickness for large thin-walled structure causes the nonlinear enhancement of local structural stiffness, which leads to that the variation is concentrated on the local assembled area. The strong geometrical nonlinearity exists in the assembly process, which causes the non-uniform constraint for the material in assembled area and the variation of assembled large thin-walled structure is difficultly predicted. In this paper, the large thin-walled structure is partitioned into the assembled area and non-assembled area. The nonlinear stiffness matrix of each area is constructed based on continuum mechanics theory. The large non-assembled area is condensed as the nonlinear stiffness constraint and attached on the small assembled area. The non-uniform stiffness condensation method is developed and a new assembly variation model is proposed for large thin-walled structure with high local stiffness. The initial bending and torsional variations are constructed according to the manufacturing process of thin-walled structure and the assembly variations of two large cylindrical thin-walled structures are calculated. The predicted results by using the non-uniform condensation model are compared with that by the commercial software and the classic method of influence coefficients, in which the accuracy of the proposed model is verified. The proposed model may predict the local variation characteristics of large thin-walled structures effectively and is significant for the analysis of variation propagation in the series assembly process of large thin-walled structures.

Stochastic dynamics of substrate non-uniform stiffness affecting molecular adhesion in cell–substrate interface subjected to tensile loading

The mechanically heterogeneous extracellular matrix (ECM) or tissues widely exist in biological systems and are capable of significantly regulating directional cell migration. However, prior to whole cell movement, how the cell senses these cues from mechanical heterogeneities of the ECM or substrate remains unclear at the molecular bond level. To address this issue, we theoretically investigate interface adhesion between a non-uniform stiffness substrate and a rigid plate via a series of receptor–ligand bonds subjected to a tensile loading by integrating substrate surface deformation described by continuum mechanics approach into the stochastic events of bond dissociation and association govern by Markov processes. Interestingly, it is found that, during stretching adhesion interface, due to the large collective contact forces near the stiff edge of the adhesion area, the crack first develops at this stiff edge and then grows to another relatively soft adhesion edge until the completed detachment achieved, which is distinct from the cracks growing from both two edges to center of adhesion area in the case of uniformly elastic solid–solid or solid–fluid interface. Moreover, the lifetime of the bond cluster, interface adhesion strength, and the effect of inter-bond distance are examined, respectively. The corresponding mechanism of dependence of the lifetime and adhesion strength on the non-uniform stiffness of the substrate and inter-bond distance is also analyzed. These findings provide a detailed mechanistic understanding of the adhesion interface responding to the mechanical heterogeneities of the substrate at the molecular bond level.

Finite element modeling of straight pipeline with partially attached viscoelastic damping patch based on variable thickness laminated element

To successfully implement the viscoelastic damping patch (VDP) for vibration reduction of the straight pipeline, it is necessary to perform dynamic modeling to guide vibration reduction design. The nonlinear vibration characteristic of the straight pipeline with partially attached VDP is studied by the FEM. A modeling method of laminated shell elements with variable thickness is proposed. Additionally, the local coordinate transformation is executed to facilitate the integration calculation of each layer. The nonlinear dynamic equation of the straight pipeline with VDP is established by considering the frequency dependence of VDP and the non-uniform continuous variable stiffness distribution of the clamp. The Vector Iteration method based on Improved Approximate Eigenvalue (VIM/IAE) is proposed to solve the nonlinear eigenvalues further. The rationality of the FE model is verified by constructing an experimental test system and compared with the ANSYS simulation and references. Finally, the vibration reduction mechanism of the clamp-straight pipeline with partially attached VDP considering frequency dependence is analyzed under different nonlinear iterative algorithms, VDP parameters (thickness, elastic modulus, and loss modulus), and boundary stiffness.

Nonuniform structural properties of wings confer sensing advantages.

Sensory feedback is essential to both animals and robotic systems for achieving coordinated, precise movements. Mechanosensory feedback, which provides information about body deformation, depends not only on the properties of sensors but also on the structure in which they are embedded. In insects, wing structure plays a particularly important role in flapping flight: in addition to generating aerodynamic forces, wings provide mechanosensory feedback necessary for guiding flight while undergoing dramatic deformations during each wingbeat. However, the role that wing structure plays in determining mechanosensory information is relatively unexplored. Insect wings exhibit characteristic stiffness gradients and are subject to both aerodynamic and structural damping. Here we examine how both of these properties impact sensory performance, using finite element analysis combined with sensor placement optimization approaches. We show that wings with nonuniform stiffness exhibit several advantages over uniform stiffness wings, resulting in higher accuracy of rotation detection and lower sensitivity to the placement of sensors on the wing. Moreover, we show that higher damping generally improves the accuracy with which body rotations can be detected. These results contribute to our understanding of the evolution of the nonuniform stiffness patterns in insect wings, as well as suggest design principles for robotic systems.

Understanding the performance of profiled composite walls in fire

To understand the performance of structural elements subject to one-side heating, the combined effects of temperature and temperature gradient (or the non-uniform temperature increase) must be accurately considered in developing structural performance models. However, due to insufficient consideration of such effects, the direct application of current understanding of general structural performance at high temperature on structural elements like profiled composite walls (PCWs) seems insufficient because of the complex role that the different materials can have in the presence of significant temperature gradients. Therefore, more research is needed to understand the performance of these structural elements when subjected to temperature increase and temperature gradients. Only then, the performance of PCWs at high temperature can be appropriately addressed. This paper presents and verifies a structural performance model that can be used to analyse the performance of PCWs subjected to combined thermal and mechanical loadings. First, details of an analytical study are presented, including thermal stress calculation within inhomogeneous and composite cross-section by fully considering the effects of non-uniform stiffness, non-linear temperature gradient, shifting of the neutral axis, and the coupling effects between stress and thermal expansion. Second, previously published experimental results into the performance of PCWs subjected to combined mechanical loading and one-side heating are then used to verify the newly-developed analytical model. It is also argued that the methodology for stress and curvature calculation developed in this study can be used to assess the performance of any structural elements (PCWs included) subjected to one-side heating. (244 words).

Flow-induced buckling of elastic microfilaments with non-uniform bending stiffness

Buckling plays a critical role in the transport and dynamics of elastic microfilaments in Stokesian fluids. However, previous work has only considered filaments with homogeneous structural properties. Filament backbone stiffness can be non-uniform in many biological systems like microtubules, where the association and disassociation of proteins can lead to spatial and temporal changes into structure. The consequences of such non-uniformities in the configurational stability and transport of these fibers are yet unknown. Here, we use slender-body theory and Euler-Bernoulli elasticity coupled with various non-uniform bending rigidity profiles to quantify this buckling instability using linear stability analysis and Brownian simulations. In shear flows, we observe more pronounced buckling in areas of reduced rigidity in our simulations. These areas of marked deformations give rise to differences in the particle extra stress, indicating a non-trivial rheological response due to the presence of these filaments. The fundamental mode shapes arising from each rigidity profile are consistent with the predictions from our linear stability analysis. Collectively, these results suggest that non-uniform bending rigidity can drastically alter fluid-structure interactions in physiologically relevant settings, providing a foundation to elucidate the complex interplay between hydrodynamics and the structural properties of biopolymers.

3D Printed Nonuniform Auxetic Structure: Programmable Local Stiffness to Improve Mechanical Property by Avoiding Buckling

With the development of 3D printing technology, programmable auxetic structures have attracted extensive attention due to their designable and abnormally mechanical properties. In this study, we design a 3D printed programmable auxetic star-like structures using number of layers [Formula: see text], per-layer dimension reduction ratio [Formula: see text] and spatial programming of unit cells to achieve a simultaneous optimization of load carrying capacity and auxetic property. Effects of layers [Formula: see text] and dimension reduction ratio [Formula: see text] on the mechanical and Poisson’s ratio behaviors of the 3D printed auxetic star-like structures are investigated by finite element method and verified by experiments. Finally, the unit cell spatial programming is designed and analyzed to avoid buckling and rotation, while increasing the load carrying capacity and auxetic property in a coordinated way. This study is expected to provide a design guideline for meta-star-like structure with both high load carrying capacity and auxetic property via a novel nonuniform stiffness structure design.

Bracing requirements for multiple parallel nonidentical columns with initial curvature

For a system consisting of multiple columns, horizontal discrete braces are often used to increase the system’s strength by decreasing the effective length of columns. Since the bracing requirements for such systems in current design standards were developed based on the assumption of identical columns with pin-ends, an analytical method is proposed to evaluate the ideal brace stiffness and brace forces for multiple columns by accounting for the stiffness interaction among columns and braces. For systems with uniform column lateral stiffness, the explicit solution for the maximum brace force is derived, and a simple formula is subsequently proposed by fitting the analytical results. The proposed formula explicitly accounts for the influences of column initial curvature and semi-rigid end connections on the maximum brace force. The method is comprehensive and applicable to multi-column systems with nonuniform column lateral stiffness, which can result from differences in column sizes, end connections, or applied loads. The results obtained from the proposed formulae are verified against those of finite element analyses. The ideal brace stiffness and brace forces for a system containing a distinctive column with a greater moment of inertia than the other columns are investigated. The results show that the location of the distinctive column affects the magnitudes of the ideal brace stiffness and the maximum brace force, which is yet to be considered in current design standards.

How Non-Uniform Stiffness Affects the Propulsion Performance of a Biomimetic Robotic Fish.

Live fish in nature exhibit various stiffness characteristics. The anguilliform swimmer, like eels, has a relatively flexible body, while the thunniform swimmer, like the swordfishes, has a much stiffer body. Correspondingly, in the design of biomimetic robotic fish, how to balance the non-uniform stiffness to achieve better propulsion performance is an essential question needed to be answered. In this paper, we conduct an experimental study on this question. First, a customized experimental platform is built, which eases the adjustment of the non-uniform stiffness ratio, the stiffness of the flexible part, the flapping frequency, and the flapping amplitude. Second, extensive experiments are carried out, finding that to maximize the propulsion performance of the biomimetic robotic fish, the non-uniform stiffness ratio is required to adapt to different locomotor parameters. Specifically, the non-uniform stiffness ratio needs to be reduced when the robotic fish works at low frequency, and it needs to be increased when the robotic fish works at high frequency. Finally, detailed discussions are given to further analyze the experimental results. Overall, this study can shed light on the design of a non-uniform biomimetic robotic fish, which helps to increase its propulsion performance.