Equivalent Stiffness Research Articles

Shake table testing and finite element modeling of a modular prefabricated concrete bridge‐like specimen accounting for geometry imperfections and additional damping

AbstractThis paper presents the shake table testing and finite element (FE) modeling of a modular prefabricated concrete bridge‐like specimen. The specimen comprised four equal‐height cylindrical reinforced concrete (RC) columns capped with an RC slab. The structural connections were non‐monolithic. Hence, controlled relative motion of the members, including rocking (uplift) of the piers, was allowed. The columns were connected to the slab with stiff tendons that provided positive post‐uplift stiffness. The specimen was subjected to 184 triaxial shake table tests, so that a statistical validation of numerical models can be performed. Subsequently, a detailed three‐dimensional FE model of the bridge was developed. The objectives of the present study were to: i) investigate the shake table response of a modular bridge with positive post‐uplift stiffness under multiple ground motions, ii) develop an FE model of the proposed structural system, iii) investigate the influence of geometrical imperfections on rocking bridges, and iv) evaluate the efficiency of using additional dissipative rebars. After being subjected to 184 shake table tests, the specimen showed zero damage, moderate displacements and tendon forces (TFs), low slab torsion, and zero residual displacements. The shake table tests were practically repeatable. The proposed FE model accurately captured the experimental results. Geometrical imperfections heavily affect the response of negative stiffness systems. However, they have a marginal influence on positive stiffness systems. When comparing systems with equivalent uplift resistance and post‐uplift stiffness, the use of additional dissipative rebars results in lower slab torsion and TFs, provided that the rebars do not fracture.

Radial Oscillations of Strange Quark Stars Admixed with Dark Matter

We investigate the equilibrium structure and radial oscillations of strange quark stars admixed with fermionic dark matter. For strange quark matter, we employ a stiff equation of state from a color-superconductivity improved bag model. For dark matter, we adopt the cold free Fermi gas model. We rederive and numerically solve the radial oscillation equations of two-fluid stars based on general relativity, in which the dark matter and strange quark matter couple through gravity and oscillate with the same frequency. Our results show that the stellar maximum mass and radius are reduced by inclusion of dark matter. As to the fundamental mode of the radial oscillations, the frequency f0 is also reduced comparing to pure strange stars, and f02 reaches the zero point at the maximum stellar mass with dM/dϵq,c=0. Therefore, the stability criteria f02>0 and dM/dϵq,c>0 are consistent in our dark matter-mixed strange quark stars with a fixed fraction of dark matter. We also find a discontinuity of f0 as functions of the stellar mass, in contrast to the continuous function in pure strange stars. And it is also accompanied with discontinuity of the oscillation amplitudes as well as a discontinuous in-phase-to-out-phase transition between oscillations of dark matter and strange quark matter.

Effect of oil film stiffness on vibration of full ceramic ball bearing under grease lubrication

PurposeThis paper aims to understand the vibration characteristics of full ceramic ball bearings under grease lubrication, reduce the vibration of the bearings and improve their service life.Design/methodology/approachThe Hertz contact stiffness formula for full ceramic ball bearings is constructed; the equivalent comprehensive stiffness calculation model and vibration model of full ceramic ball bearings are established. The dynamic characteristic test of full ceramic ball bearing under grease lubrication was carried out by using the bearing life testing machine, and its vibration was measured, and its vibration acceleration root-mean-square was obtained by software calculation and compared with the simulation results.FindingsAt the rotational speed of 12,000 r/min, the root-mean-square value of vibration acceleration is maximum 10.82 m/s2, and the error is also maximum 7.49%. As the rotational speed increases, the oil film stiffness decreases. In the radial load of 600 N, the vibration acceleration root-mean-square is minimum 6.40 m/s2, but its error is maximum 6.56%. As the radial load increases, the vibration of the bearing decreases and then increases, so under certain conditions increasing the radial load can reduce the bearing vibration. With different types of grease, the best preload is also different; low-speed heavy load should be used when the viscosity of the grease is large, and high-speed light load should be used when the choice of smaller viscosity grease is made.Originality/valueIt provides a theoretical basis for the application of full ceramic ball bearings under grease lubrication, which is of great significance for reducing the vibration of bearings as well as enhancing the service life of bearings.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2024-0094/

Effect of repeated pulling loads on Norway spruce (Picea abies (L.) Karst.) trees

Artificial pulling tests are the most practical method of assessing the maximum resistance of trees to lateral forces (e.g., from the wind), particularly in relation to their anchoring capacity in the ground. The traditional method is to pull the tree monotonically until failure. However, there are still many uncertainties regarding the possibility of mimicking wind gusts in such a tree pulling test. More specifically, it is supposed that a succession of wind gusts during a windstorm may cause fatigue to the root system, leading to a propagation of damage at the root-soil interface which will eventually lead to the collapse of the tree. This work aims to provide initial insights into the biomechanical response of shallow-rooted Norway spruce (Picea abies (L.) Karst.) growing in mineral soils by repeatedly pulling to failure six trees with increasing load magnitude. The mechanical behaviour of the tested trees was first analysed using a classical equilibrium approach by calculating peak applied loads, stem base rotation, equivalent stiffness trend over subsequent cycles and residual rotations. Then, the biomechanics of the trees were analysed using an energetic approach, focusing on the energy absorbed and dissipated during either the single load cycle or the complete cyclic test, by applying consolidated procedures used in the field of mechanical engineering.Results show how small but measurable residual rotations were measured after each load repetition, indicating permanent damage even in seemingly undamaged trees. Additionally, loads producing base rotations about 0.3–0.4 times those corresponding to the peak resistance dissipate less than 1 % of the maximum dissipated energy calculated at the same peak point. Additionally, this peak energy is found to be strongly correlated to both the peak moment and a typical stem volume predictor such as diameter at breast height squared times height.All these outcomes are intended to provide a starting point for the development of a different characterisation of tree resistance as an alternative to the current methodologies, especially when it is important to consider the effects of repeated loading on trees.

Generalized Quasi-Static Mooring System Modeling with Analytic Jacobians

This paper presents a generalized and efficient method for quasi-static analysis of mooring systems, including complex scenarios such as when shared mooring lines interconnect multiple floating wind or wave energy devices. While quasi-static mooring models are well established, most published formulations are focused on specific applications, and no publicly available implementations provide efficient handling of large mooring system networks. The present formulation addresses these gaps by: (1) formulating solutions for edge cases not typically supported by quasi-static models; (2) creating a fully generalized model structure such that any combination of mooring lines, point masses, and floating bodies can be assembled; and (3) deriving analytic expressions for the system Jacobians (stiffness matrices) so that systems with many degrees of freedom can be solved efficiently. These techniques form the theory basis of MoorPy, an open-source mooring analysis library. The model is demonstrated on nine scenarios of increasing complexity with features of interest for offshore renewable energy applications. When compared with steady-state results from a lumped-mass dynamic model, the results show that the quasi-static formulation accurately calculates profiles and tensions and that its analytic approach provides more efficient and reliable computation of system stiffness matrices than finite-differencing methods. These results verify the accuracy of the MoorPy model.

MEMS reservoir computing system with stiffness modulation for multi-scene data processing at the edge

Reservoir computing (RC) is a bio-inspired neural network structure which can be implemented in hardware with ease. It has been applied across various fields such as memristors, and electrochemical reactions, among which the micro-electro-mechanical systems (MEMS) is supposed to be the closest to sensing and computing integration. While previous MEMS RCs have demonstrated their potential as reservoirs, the amplitude modulation mode was found to be inadequate for computing directly upon sensing. To achieve this objective, this paper introduces a novel MEMS reservoir computing system based on stiffness modulation, where natural signals directly influence the system stiffness as input. Under this innovative concept, information can be processed locally without the need for advanced data collection and pre-processing. We present an integrated RC system characterized by small volume and low power consumption, eliminating complicated setups in traditional MEMS RC for data discretization and transduction. Both simulation and experiment were conducted on our accelerometer. We performed nonlinearity tuning for the resonator and optimized the post-processing algorithm by introducing a digital mask operator. Consequently, our MEMS RC is capable of both classification and forecasting, surpassing the capabilities of our previous non-delay-based architecture. Our method successfully processed word classification, with a 99.8% accuracy, and chaos forecasting, with a 0.0305 normalized mean square error (NMSE), demonstrating its adaptability for multi-scene data processing. This work is essential as it presents a novel MEMS RC with stiffness modulation, offering a simplified, efficient approach to integrate sensing and computing. Our approach has initiated edge computing, enabling emergent applications in MEMS for local computations.

Diaphragm wall lateral movement in deep excavations in Bangkok clays: impacts and influencing factors

Deep excavation in Bangkok clay layers involving diaphragm walls can cause ground movement, potentially affecting nearby structures. Understanding the magnitude and profile of this movement is crucial for assessing its impact on adjacent buildings. This study examines factors influencing the lateral displacement of rigid diaphragm walls in Bangkok's deep excavations, including construction methods, excavation duration, depth ratios, soft clay depth, and system stiffness. The research data were collected from 230 dataset of lateral movement in diaphragm walls with a thickness ranging from 0.60m to 1.50m. These walls had toe depths between 14m and 65m, across various excavation depths (He) from 6m to 35m. Maximum lateral wall displacements ranged from 0.10%He to 0.27%He for the top-down method, and from 0.20%He to 0.50%He for the bottom-up method. If the system stiffness is sufficient, variations in wall thickness and construction method have minimal impact on wall deflection. However, with the bottom-up method and 1.0m thick walls, long excavation times can lead to displacements up to 0.60%He. This is mainly due to consolidation and creep in the clay beneath the area where the base slab construction is delayed.

Elastic solution of surface-loaded one-dimensional hexagonal quasicrystal layered elastic media

This study aims to investigate the elastic response of a two-dimensional, surface-loaded substrate coated by a multi-layered system consisting of one-dimensional hexagonal quasicrystal materials. A linear elasticity theory for quasicrystals is adopted to simulate phonon and phason elastic fields. First, a set of governing differential equations for each layer is established in terms of the phonon and phason displacements. The general solution for a generic layer is constructed through the Fourier transform method in a closed form in the transform space. This solution is then utilized to formulate a layer stiffness equation. Adopting a direct stiffness method along with continuity along the layer interfaces, a stiffness equation for the multi-layered coated substrate is derived. An efficient quadrature is adopted to evaluate all involved integrals resulting from Fourier integral inversion. After verification with benchmark cases, the capability of the derived solutions are demonstrated by investigating the influence of various parameters such as layer thickness, layer arrangement, and loading conditions on the predicted response. Finally, applications of the developed multi-layer scheme to tackle a functionally graded quasicrystal layer are elucidated.

Experimental response characterization and comparative seismic performance assessment of a long-stroke shape memory alloy bridge restrainer

In this study, a long-stroke SMA Restrainer (LSR) device was fabricated and its response was characterized through experimental testing. The LSR consists of a long SMA bar encased in a steel tube to prevent its buckling. First, an optimal heat treatment procedure was identified to obtain superelastic response for SMA bars. Subsequently, the LSR underwent testing using an increasing amplitude tension-compression loading protocol and its mechanical properties such as equivalent stiffness and equivalent viscous damping ratio were computed. Based on the experimental findings, a high-fidelity 3D finite element model of LSRs was developed, which then used to design a full-scale LSR and verify its performance. Nonlinear time history analyses were conducted to assess the seismic performance of the proposed restrainers when used in a four-span simply supported bridge structure. The response of a case-study bridge equipped with steel cable restrainers, SMA bar restrainers, or LSRs were comparatively evaluated using a set of 40 near-fault ground motion records. Both SMA bar restrainers and LSRs were able to effectively limit the displacement response and provide the re-centering capabilities, while LSRs producing similar moments on piers compared to steel cable restrainers. In addition, compared to tension-only SMA bar restrainers, the LSRs require about only a quarter of SMA materials used in SMA bar restrainers.

Dynamic Modeling and Experimental Modal Analysis for the Central Rod-Fastened Rotor With Hirth Couplings Based on Fractal Contact Theory

Abstract The central rod-fastened rotor of gas turbine exhibits pronounced noncontinuous characteristics due to the large number of contact interfaces between the compressor and turbine disks. It is necessary to establish an accurate dynamic modeling method for the central rod-fastened rotor that fully considers the contact surface effect. In this work, the contact behavior of the rough surface is characterized by the fractal theory. The normal and tangential contact stiffness models are developed, and the influence of fractal parameters is discussed. Besides, the finite element model for the central rod-fastened rotor is established by developing an improved contact element considering the equivalent stiffness segment of Hirth couplings. Finally, the proposed model is verified by conducting the modal testing and measuring the first four modes of natural frequencies and modal shapes of the central rod-fastened rotor. The results show that the numerical results are in good agreement with the experimental ones, and the fractal contact model can effectively predict the connection stiffness of Hirth couplings, which in turn improves the simulation accuracy for the modal characteristics of the central rod-fastened rotor and provides a dynamic modeling approach with high efficiency and less computational complexity.

Numerical Investigation of the Seismic-Induced Rocking Behavior of Unbonded Post-Tensioned Bridge Piers

It is essential and convenient to use accurate and validated numerical models to simulate the seismic performance of post-tensioned (PT) rocking bridge piers, with a particular emphasis on accurately capturing rocking behavior. The primary contribution of this study is a comparison of the effectiveness of four commonly used numerical base rocking models (namely, the lumped plasticity (LP) model and the multi-contact spring (MCS) models with linear elastic (MCS-LE), bilinear elastic–plastic (MCS-EP) and nonlinear plastic (MCS-NP) material behavior, respectively) in modeling both the cyclic and seismic responses of PT rocking bridge piers. Also, this study validates the 3D contact stiffness equation for numerical models and assesses the differences between the dynamic and static stiffness values of the contact springs. Both quasi-static and shaking table tests of typical PT rocking piers are adopted to calibrate/validate these numerical models. These models describing the PT rocking piers’ seismic performance are formulated and calibrated, showing good agreement with test results for test specimens. Additionally, the suggested values of model spring stiffness for dynamic and quasi-static analyses are identified by parametric analysis. All base rocking models can predict the pier’s cyclic and seismic behavior after the calibration of contact spring stiffness values. The recommended contact stiffness for the dynamic analysis of PT rocking piers is smaller than that used for the quasi-static analysis. The results and findings provide a valuable reference and solution for the numerical simulation of PT rocking piers.

Improved calculation method for corresponding characteristics of foundation pit excavation on the diaphragm wall

The excavation of the pit causes displacement of the surrounding soil, and the excessive deformation causes damage to the existing support structure, which in turn affects the safety of the pit. Reasonable calculation of structural deformation and internal force is crucial for design and construction. Most of the existing theoretical methods simplify the diaphragm wall(DW) as an Euler-Bernoulli beam acting on the Winkler foundation, consider beam-soil interaction, and simplify the soil as isotropic and continuous. However, the shear effects due to the differential deformation of the structure, the unloading stresses acting on the structure due to foundation excavation, and the discontinuous nature of the multilayered soil are neglected. In this paper, an improved analysis method is proposed based on the elastic foundation beam theory. The DW is simplified as a Timoshenko beam and the foundation is simplified as a Vlasov two-parameter model, and a proposed model considering the shear effect of the DW and the interaction of adjacent springs is established, and the proposed method for the deformation and internal force of the DW is obtained by the finite-difference method. The correctness and applicability of the proposed method are verified by numerical simulation and field monitoring data. The effects of equivalent bending stiffness, equivalent shear stiffness, soil elastic modulus, and excavation depth on the deformation and internal force of the DW were further analyzed. The results show that the proposed method can accurately solve the deformation and internal force of the DW, and the maximum errors between the proposed method and the numerical simulation results are only 4.5 % and 1.3 %, respectively. The equivalent bending stiffness of the DW and the elastic modulus of the soil have more significant effects on the horizontal deformation and internal force. The excavation depth is more sensitive to the deformation of the DW, and there is an exponential decay trend between the two. When the equivalent shear and bending stiffnesses reach 6.8×107 kN·m2 and 2.9×107 kN/m, the effect on the horizontal deformation is no longer obvious. The proposed method in this paper can accurately calculate the internal force and deformation of the DW.

Cracking characteristics and axial capacity degradation of precast segmental bridge piers connected with corroded tapered sleeve locking-type splicing

The tapered sleeve locking-type splicing (TSLTS) reinforcement joint is a new method of steel mechanical connection. When applying the TSLTS reinforcement joints to precast segmental bridge (PSB) piers in coastal environments, the durability need to be taken into account. After the TSLTS reinforcement joint is corroded, the connection performance of the TSLTS reinforcement joint is degraded. Therefore, the mechanical properties of PSB piers decrease due to the corrosion of the joints, which brings some potential hazards. In this paper, the durability of PSB piers with TSLTS reinforcement joints in coastal environments was studied. The corrosion-induced cracking characteristics, failure mode and axial capacity of PSB piers with TSLTS reinforcement joints were investigated by means of accelerated corrosion test and axial loading failure test. The results indicated that, with increasing corrosion time, the total length of the corrosion-induced cracks on the surface of the pier specimens increased, but the increasing rate of the total length decreased. The mass loss of TSLTS reinforcement joints increased linearly with the maximum width of longitudinal corrosion-induced cracks on the concrete cover of the self-compacting concrete (SCC) segment, and the critical mass loss of TSLTS reinforcement joints was approximately 4.0 % when longitudinal corrosion-induced cracks appeared. The probability distribution type of the width of longitudinal corrosion-induced cracks on the surface of pier specimens was mainly a lognormal distribution. When the mass loss of TSLTS reinforcement joints was less than 7.2 %, the damaged area of the pier specimens was mainly concentrated in the SCC segment, while when the mass loss of TSLTS reinforcement joints was higher than 8.8 %, the damaged area was located in the ordinary Portland concrete segment near the top of the pier specimens, and the corroded TSLTS reinforcement joints could still maintain their connection performance. With an increase in the corrosion degree of the steel bars, the axial capacity of the pier specimens decreased, and the equivalent stiffness also degraded. The degradation rate of the axial capacity of the pier specimens increased linearly with the mass loss of the TSLTS reinforcement joints, and the degradation of the axial capacity occurred only when the mass loss of the TSLTS reinforcement joints was greater than 4.6 %. The research results can provide a theoretical reference for the application of TSLTS reinforcement joints in PSB piers.

INTELLIGENT NUMERICAL METHOD FOR STUDYING MAXWELL WILLIAMSON NANOFLUID FLOW WITH ACTIVATION ENERGY

The use of artificial intelligence and its techniques has become increasingly widespread in recent times. It is being used to solve stiff non-linear equations. Additionally, nanofluids play a pivotal role in studying heat transfer. All of this was the motivation for doing this work. This work investigates a two-dimensional magnetohydrodynamic stretched flow (2D-MHDSF) of Maxwell Williamson nanofluid (MWNF) affected by bioconvection and activation energy numerically through Levenberg-Marquardt backpropagation method (LMBM)-based artificial neural network approach. The mathematical formulation for the problem was obtained through non-linear partial differential equations (PDEs). The leading PDEs were transmitted into non-linear ordinary differential equations by similarity transformation variables. The reference results for the 2D-MHDSF-MWNF model are produced by the Lobatto IIIA method through different scenarios of specific parameters for the flow velocity, fluid temperature, nanoparticle concentration, and motile density profiles. Using obtained results as a dataset to apply the testing, training, and validation steps of the suggested LMBM for the 2D-MHDSF-MWNF model. The mean squared error, analysis of regression, and error histograms are presented to prove the efficiency and precision of the proposed method. The numerical results of LMBM are displayed as a study of the effects of different physical factors on flow dynamics for 2D-MHDSF-MWNF.

Deferred correction neural network techniques for solving ordinary differential equations

Neural network technology is widely used to solve problems across science and engineering fields. In this paper, a neural network technique is applied to solve ordinary differential equations (ODEs), instead of using conventional time marching techniques with discretization for ODEs. A numerical solution to ODEs is defined with polynomial basis, and each coefficient of the expansion is calculated through an unsupervised neural network structure in the entire time domain. To make the calculated solution more accurate, we consider the deferred correction technique for calculating a numerical residual with a physics-informed neural network. The empirical results show that the proposed scheme with polynomial basis can influence calculation accuracy depending on the order of basis polynomials, providing the possibility of improving accuracy and efficiency by increasing the order of basis. Several numerical tests confirm that the proposed deferred correction network (DCNet) model has an accuracy approximately 100 and 10 times higher than that of the learning polynomial neural network (LPNet) and the standard existing method, physics-informed neural network (PINN), respectively. Additionally, the proposed schemes generate stable results even for stiff problems and preserve the conservation property for Hamiltonian systems.

A conceptual examination of an additive manufactured high-ratio coaxial gearbox

This research introduces the novel “Kraken-Gear” mechanism, emphasizing the advantages of additive polymer 3D printing in high-ratio gearbox systems for lightweight robotic applications, such as surgical instruments. The innovative kinematic solution provides high torsional system stiffness, substantial gear ratios, and backlash-free transmission. Leveraging the “hot lithography” additive manufacturing method ensures precise and warp-free gearbox components. Targeting medical technology, the gearbox meets stringent requirements: backlash-free, minimal vibration, high precision, and torque, with minimized weight for ergonomic comfort and fatigue mitigation. Computational simulations assess forces and stresses, highlighting the potential of additive manufacturing for cost-effective and functionally efficient gearbox fabrication. Nevertheless, careful material selection remains imperative for optimal functionality, especially in demanding medical applications. In summary, this research underscores a promising approach to gearbox fabrication, emphasizing the critical role of material selection and simulation-based assessments for optimal performance.

Linear Contact Load Law of an Elastic–Perfectly Plastic Half-Space vs. Sphere under Low Velocity Impact

The impact of contact between two elastic–plastic bodies is highly complex, with no established theoretical contact model currently available. This study investigates the problem of an elastic–plastic sphere impacting an elastic–plastic half-space at low speed and low energy using the finite element method (FEM). Existing linear contact loading laws exhibit significant discrepancies as they fail to consider the impact of elasticity and yield strength on the elastic–plastic sphere. To address this limitation, a novel linear contact loading law is proposed in this research, which utilizes the concept of equivalent contact stiffness rather than the conventional linear contact stiffness. The theoretical expressions of this new linear contact loading law are derived through FEM simulations of 150 sphere and half-space impact cases. The segmental linear characteristics of the equivalent contact stiffness are identified and fitted to establish the segmental expressions of the equivalent contact stiffness. The new linear contact loading law is dependent on various factors, including the yield strain of the half-space, the ratio of elastic moduli between the half-space and sphere, and the ratio of yield strengths between the half-space and sphere. The accuracy of the proposed linear contact loading law is validated through extensive Finite Element Method simulations, which involve an elastic–plastic half-space being struck by elastic–plastic spheres with varying impact energies, sizes, and material combinations.

Static performances of scissor structures

Scissor structures have very promising applications and have attracted much attention due to their novel characteristics of being deployable and foldable. However, most of the current studies have focused on its geometric and kinematic characteristics, while neglecting the analysis of their mechanical properties as load-bearing structures. In this study, general formulas for calculating the internal forces and equivalent bending stiffness of scissor structures are derived and verified using finite element method. The results show that the analytical and numerical simulation solutions are in good agreement and the expansion angle is the main factor affecting the static performances of the scissor structures. In particular, the extreme increase in axial force at expansion angles above 60°will lead to instability problems. Therefore, special attention should be paid when determining the expansion angle at or above 60°. Herein, the bending moment dominates the internal forces and the stresses generated by the bending moment exceed the axial forces by a factor of about 10–30. This study is expected to contribute greatly to scissor structure design by quantitatively evaluating preliminary design, exploring the impact of various parameters, optimizing design, and understanding limitations and potential issues.

Superfluid stiffness and Josephson quantum capacitance: Adiabatic approach and topological effects

We bring forward a unified framework for the study of the superfluid stiffness and the quantum capacitance of superconducting platforms exhibiting conventional spin-singlet pairing. We focus on systems which in their normal phase contain topological band touching points or crossings, while in their superconducting regime feature a fully gapped energy spectrum. Our unified description relies on viewing these two types of physical quantities as the charge current and density response coefficients obtained for slow spatiotemporal variations of the superconducting phase. Within our adiabatic formalism, the two coefficients are given in terms of Berry curvatures defined in synthetic spaces. Our paper lays the foundation for the systematic description of topological diagonal superfluid responses induced by singularities dictating the synthetic Berry curvatures. We exemplify our approach for concrete one- and two-dimensional models of superconducting topological (semi)metals. We discuss topological phenomena which arise in the superfluid stiffness of bulk systems and the quantum capacitance of Josephson junctions. We show that both coefficients become proportional to a topological invariant which counts the number of topological touchings or crossings of the normal phase band structure. These topological effects can be equivalently viewed as manifestations of chiral anomaly. Our predictions appear experimentally testable in topological semimetals with proximity-induced pairing, such as in graphene-superconductor hybrids at charge neutrality. Published by the American Physical Society 2024

A concave X-shaped structure supported by variable pitch springs for low-frequency vibration isolation

Based on the known X-shaped structure, a concave X-shaped structure (CXSS) featuring custom-designed variable pitch springs (VPS) is proposed. This design aims to enhance the displacement range of the quasi-zero stiffness (QZS) system and improve its performance in isolating low-frequency vibrations. The CXSS is obtained by merging two semi-X-shaped structures. The negative stiffness property of the concave structure can be improved by utilizing the motion limitations of the mechanical structure. Of particular concern is the VPS, it can provide nonlinear restoring force and variable stiffness by self-adjusting the effective number of coils. This special spring is suitable to neutralize the negative stiffness of the concave structure, enabling a wider range of QZS properties than linear springs and magnets. The average error between the practical and theoretical restoring force of the VPS is less than 10 %. Based on a special compression coefficient, the objective-load design method (OLDM) is proposed to obtain the stiffness conditions implementing QZS properties against rated mass. The stiffness obtained by the OLDM is considerably accurate. Under this condition, the vibration transmissibility is about 0.45 at 3.5 Hz and 0.1 at 14 Hz, which is lower than that of the unmatched load and stiffness coefficients. Compared with the X-shaped structure, the proposed structure has better low-frequency vibration isolation performance with a natural frequency of about 2 Hz. The vibration transmissibility is about 0.2 at 5 Hz and is about 0.1 at 10 Hz. Pulse excitations with an amplitude of 16 g can be attenuated to about 0.51 g through the CXSS compensated by VPS. It is convenient and efficient to implement QZS properties using the VPS to compensate negative stiffness.