Effective Stiffness Research Articles

A comparative study on rotordynamics characteristics of hole-pattern damping seals with different cavity shapes

PurposeThe purpose of this paper is to improve the seal performance by proper design of the cavity shape of the damping holes, especially the rotordynamics characteristics of the hole-pattern damped seal (HPDS).Design/methodology/approachA new damping seal structure that comprises a circle-shaped cavity and two directional leaf-shaped cavities with a dovetail-shaped diversion groove is proposed. The comparative study on the sealing characteristics of dovetail-shape, leaf-shape and classical circular HPDSs was carried out using ANSYS CFX.FindingsThe dovetail-shaped HPDS significantly outperformed two other damping seal designs in leakage and rotordynamic performance. At a rotating speed of 7,500 rpm, it showed a 25% reduction in leakage, a 23% increase in average effective damping and a 119% increase in average effective stiffness. The cross-coupled stiffness Kxy shifted from positive to negative, reducing circumferential flow. The dovetail's inclined leaf-shaped grooves create a double vortex that slows jet velocity in the seal clearance and alters spiral flow direction, resulting in a uniform pressure distribution and enhanced rotor stability at low frequencies.Originality/valueThis study proposes a novel HPDS with dovetail-shaped diversion grooves. The seal can realize the simultaneous improvement of rotordynamics and leakage characteristics compared to the current seal structure.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-04-2024-0127/

Structure, control, and dynamics of altermagnetic textures

We present a phenomenological theory of altermagnets, that captures their unique magnetization dynamics and allows modeling magnetic textures in this new magnetic phase. Focusing on the prototypical d-wave altermagnets, e.g., RuO2, we can explain intuitively the characteristic lifted degeneracy of their magnon spectra, by the emergence of an effective sublattice-dependent anisotropic spin stiffness arising naturally from the phenomenological theory. We show that as a consequence the altermagnetic domain walls, in contrast to antiferromagnets, have a finite gradient of the magnetization, with its strength and gradient direction connected to the altermagnetic anisotropy, even for 180° domain walls. This gradient generates a ponderomotive force in the domain wall in the presence of a strongly inhomogeneous external magnetic field, which may be achieved through magnetic force microscopy techniques. The motion of these altermagentic domain walls is also characterized by an anisotropic Walker breakdown, with much higher speed limits of propagation than ferromagnets but lower than antiferromagnets.

Steel I-girder geometries for enhanced stability in shear loading

This paper challenges the design provisions that rely on the traditional assumptions of simply supported web boundary conditions for shear. While some literature discuss the flange stiffening effect on the web, the detrimental impact of flexible flanges on the shear strength has not been addressed before. Through a detailed analysis of excessive deformations at the web-flange junctions, this study shows that the assumption of simply supported web boundary conditions may be unsafe, contradicting expectations of conservative design in some girders that comply with current design specifications. Accordingly, minimum flange dimensions are proposed to ensure adequate support at the web edges. In addition to categorizing cross-sections that do not achieve simply supported boundary conditions, the paper proposes a modified elastic shear buckling coefficient, which can enhance the estimate of elastic shear buckling stresses of I-girders by up to 60% compared to simply supported web plates. The improved elastic buckling stress is also shown to improve the overall shear strength predictions of I-girders by means of geometric and material nonlinear analyses. This revised coefficient considers the intricate interplay between the flanges, transverse stiffeners, and the web, which shall enable a more mechanistic and consistent interpretation of the ultimate shear capacities in future studies. The findings presented in this paper have implications for cross-sectional proportioning and shear design of plate girders, given that the ultimate design shear capacities of I-girders are typically estimated by summing the web elastic shear buckling stresses with their post-buckling strengths.

Low-frequency multiple topological interface modes in metamaterial beams with quasi-zero-stiffness resonators

To achieve multiple low-frequency topological interface modes (TIMs) while maintaining lightweight and load-bearing capacities in metamaterial beams, we propose novel topological beams equipped with double quasi-zero-stiffness (QZS) resonators. Following the introduction of the negative stiffness (NS) mechanism, we derived the dispersion relations of the topological beams with double QZS resonators using the transfer matrix method (TMM), and performed comparative and parametric analyses of stiffness ratio on folded Dirac cones (DCs) and locally resonant band gaps (LRBGs). Thanks to the NS mechanism and the double degrees of freedom (DOFs) in the QZS resonators, we can realize double low-frequency DCs (< 500 Hz) in metamaterial beams. It is notable that adjusting the stiffness of oblique springs can tune the resonators’ effective stiffness, implying that we can custom the frequency of DCs and LRBGs by adjusting the QZS resonator. By altering the distance between two QZS resonators, we obtain two topologically distinct unit cells. Transmission simulations confirm the presence of multiple low-frequency TIMs at the interface between these two domains. We also find that the effect of mass and geometric defects at various positions on TIMs is minimal. The proposed metamaterial beams could inspire innovative low-frequency vibration energy harvesters and lightweight topological devices.

Parametric Study of Structural Seismic Response: Correlation Between Lateral Load, Displacement, and Stiffness

Indonesia, located near the convergence of major tectonic plates, often experiences significant earthquakes that impact buildings. Many houses damaged by earthquakes are simple structures with red brick masonry. This study analyzes the seismic performance of masonry houses using ETABS software, assuming the houses are in seismic zone 4 and built on soft soil. The analysis focuses on the correlation between lateral loads, displacement, and structural stiffness. The results indicate that the maximum lateral load occurs in the X direction, while the maximum displacement occurs in the Y direction, indicating higher flexibility in the Y direction. Higher structural stiffness reduces displacement but also increases inertia forces. The nonlinear correlation between lateral loads and displacement, as well as the decrease in effective structural stiffness with increasing lateral loads, underscores the importance of balancing stiffness and flexibility in structural design. This study provides valuable insights for earthquake-resistant building design, particularly for masonry houses in earthquake-prone areas of Indonesia. The analysis emphasizes the importance of reinforcing critical areas and ensuring a more uniform distribution of lateral loads to enhance structural resilience to earthquakes. Keywords: ETABS, House, Life Safety, Performance, Seismic

Unlocking slip-mediated bending in multilayers: Efficient modeling and solutions with high precision and simplicity

This work introduces a novel approach to understanding the bending behavior of multilayer structures with weak interfaces. Despite the existence of various theoretical models, achieving high accuracy and computational efficiency remains a challenge. To address these limitations, we propose a Non-uniform Slip Model (NSM) governed by two essential dimensionless parameters: the number of layers and the shear factor. Utilizing the Semiparametric Hybrid Variational (SHV) method, we derive theoretical solutions that require less computational effort and offer enhanced accuracy. We further simplify the NSM through homogenization to the Uniform Slip Model (USM), yielding clear and concise analytical solutions for deflection curves and effective bending stiffness with high precision. The USM is also extended to account for nonlinear slipping interfaces with continuous shearing flow, providing an analytical stiffness expression that includes the bending angle. This extension explains the experimental observation of multilayered graphene’s bending stiffness, which decreases from cubic to linear with increasing number of layers due to continuous slip and dislocation between atomic layers. Our study delivers theoretical insights for analyzing slip-mediated bending in laminated materials, paving the way for the design and optimization of such structures.

Planar biaxial testing of CXL strengthening effects

The stiffening effect of corneal crosslinking (CXL) treatment, a therapeutic approach for managing the progression of keratoconus, has been primarily investigated using uniaxial tensile experiments. However, this testing technique has several drawbacks and is unable to measure the mechanical response of cornea under a multiaxial loading state. In this work, we used biaxial mechanical testing method to characterize biomechanical properties of porcine cornea before and after CXL treatment. We also investigated the influence of preconditioning on measured properties and used TEM images to determine microstructural characteristics of the extracellular matrix. The conventional method of CXL treatment was used for crosslinking the porcine cornea. The biaxial experiments were done by an ElectroForce TestBench system at a stretch ratio of 1:1 and a displacement rate of 2 mm/min with and without preconditioning. The experimental measurements showed no significant difference in the mechanical properties of porcine cornea along the nasal temporal (NT) and superior inferior (SI) direction. Furthermore, the CXL therapy significantly enhanced the mechanical properties along both directions without creating anisotropic response. The samples tested with preconditioning showed significantly stiffer response than those tested without preconditioning. The TEM images showed that the CXL therapy did not increase the diameter of collagen fibers but significantly decreased their interfibrillar spacing, consistent with the mechanical property improvement of CXL treated samples.

Ultra-broad sensing range, high sensitivity textile pressure sensors with heterogeneous fibre architecture and molecular interconnection strategy

Textile-based pressure sensors have garnered extensive attentions owing to their potentials in health monitoring, human–machine interactions, wearable human–machine interfaces (HMIs) and soft robotics. High sensitivity over a broad sensing range are highly desired yet challenging for textile pressure sensors due to the incompressibility of matrix materials and the stiffening of microstructures. Herein, we developed a high performance pressure sensor based on the silk/3-Aminopropyltriethoxy-silane/titanium carbide (Silk/APTES/MXene) film. The silk is designed with heterogeneous fiber architecture, which enables rich and multi-level contact pattern and could compensate for the effect of structural stiffening. Furthermore, APTES molecules are used to enhance the interface bonding between MXene and silk, promoting the mechanical stability of the sensor. Benefiting from these advantages, the Silk/APTES/MXene sensor device is achieved with high sensitivity of 17.1 KPa−1 over an ultra-broad sensing range up to 3.3 MPa (R2 = 0.997), ultra-low detection limit (0.25 Pa), and low fatigue toughness after 5000 cycles loading and unloading. With these merits, we have demonstrated its capability for a series of human motion detection (such as foot movement detection, arm/wrist/finger bending, etc) and an overall accuracy of 95 % is obtained with the help of CNN-based convolution neural architecture. More significantly, we have built an entire intelligent human–machine dialogue system and a patient-audience dialogue system, from lip/sign language recognition to real-time screen display and final voice output.

Numerical Evaluation of the Influence of Using Carbon-Fiber-Reinforced Polymer Rebars as Shear Connectors for Cross-Laminated Timber–Concrete Panels

Carbon fiber-reinforced polymer (CFRP) sheets have been used to reinforce cross-laminated timber (CLT)–concrete systems in recent years. The existing studies have indicated that the use of CFRP rebars as shear connectors in CLT–concrete panels can improve the structural performance of these elements. However, the application and understanding of CFRP rebars as shear connectors still need to be improved, since comprehensive studies on the subject are not available. Therefore, this research aimed to evaluate the structural performance of CLT–concrete panels with CFRP rebars as shear connectors through finite element (FE) numerical simulation. A parametric study was conducted, varying the connector material, the number of CLT layers, the connector insertion angle, and the connector embedment length. According to the results, panels with CFRP connectors showed a higher maximum load, bending strength, and maximum bending moment than panels with steel connectors. The regression models revealed that the parameters analyzed explained between 80.2% and 99.9% of the variability in the mechanical properties under investigation. The high explanatory power (R2) of some regression models in this study underscores the robustness of the models. The number of CLT layers and the connector material were the most significant parameters for the panels’ maximum load, displacement at the maximum load, ductility, bending strength, and maximum bending moment. The number of CLT layers and the connector insertion angle were the most significant parameters for the panels’ effective bending stiffness. This research highlights the importance of studies on CLT–concrete composites and the need to develop equations to estimate their behavior accurately. Moreover, numerical simulations have proven very valuable, providing results comparable to laboratory results.

Shear buckling behaviour of sinusoidal corrugated web girders with stiffened circular openings

The mechanical properties and failure behaviours of three different specimens of sinusoidal corrugated web girders with stiffened circular openings were investigated experimentally and numerically. The experimental outcomes showed similarities in the mechanical properties and failure model of the specimens, despite differences in the geometric dimensions. The numerical simulations further confirmed the buckling as well as post-buckling behaviours of the experimental results. The influence of initial geometric imperfections on the shear buckling load of the corrugated web girders was quantified and neglecting geometric imperfections led to an overestimation of the actual shear load capacity, emphasizing the importance of considering imperfections in the design of structural components. The investigation results showed that the shear load capacities of the girders were significantly affected by the thickness of the opening stiffeners, and that the presence of openings reduced the load carrying capacity and the overall stiffness of the beams, whereas the existence of opening stiffeners increased both the ultimate load bearing capacity and the global stiffness. However, the strengthening effect of the opening stiffener becomes less pronounced beyond a specific thickness. Besides, a comparison between hand calculations and numerical simulations show that the recently developed calculation method provided a more reliable prediction of the shear buckling resistance of corrugated web with stiffened openings. This investigation provides valuable guidance on the shear buckling behaviour of sinusoidal corrugated web girders with circular opening stiffeners, thus benefiting the design and analysis of steel structural components with sinusoidal corrugated web.

Design, Fabrication, and Dynamic Analysis of a MEMS Ring Resonator Supported by Twin Circular Curve Beams.

In this paper, we present a compressive study on the design and development of a MEMS ring resonator and its dynamic behavior under electrostatic force when supported by twin circular curve beams. Finite element analysis (FEA)-based modeling techniques are used to simulate and refine the resonator geometry and transduction. In proper FEA or analytical modeling, the explicit description and accurate values of the effective mass and stiffness of the resonator structure are needed. Therefore, here we outlined an analytical model approach to calculate those values using the first principles of kinetic and potential energy analyses. The natural frequencies of the structure were then calculated using those parameters and compared with those that were simulated using the FEA tool ANSYS. Dynamic analysis was performed to calculate the pull-in voltage, shift of resonance frequency, and harmonic analyses of the ring to understand how the ring resonator is affected by the applied voltage. Additional analysis was performed for different orientations of silicon and assessing the frequency response and frequency shifts. The prototype was fabricated using the standard silicon-on-insulator (SOI)-based MEMS fabrication process and the experimental results for resonances showed good agreement with the developed model approach. The model approach presented in this paper can be used to provide valuable insights for the optimization of MEMS resonators for various operating conditions.

A metamaterial with enhanced effective stiffness and negative Poisson's ratio for frictional energy dissipation

Unlike traditional energy dissipation structures that dissipate energy through irreversible plastic deformation or collapse, metamaterials based on friction energy dissipation have attracted attention due to their reusability. This article proposed a novel energy dissipation metamaterial by integrating friction energy dissipation mechanism into negative Poisson's ratio (NPR) structures. The integration of friction energy dissipation mechanism can simultaneously enhance the effective stiffness and NPR effect. The mechanical properties of the proposed structure were investigated using theoretical analysis, experiments, and finite element (FE) simulations. The influence of variables such as internal concave angle, friction coefficient, and number of reinforcing ribs was discussed. The results indicate that both unit cell and honeycomb structure can repeatedly dissipate energy within the elastic range. Compared with the traditional concave hexagonal structure, the effective stiffness and NPR effect were enhanced. This work provides a novel idea for the design of NPR energy dissipation structures.

Preparation and characterization of lignin copolymerized phenolic resins with superior stiffening effect for natural rubber composites

The development of lignin-derived functional additives for rubber composites has gained growing importance in light of biomass valorization. This work aims at preparing phenolic novolak resin with lignin as one building block for reinforcing natural rubber. A one-pot two-step synthetic approach involving phenolation and copolymerization was developed to prepare lignin-phenol-formaldehyde resins (LPF), wherein 30 wt% of phenol was substituted by lignin. With increasing the ratio of formaldehyde/phenol functionality (F/P), resins show increased molecular weight, elevated glass transition temperature and declined curing activity. The resin with F/P of 0.68/1 exhibits a higher stiffening effect compared to the control without lignin. This enhancement is attributed to lignin's ability to form a hyperbranched structure with multiple phenolic arms as implied by GPC results, acting as a crosslinking hub and facilitating the formation of an effective network. Furthermore, we introduced cardanol with a flexible alkene chain to prepare cardanol-lignin-phenol-formaldehyde resins (CLPF). The CLPF15 resin with cardanol/lignin/phenol of 15/30/55 wt% achieves the maximum stiffening effect due to improved compatibility with natural rubber. This study provides insights into the design and optimization of lignin-copolymerized resins for enhancing the mechanical properties of rubber composites.

A fast and effective stiffness prediction method for short fiber reinforced composites with skin‐core structure

AbstractThe extrusion procedure used to manufacture Short Fiber Reinforced Composites (SFRCs) results in significant anisotropy in the components due to the skin‐core structure. While there are existing accurate stiffness prediction methods available, there is still a need in engineering for an efficient and cost‐effective prediction method. This work proposes an efficient, low‐cost and effective stiffness prediction method for skin‐core structure using the orientation averaging method and series–parallel model. Initially, the sample is analyzed using industrial CT and metallographic microscopy to ascertain the fiber characteristics and skin‐core dimensions. Furthermore, it is presumed that the skin and core are distinct materials and their stiffness is determined using the orientation averaging method. Finally, the stiffness of the sample is determined by employing a series–parallel model for analyzing stress–strain transmission, which involved merging the skin and core components. Experimental and finite element results confirm the method's accuracy, boasting a calculation time of 31.36 s and a maximum stiffness error below 10%. This method is expected to be applied to automotive, construction and other engineering fields to meet the demand for fast, cost‐efficient and effective stiffness prediction of SFRCs.Highlights A stiffness prediction method is proposed, which is no modeling required. Combined with Hashin‐Tsai, orientation average method and series–parallel model. The stiffness of skin‐core structure is predicted by this method within 31.36 s. This method can be extended to more complex fiber orientation examples.

Mechanical response of 3D printed irregular sutural tessellations with Voronoi tile patterns under tension

The mechanical response of bio-inspired irregular sutural tessellations with Voronoi tile patterns are designed and fabricated via multi-material 3D printing. The effective mechanical properties of the designs were characterized via uni-axial tension mechanical experiments on the 3D printed specimens. Systematic nonlinear finite element simulations are conducted to explore the damage initiation and evolution of the designs. The influences of important design parameters, including tile length aspect ratio R, tile size irregularity Cstd, suture amplitude irregularity Astd, and stiffness ratio between the soft and hard phases, were evaluated. The effective stiffness, Poisson’s ratio, strength, toughness, and failure mechanisms are systematically quantified. The results demonstrate that an optimized level of suture irregularity exists for maximizing the modulus of toughness. The results provide a general design guideline for designing functionally graded two-phase tessellations with high mechanical performance.

Effective Stiffness and Damping Analysis of Steel Damper to Lateral Cyclic Loading

Steel dampers are components used in building structures to reduce vibration and energy generated by dynamic loads such as earthquakes. Several factors affect the effectiveness of steel dampers in reducing energy, including the cross-sectional area, mass distribution, cross-sectional geometry, and material stiffness. The cross-sectional geometry or shape of the steel damper can affect how energy is absorbed and dissipated in the structural system. Cross sections with different geometric variations can have different mechanical responses to dynamic loads. This study aims to analyze which type of steel damper is effective in terms of stiffness and damping capacity against lateral cyclic loads. The steel damper cross-sectional variations used are slit steel dampers (SSDs), tapered steel dampers (TSDs), and oval steel dampers (OSDs). Cyclic testing of the dampers used displacement control with the same target deviation for all three damper types. The results showed that the stress and strain distributions of the oval steel damper were more even than those of the other two models. The variations in the energy dissipation capacities of the three cross-section variations are relatively the same. However, the slit steel damper type has the best stiffness compared to the other two types. This research is ultimately expected to influence the science of the structure of a building in preventing and anticipating earthquakes or other disasters. Doi: 10.28991/CEJ-2024-010-07-017 Full Text: PDF

Effective response and microstructure evolution for shape memory alloy laminated composites

A model for the macroscopic mechanical behavior of rank-1 laminates including two shape memory alloy (SMA) phases is presented. The model expresses the general behavior of the composite with phases undergoing rate-independent elastic and inelastic deformations. Homogenization techniques (including the rank-1 laminate model) are used to establish the effective behavior of the SMA laminated composite (SLC) based on the information about the mechanical response of the individual phases and their volume concentrations. A stress-control algorithm is put forward to implement the model. With the aid of the stress-control algorithm, an implicit expression for the effective tangent stiffness and an evolution equation for the effective inelastic strain are derived. Results are compared with the outcomes of an FE-based computational homogenization and a very good agreement is seen. By using a constitutive model with internal variables for the dense SMA, the overall response of the SLC under different mechanical loadings is evaluated. The effective response of the SLC for various volume concentrations of the phases is assessed and exclusive comparisons are illustrated. Furthermore, the influence of different temperatures on the effective superelastic behavior of the SLCs is studied. The findings have implications for the analysis and the design of more complex shape-memory-alloy laminated composites for high-end applications.

Theoretical model for elastic modulus prediction on basis of atomic structure information: Beginning from amorphous carbon to covalent bonding materials

The mechanical property is one of the most important properties of a material and is determined by the atomic-scale structure. It is thus crucial to establish the theoretical model for the prediction of materials' mechanical properties, benefiting the material design. In our previous work, we proposed an atomic-scale structure-based model for predicting the Young's modulus of hydrogenated amorphous carbon; however, the application range of this model is too narrow to be used practically for the materials development. Therefore, in this work, an extended prediction model of Young's modulus of materials with wide applicability is successfully constructed, based on the two important inherent properties of materials: one is effective coordination number (CNeff) evaluating how densely atoms are structured and the another one is effective bond stiffness (Keff) that is first proposed here and indicates how bonding types contribute the elastic properties. Through the high-throughput molecular dynamics simulations, the predictive model of Young's modulus (E) is determined as E = 3.37Keff (CNeff - 2.0)1.5. Then we demonstrate that this model is valid for a large variety of materials including both amorphous and crystalline structures, and the accuracy is proven by comparing with other work. Overall, this fundamental work may benefit the preparation, development, and utilization of new materials.

Effect of partition walls on the vibration serviceability of cross-laminated timber floors

The current standards need more specific serviceability criteria for Cross-Laminated Timber (CLT) floors. This paper presents a comprehensive analysis of a relevant case study in Norway, which presented unexpectedly high accelerations in the CLT floors after construction. The lack of a sufficiently detailed design process resulted in the poor vibration performance of the floors, which partially compromised their functionality. The paper thoroughly investigates and discusses the experimental dynamic characterization of seven CLT floors within the considered building. The authors estimated the modal parameters and serviceability metrics based on both Eurocode 5 (EC5) and the new draft version of it. Specifically, the authors compared the analytical predictions of the fundamental frequency and the root mean square acceleration against the corresponding experimental estimations. Using a sensor-roving approach, a dense sensor configuration was adopted to describe seven floors’ mode shapes and serviceability metrics. These metrics include mean square acceleration and Vibration Dose Value. The scenarios examined in this study shed light on the significance of partition walls, a factor not considered in the practical design for serviceability verifications. The presence of partition walls can enhance the vibration comfort of timber floors by providing a stiffening effect, leading to a significant increase in the first fundamental frequency. A parametric finite element model was developed using OpenSeesPy to investigate this phenomenon further. The model, firstly validated against selected experimental results, is employed to assess the influence of partition walls on floor dynamics. The model predicts the increase in the first frequency caused by randomly generated partition walls. The paper proposes an empirical expression calibrated on the simulated data to estimate the relative increment of the floor’s fundamental frequency based on the partition walls’ layout. This formulation can be included in the analytical expression enclosed in the EC5 draft to predict the fundamental frequency of timber floors.

Effects of Matrix Cracking-Induced Delamination on Thermal Buckling of Composite Laminate

Abstract Delamination and matrix cracking are common damage modes in composite laminates, significantly impacting their structural integrity and performance. Under elevated temperatures, the collision of anisotropic thermal expansion and nonlinear stiffness responses affect the onset of thermal buckling in flying vehicles. This study implements a multi-scale analysis framework, incorporating finite element modeling and analytical methods to obtain the reduction in mechanical properties of the composite laminate and its stiffness degradation based on an effective stiffness model due to pre-existing matrix cracking in plies. Based on non-linear equations, obtained from the principle of virtual work, in combination with first-order shear deformable theory and von Kármán strain-displacement relations, the thermal buckling temperature, post-buckling behavior of composite laminates are investigated. This work paves the way for developing a model to predict the influence of the laminate stiffness, delamination size, transverse crack location, stacking sequence, and plies thickness on the laminate.