Equivalent Stiffness Research Articles

The Efficiency of Block Hybrid Method for Solving Malthusian Growth Model and Prothero-Robinson Oscillatory Differential Equations

The efficiency of block hybrid method for solving Malthusian Growth Model, Prothero-Robinson equation and highly stiff oscillatory differential equations was proposed using a power series polynomial through interpolation and collocation. The new method's basic properties, including order, error constant, consistency, zero-stability, and stability regions, were comprehensively analyzed and satisfied all necessary conditions for analysis. Tested on various real-life problems, the new method demonstrated superior performance compared to existing techniques. The study highlights the innovative approach's enhanced convergence and stability properties, providing a more reliable numerical analysis tool for researchers and practitioners. Practical applications validate the method's effectiveness, showcasing its superior performance across different examples and establishing it as a highly effective solution for Malthusian growth model and oscillatory differential equations.

Integration of 3-D 4-directional braided composites into dynamic modeling of plates with large overall motions

In this study, a dynamic model of a 3-D 4-directional braided composite plate with large overall motions is proposed. Based on the Kirchhoff’s plate hypothesis, the deformation of the orthotropic plate is described. The assumed mode method is employed to discretize the displacement variables, and the rigid-flexible coupled dynamic model of the plate is derived from the Lagrange equation. The equivalent stiffness matrices of 3-D 4-directional braided composites with different braided angles are obtained using the homogenization method. The effects of different velocities and braided angles on the dynamic characteristics of the plate with translational motion and fixed-axis rotation, respectively, are investigated. The present study lays the theoretical foundation for analyzing the dynamic properties of orthotropic plates in engineering components. For example, the dynamic model established in this study can be used to estimate the dynamic responses of braided composite parts in aeronautical structures.

Ultra-Low-Frequency Energy Harvesting in Quasi-Zero Stiffness Systems with Inertial Amplifiers Under Mixed Harmonic Excitation

Ultra-Low-Frequency Energy Harvesting in Quasi-Zero Stiffness Systems with Inertial Amplifiers Under Mixed Harmonic Excitation

Study on characterization of moderate energy impact response of elastic-plastic plate structure

This paper presents a study on the characterization of the moderate energy impact response between the elastic-plastic plate and the elastic-plastic sphere. An equivalent contact stiffness is proposed to substitute the linear contact stiffness, and a universal analytical expression is presented according to the intensive FE simulations for different material combinations under moderate impact energy. Then, a modified characterization diagram is suggested using the analytical expression. The modified diagram is validated by the FE simulations and experimental results. The results show the modified diagram can predict the maximum impact force and the response type in a fast and simple way.

An analytical model to calculate the forced vertical vibrations of two rails subjected to the dynamic loads of ballasted railway track

The railway track consists of two rails which are solicited the loads from passing trains. Due to the dynamic nature of these loads, the total forces applied to each rail are unequal and asymmetric. However, analytical models that simplify the track as a single beam cannot accurately describe the track responses. In this paper, we calculate the forced vertical vibration of a ballasted railway track subjected to dynamic loading with dual rails. Each rail is modelled as a uniform Euler–Bernoulli beam of infinite length, positioned on a system of periodic and identical supports. The forced vibration of the rail is determined using Floquet’s theorem. Additionally, a model of a beam on a continuous foundation is employed to describe the dynamic behaviour of each support. In the frequency domain, each support is represented as a spring with an equivalent stiffness. By combining these two developed models, we analytically obtain the forced vibrations of two rails in the frequency domain. In the symmetric configuration, our results show a similarity of the rail responses with an existing model, particularly at the pin-pin resonance. The differing peak resonances at low-band frequencies are attributed to the different types of support. Subsequently, we apply this new model to investigate the forced vibrations of two rails in a non-symmetric configuration. The numerical tool visually illustrates the influence of load positions on rail responses and reaction forces in the time domain. This analytical model proves valuable for studying the rail noise and vibration of ballasted railway tracks.

Hybrid block formulae whose eigenvalues of Jacobian matrices are close to the imaginary axis of the complex plane

Methods for integrating stiff initial value problems are required to be A-stable. Of great interest are A-stable methods whose Jacobian matrices have their eigenvalues close to the imaginary axis of the complex plane. This class of A-stable methods are very rare. This paper is on the development of a new family of A-stable hybrid block method whose Jacobian matrices possess eigenvalues on the imaginary of the complex plane via interpolation and collocation techniques. The family of methods developed herein are A-stable for order p ≤ 18. Numerical solutions generated by the new method are compared with existing methods in the literature. The numerical results show that the new class of methods are more efficient and accurate.

Abstract 61: Protective role of caspase-1 inhibition in experimental model of neonatal hyperoxia-induced cardio pulmonary dysfunction in adults born preterm.

Background: Adults born preterm are at an increased risk of systemic hypertension and cardiopulmonary morbidities. However, little is known of the underlying mechanisms connecting neonatal hyperoxia (O 2 ) exposure to these long-term cardiovascular consequences in adults born preterm. Pro-inflammatory caspase-1 mediates the activation of cytokines IL-1β, and pore-forming protein Gasdermin-D. Objective: Test the hypothesis that caspase-1 inhibition prevents long-term cardiopulmonary consequences of preterm birth. Design/Methods: Newborn mice (n=60) exposed to normoxia (RA) or hyperoxia (O 2 ) from postnatal day (P) 1 to 14 were randomly assigned to receive daily intraperitoneal (IP) injections of caspase-1 inhibitor (VX-765, 50 ug/Kg) or DMSO as placebo. The mouse pups recovered in RA into adulthood until 3 months of age. The effect of caspase-1 inhibition on Blood pressure (BP), exercise endurance, cardiac function, systemic vascular stiffness, pulmonary vascular remodeling was assessed at 3 months. Results: Adult rats exposed to neonatal O 2 had significantly increased BP associated with vascular stiffness, reduced exercise capacity, cardiac hypertrophy, and cardiovascular inflammation. Caspase-1 inhibition prevented systemic hypertension, systemic vascular stiffness, improved exercise tolerance and decreased cardiac hypertrophy (Fig 1A-D) in adult mice exposed to neonatal O 2 . Moreover, caspase -1 inhibition improved pulmonary vascular remodeling and pulmonary hypertension in these mice (Fig 2A-E). Additionally, western blot analysis demonstrated that early supplementation of VX-765 in O 2 exposed mice led to reduced cardiac proinflammatory markers GSDMD and IL-1β in adulthood (Fig 3A-B). Conclusion: Neonatal O 2 exposure predisposes to cardiopulmonary morbidities in adults born preterm. Inhibition of caspase-1 reduces cardiovascular inflammation and cardiopulmonary dysfunction in mice exposed to hyperoxia during the neonatal period. The functional and molecular impact of the use of caspase-1 suggests that it can be used as a novel preventive strategy for long-term cardiopulmonary dysfunction due to neonatal O 2 exposure in preterm survivors.

Design optimization of stiffening system for ocean thermal energy conversion (OTEC) cold water pipe (CWP)

Ocean thermal energy conversion (OTEC) uses heat from seawater to generate electrical energy by utilizing the temperature difference between the surface and deep ocean layer. Cold water pipe (CWP) attached to transport cold seawater over distances of up to 600 m to the plant is susceptible to failures caused by environmental loads. At this point, the CWP should be strengthened to prevent structural failure by inducing ring stiffeners along the pipe. To ensure its structural integrity, this study conducts a design optimization by investigating how the variation of ring stiffening system parameters such as height, thickness, distance between stiffeners, and shape of stiffeners influence the load-carrying capacity of the pipe using a Finite Element Analysis. Initially, the benchmarking procedure is done to ensure the reliability of the FEM modeling. After being verified, the modeling procedure is used for parametric study analyses. Results state that the higher and thicker stiffener ring increases the structural strength. In the case of the ring stiffener distance, as predicted, reducing the spacing between reinforcements is preferable to increasing the bending strength of CWP OTEC. Analyzing the variation of reinforcement height, thickness, and spacing, it was found that thickness had the most significant influence, followed by reinforcement height, and reinforcement spacing had the least. Additionally, changes in the shape of the reinforcement have minimal impact on the flexural strength of the structure when regions of identical moments of inertia exist.

Steel Arch Structures with Prestressed Concrete Deck

AbstractFootbridges with prestressed concrete deck, which are suspended on steel arch ribs, are described in terms of the structural arrangement, static function and erection. These bridges create stiff structural systems which guarantee the bridges' favourable dynamic response. While steel arch ribs allow easy erections, the concrete deck guarantees structural integrity. The footbridges are structurally efficient, they are light and transparent, corresponds to the scale of the landscape and all structural members have human dimensions. They were erected with a minimum impact on the environment. Their structural arrangement is illustrated on examples of four bridges.

Axial vibration characteristics analysis of transformer windings based on magnetic‐structural coupling correction model

AbstractDue to the strong coupling effect between the internal magnetic field and the structural field of the transformer, the magnetic‐structural coupling should be considered in axial vibration process of the winding short‐circuit impact. A 110 kV transformer is taken as the research object. Firstly, the vibration modal characteristics of the transformer are calculated using the classical axial vibration model, and the spatial distribution of the leakage magnetic flux density of the iron core window is obtained based on the image method, which is used as the basis for calculating the excitation electromagnetic force. With the consideration of the non‐linear mechanical characteristic of the pad, the dynamic stiffness equation is analysed and established and the magnetic‐structural coupling correction model is constructed. Finally, the winding vibration amplitudes obtained respectively by the classical model, the magnetic‐structural coupling model, and the magnetic‐structural coupling correction model considering the dynamic stiffness are compared. The results show that, compared with the classical model, the vibration amplitude increment with the magnetic‐structural coupling correction model is less. The dynamic stiffness will hinder the vibration intensification. The magnetic‐structural coupling correction model can provide a more accurate calculation scheme for the winding vibration characteristic analysis.

Frequency-domain axisymmetric and thermomechanical viscoelastic analysis of thermoplastic composite pipe

ABSTRACT Thermoplastic composite pipe (TCP), composed of polymers and composite laminates, shows significant potential for deep-water offshore oil field development due to its lightweight and high strength. However, current mechanical studies primarily focus on the elastic domain, ignoring the critical viscoelasticity of non-metallic materials. To solve this, we introduce a comprehensive theoretical model that incorporates viscoelastic properties under both axisymmetric and thermal loads, considering radial convective thermal gradients and axial heat conduction. This model accurately predicts TCP's mechanical behavior by using stiffness coefficients, differential geometry, and radial-axial temperature transfer curves. By applying the principle of elastic-viscoelastic correspondence, we obtain viscoelastic solutions in the frequency domain, showing strong agreement with Finite Element (FE) models particularly under cyclic loading. Viscoelasticity introduces larger equivalent axial stiffness and viscoelastic damping within complex structures, which become more obvious with temperature fluctuations.

Variable stiffness performance analysis of layer jamming actuator based on bionic adhesive flaps

Soft actuators made of soft materials cannot generate precisely efficient output forces compared to rigid actuators. It is a promising strategy to equip soft actuators with variable stiffness modules of layer jamming mechanism, which could increase their stiffness as needed. Inspired by the gecko's the array of setae, bionic adhesive flaps with inclined micropillars are applied in layer jamming mechanism. In this paper, after the manufacturing process of the layer jamming actuator based on the bionic adhesive flaps is described, the equivalent stiffness models of the whole actuator are established in the unjammed and jammed states. And the shear adhesive force of a single micropillar is calculated based on the Kendall viscoelastic band model. The finite element simulation results of two bionic adhesive flaps show that the interlaminar shear stress and stiffness increase with the increase of pressure. The measurement of shear adhesive force show that the critical shear adhesive force of the bionic adhesive material is 3.2 times that of polyethylene terephthalate (PET) material, and exhibit the ability of anisotropic adhesion behavior. The variable stiffness performance of the layer jamming actuator based on bionic adhesive flaps is evaluated by three test methods, and the max stiffness reaches 8.027 N mm-1, which is 1.5 times higher than the stiffness of the layer jamming actuator based on the PET flaps. All results of simulation and experiment effectively verify the validity and superiority of applying the bionic adhesive flaps to the layer jamming mechanism to enhance the stiffness.

Static and Dynamic Characteristics of 3D-Printed Orthogonal Hybrid Honeycomb Panels with Tunable Poisson’s Ratio

By adjusting the two wall angles of the orthogonal hybrid honeycomb (OHH), the tunable Poisson’s ratio change from negative to positive values and the variation in stiffness can be achieved. To effectively analyze its static and dynamic characteristics, a two-dimensional equivalent Kirchhoff–Love model (2D-EKM) is established based on the variational asymptotic method (VAM).This model aids in effectively addressing the complexity arising from anisotropy. The obtained equivalent orthotropic properties are validated through unit-cell uniaxial compression tests and three-point bending experiments on 3D-printed specimens. The numerical simulation results suggest that the VAM-based 2D-EKM can predict the in-plane and out-of-plane static behaviors of OHH panels, with a maximum error below 10%. Particularly in the dynamic analysis of a four-sided fixed OHH panel, the analysis time required by 2D-EKM is only 0.37% of that needed for the 3D FE model. The OHH-ZPR panel exhibits exceptional resistance to deformation, with a maximum deformation under in-plane tension reaching only 27% of that in the OHH-PPR panel. Moreover, each 1% increase in the height–length ratio results in a respective increase of 275.62% and 281.93% in equivalent bending stiffness along both directions. This highlights that enhancing this ratio effectively boosts the fundamental frequency compared to the elastic modulus ratio, effectively prevents low-frequency resonance occurrences, and offers vital insights for the design and optimization of OHH panels.

Performance enhanced magnetic negative stiffness eddy-current damper: Numerical simulation and experimental investigation

Passive negative stiffness dampers (NSDs) possess significant advantages and promising application prospects in the field of structural vibration control. NSDs with high energy dissipation capability are desired to satisfy the vibration mitigation requirements for large-scale engineering structures, such as high-rise buildings and long-span bridges. However, in practical applications, due to the constraints of mounting space and additional weight, the negative stiffness and damping coefficient of existing NSDs are generally not very large and with poor adjustability. To overcome these limitations, this study develops a novel magnetic negative stiffness eddy-current damper (MNSECD) with enhanced overall performance. This damper consists of a magnetic negative stiffness system (MNSS), a multi-layer-plate-type eddy-current damping system (ECDS) in parallel, and a bidirectional ball screw transmission system. Firstly, different magnetic arrays are designed to optimize the magnetic fields of the MNSECD, and to enhance its magnetic negative stiffness and eddy-current damping without adding extra dimensions and weight. Subsequently, the electromagnetic finite-element models (FEMs) of the MNSECD are established to precisely simulate its magnetic negative stiffness and eddy-current damping forces, and these models are further utilized to elucidate the enhancement mechanism of different magnetic arrays. Finally, based on the numerical simulation results, the best performing magnetic array is selected respectively for the ECDS and MNSS systems to carry out experimental studies on a small-scale prototype. Numerical and experimental results indicate that the selected magnetic array for the MNSS proves highly effective in enhancing the magnetic negative stiffness of the MNSECD, while the selected magnetic array for the ECDS also demonstrates superior effectiveness in enhancing the eddy-current damping of the damper. These findings suggest that the novel MNSECD can be readily used in the vibration control of large-scale engineering structures.

Development of novel low-cost isolator UMELI (unbonded mesh elastomeric layered isolator): experimental investigations

Seismic isolation is a highly efficacious method for reducing the seismic load on structures. This technique is widely adopted to safeguard structures from earthquakes. Despite the promising results demonstrated by numerous isolation techniques, their implementation remains a significant challenge, particularly in developing countries, due to the high costs associated with manufacturing. Therefore, a novel and affordable base isolation technique has been proposed, namely unbonded mesh elastomeric layered isolator (UMELI). UMELI consists of steel mesh sandwiched between the unbonded layers of elastomers, resulting in an affordable isolator to be used for lightweight, low-rise structures. One of the crucial characteristics of this novel isolator is that it does not require a specialised manufacturing process unlike other elastomeric isolators. In the present study, experimental investigations are conducted to evaluate the dynamic characteristics such as dynamic vertical stiffness, equivalent lateral stiffness, and equivalent viscous damping ratio of UMELI. Its characteristics were studied for different layered isolators and are compared with the unreinforced elastomeric isolator. The investigations have demonstrated the effectiveness of the UMELI by increasing its vertical stiffness and reducing lateral stiffness, thereby enhancing the isolation period with the addition of a steel mesh layer.

Numerical investigation on loading pattern of railway concrete slabs

Despite the recent surge in the construction of ballastless railway tracks, there exists a notable research gap concerning the rail seat load (RSL) associated with these track types. The RSL is the load transferred from the rail to the fastening system, the plate beneath the rail and the rail pad. The prediction of RSL in ballasted track systems is widely investigated, however, there has been a relative lack of research into the ballastless railway track systems. In this paper, a 2D finite element model (2D FEM) was adopted to evaluate the RSL concerning the effective parameters, including sleeper spacing, fastening system stiffness and the flexural modulus of the rail. The numerical model was validated through a field test performed in the study. Moreover, a mathematical expression was proposed to determine the RSL ratio for concrete slab tracks. The RSL directly correlates with the sleeper spacing and the fastening stiffness, while this relation with the flexural rigidity is inverse. Based on the results, it was found that the RSL ratio obtained from the conventional methods differed considerably from the proposed mathematical expression. More specifically, this difference was observed in almost all of the values in the sleeper spacing and flexural rigidity of rail for the Kerr model except 0.68 m and 5 MN.m2, respectively.

Buckling and vibro-acoustic behavior analysis of laminated immersed cylindrical shells with hydrostatic pressure based on Chebyshev-Fourier spectral approach

The buckling and vibroacoustic behaviour of laminated cylindrical shell structures is vital for the safety and operational efficiency of underwater vehicles. This paper introduces a Chebyshev-Fourier spectral approach for the comprehensive analysis of buckling and vibro-acoustic behaviour in water-immersed laminated cylindrical shells under external hydrostatic pressure. The approach combines Chebyshev polynomials and Fourier series to approximate the displacement of shell and acoustic pressure of the fluid-structure-interaction (FSI) surface in cylindrical coordinates. An approximate solution is used in the axial direction, while an analytical solution is used in the circumferential direction, allowing for the analysis of different circumferential wave numbers n. The influence of external fluid pressure is characterized through the Helmholtz boundary integral equation, while the effect of hydrostatic pressure is deduced using linear elastic theory. From a theoretical derivation standpoint, hydrostatic pressure leads to a reduction in equivalent stiffness, while the external fluid contributes to an increase in the effective mass matrix. Validated against established literature analysis, the study finds that hydrostatic pressure decreases the natural frequencies, though the impact is less significant for lower circumferential wave numbers. For these lower wave numbers, the overall radiated sound power remains largely independent of external hydrostatic pressure, regardless of being in air or water. However, at higher circumferential wave numbers, the effect is more pronounced. This study not only advances the theoretical framework for analysing submerged cylindrical shells but also provides crucial insights into designing more robust structures for underwater applications.

A novel design of compact elastomer shock absorption system to protect sensitive objects from underwater shock for naval application

This research paper proposes a unique way to safeguard delicate systems on submerged platforms from the undesirable effects of underwater explosion shock loads. The underwater detonation of an explosive charge and mines produce devastating underwater shocks against underwater platforms. Shock load developed underwater has been analyzed, and a shock response spectrum (SRS) approach to compute shock peak responses has been adopted. SRS shock absorption frequency satisfies requirements for both shock absorption and delicate systems. The shock load was reduced to 2g by altering the delicate system stiffness and damping properties. The analytical model for a single DOF system was formulated, and simulation was carried out using ANSYS solver. The stiffness has been spread across various points along the length of the delicate system, allowing it to undergo translational oscillations when subjected to shock loads. This research paper presents an innovative design approach for a shock absorption system intended for underwater sensitive objects, emphasizing simplicity, distinctiveness, compactness, reliability, and electromagnetic compatibility. Experimental testing validated the shock absorption design on the prototype. Shock testing determined the absorber’s maximum displacement and sensitive object acceleration.

Geometrically nonlinear design of a rhombus-nested compliant amplification mechanism for use in precision actuators and sensors

A rhombus-nested compliant amplification mechanism is proposed for versatile usages of precision actuators and force sensors with an easy tuning of stiffness. Such a monolithically planar rhombus-nested compliant mechanism has the dual functions of two-stage displacement or force amplification by changing the input and output ports. It features a large ratio of inter-stage stiffness, thus resulting in an enhanced amplification ratio, load capacity and dynamic bandwidth. The geometrically nonlinear analytical equations of displacement amplification ratio and input stiffness are derived in the presence of pronounced axially-loaded stiffening and kinematic-arching effects based on the beam constraint model. It allows an insightful evaluation of geometrically nonlinear deformation behaviors sensitive to structural dimensions in a parametric way. Insights into geometrically nonlinear behaviors in the case of large-stroke and axially-loaded motions are discussed as well. A proof-of-concept prototype with embedded piezoelectric stacks is fabricated with the dimensions of 74mm × 60mm × 10 mm. The dual functions of precision actuator with amplified motion strokes and force sensor with enhanced sensitivity are experimentally demonstrated.

Stability of cold-formed steel stud walls subjected to vertical compression

Cold-formed steel (CFS) stud walls are the primary vertical load-bearing units in CFS residential systems. These walls need to meet both strength requirements and good stability. In this study, a CFS stud wall was simplified into a mechanical model of an orthotropic plate rib system using the orthotropic plate (OP) method. A formula for calculating the equivalent stiffness of the stud wall was obtained, and the correctness of the simplified calculation model and equivalent stiffness calculation formula was verified by finite element analysis. Various factors that affected the equivalent stiffness of the wall were investigated. Additionally, the stability of the stud walls under a vertical load was derived by considering the stability theory of the plate. The results indicated that the stability of the stud walls was mainly related to the height-thickness ratio of the walls. Finally, the correction factor of the allowable height-thickness ratio of the walls was obtained by analyzing the parameters of the wall thickness, stud spacing, sheathing materials, and wall opening, and a case study was used to illustrate the procedure of this simplified method.