Equivalent Stiffness Research Articles

POSTURAL CONTROL IMPAIRED IN MYOARTHROKINETIC AND NEURO-SENSORY DISORDERS

Interdependent subsystems involved in dynamic posture and locomotion are represented by osteoarticular, neuromuscular, sensory systems. Postural control is maintained by somato-sensory, visual vestibular feedback, integrated at the level of the locomotor system and the central nervous system. Postural stability is disturbed in mio-arthro-kinetic disorders. In proprioceptive loss, the automatic postural responses are diminished in amplitude and delayed in time; stretch reflexes in soleus and medial gastrocnemius are severely diminished; balance-correcting responses in tibialis anterior are diminished and delayed; backward motion of the trunk is reduced; movement strategies and synergies are disturbed. In peripheral vestibular loss, there are increased trunk responses to disruptive stimuli, with hypermetric trunk muscle responses and hypometric knee responses, but unchanged synergies; pathological changes to the modulation depth are produced; the amplitude of balance correcting responses in ankle muscles is severely reduced. Visual input serves to decrease the stiffness of the musculoskeletal system; it can be accomplished by decreasing the level of muscular activity across the joints of the lower limbs (in eyes-open subjects) or by reducing the gains of the other postural feedback mechanisms, the proprioceptive or vestibular systems (in eyes-closed subjects). Keywords: postural control, proprioceptive insufficiency, vestibular impairment.

A rapid prediction model for the radiation efficiency of baffled constrained layer damping plate

It’s well-known that constrained layer damping (CLD) can effectively reduce the vibration and radiation noise from the (plate-like or shell-like) thin-walled structures under various of dynamic excitations. As one of the key properties deciding the CLD’s performance, the CLD’s acoustic radiation characteristics has always been a focus of researchers. In this study, an analytical model based on equivalent principle is proposed to predict the acoustic radiation efficiency of the CLD plate. In this model, a laminated CLD plate is equivalent to a single-layer plate and the equivalent stiffness and loss factor are obtained using the strain energy method. The vibration velocity of the plate is calculated using mode-superposition method and the sound pressure on the plate surface is calculated using Rayleigh integral formula. Variable mesh sizes and frequency steps are employed to improve the calculation efficiency. The difference between the base and CLD plates in sound radiation characteristics is investigated using this model. The results indicate that CLD involving a damping layer with a low Young’s modulus can mitigate more vibration at low frequencies. A higher Young’s modulus of the damping layer results in a higher radiation efficiency of the CLD plate between the fundamental and critical frequencies. By increasing the loss factor, the spatially averaged mean square velocity would decrease, more modes would contribute to the response, and the CLD plate can consequently achieve a higher radiation efficiency below the critical frequency. Moreover, the simplified formulae for the average radiation efficiency of the CLD plate is developed to achieve the rapid calculation. Its accuracy is then validated by comparing the results to the more comprehensive model.

A Review of Cross-Scale Theoretical Contact Models for Bolted Joints Interfaces

Bolted joints structures are critical fastening components widely used in mechanical equipment. Under long-term loading conditions, the bolted joints interface generates strong nonlinearities within the system. The nonlinear stiffness inside the bolt leads to changes in the stiffness of the whole system. This affects the dynamic characteristics of the whole system. It brings challenges and difficulties to the performance prediction and reliability assessment of the equipment. A cross-scale theoretical model study based on the microscopic contact mechanism can provide a more comprehensive understanding and cognition of the degradation behavior of bolted joints interfaces. The current development status and deformation process of asperity models are summarized. The research progress of statistical summation model and contact fractal model based on microscopic contact mechanism is analyzed. The experimental methods for parameter identification of connection interfaces are reviewed. The study of numerical modelling of bolted joints structures from the surface contact mechanism is briefly described. Future research directions for cross-scale modelling of bolted joints structures are outlined.

TSDT vs CPT and FSDT for Free Vibration Analysis of Functionally Graded Incompressible Plates

This article studies vibrational behavior of incompressible functionally graded plates through utilizing classical, first-order shear, and third-order shear deformation plate theories. Plate material properties are presumed to differ continuously in the thickness direction concurringto a power law function. The motion and continuity equations are produced using three different plate theories, and then they are analytically solved for rectangular plates with simple supports utilizingNavier's method. The results are verified by obtaining the plate natural frequency for the power law index value equals zero and comparing them to those reported in previous works. It is shown that transverse vibrational analysis of the classical and first-order shear deformationplate theories for incompressible plates are not as precise as thecompressible ones. It is shown that this issue is due to the fact that according to those theories, unlike the higher order theories, the hydrostatic pressure cannot participate in carrying the bending loads. Consequently, the equivalent flexural stiffness and as a result flexural frequencies decrease. So, to analyze the vibrational behavior of functionally graded incompressibleplates, whether the plate is either thin or thick, higher order theories should be adopted. Also, it is demonstrated that TSDT is the simplest shear deformation plate theory for which the hydrostatic pressure can contribute to withstandig the bending moments. So, it can be a practical theory for free vibration analysis of functionally graded incompressible plates. Finally, this theory has been taken into consideration to analyze the vibrational behavior of rectangular plates made of functionally graded incompressible materials Also detailed parametric studies have been carried out.

Experimental Research on the Floating Amount of Shield Tunnel Based on the Innovative Cumulative Floating Amount Calculation Method

The study of shield tunnel segment flotation is crucial for controlling the precision of underground excavation projects. Based on Winkler’s beam foundation theory, the load structure method, and the equivalent continuous beam model, and by considering the mechanical and spatial conditions that cause segment flotation, a novel theoretical calculation method for cumulative flotation is proposed using a simplified equivalent stiffness model of the tunnel. Additionally, a new concept of “equivalent flotation force” is introduced. The rationality and applicability of this theoretical calculation method are verified by comparing it with on-site construction data from the Yuanjiang River Crossing Tunnel Project in Changde, Hunan Province, China. The experimental results demonstrate that the theoretical calculation closely approximates the surface deformation monitoring data of the tunnel alignment in the eastern section of the project, and their deformation patterns are similar. Near the starting shaft, there is significant settlement influenced by stratum loss due to smaller tunnel flotation, with greater settlement occurring in the upper part. However, at approximately 45 m into both sections, they enter a deformation stability zone showing significant correlation in longitudinal deformation. Through comparison and verification of on-site experiments and theoretical model analysis, we preliminarily elucidate the feasibility of this innovative cumulative flotation theoretical calculation method which provides an important theoretical basis for assessing segment flotation issues in subsequent tunnel shield construction evaluations.

Equivalent single-layer model for hierarchical diamond honeycomb sandwich panels using variational asymptotic method

Sandwich panels with a hierarchical core facilitate the optimal utilization of limited materials to enhance bearing capacity in strategic locations. Nevertheless, the complex sub-structural cells have hindered extensive investigation into their static and modal characteristics. The objective of this study is to obtain the effective plate properties by homogenizing the representative unit cell and subsequently applying them to a two-dimensional equivalent single layer model (2D-ESL) based on the variational asymptotic method (VAM). Furthermore, three-point bending test of 3D-printed specimen and 3D detailed finite element results are employed to confirm the predictions of 2D-ESL under various load and boundary conditions. The effects of material factors (such as fiber volume fraction and layup configuration) and structural parameters (including aspect ratio, hierarchy ratio, and slenderness ratios of ribs and ligaments) on the equivalent stiffness and modal characteristics are also examined. Moreover, sandwich panels with different hierarchical configurations (including 2, 3 and infinite segments within the inclined ribs) are investigated to provide valuable insights for selecting appropriate hierarchies based on specific conditions. Notably, the transition from polyline to arc-shaped segments has been proven to effectively mitigate local stress concentration, leading to a more uniform distribution of local displacement.

Stability prediction for robotic milling based on tool tip frequency response prediction by considering the interface stiffness of spindle-tool system

The change of tool tip frequency response caused by the posture dependence of robot dynamic is one of the key problems that make it difficult to accurately predict the milling stability of robot. In this paper, a tool tip frequency response prediction method considering the interface stiffness characteristics of spindle-tool system is proposed for stability prediction of robotic milling under the condition of posture variation. Firstly, the interface stiffness models of spindle-toolholder, toolholder-spring clip and spring clip-tool are established based on Yoshimura's unit area method. Then, The dynamics model for the robot body and the interface stiffness models for spindle-tool system are imported into the finite element analysis model of the spindle system, so that the prediction of the tool tip frequency response is realized by harmonic response analysis. Compared with the experimental results, the maximum error of the natural frequency was not more than 2 %, and the maximum error of the amplitude was not more than 12 %. Finally, the 2 DOF robot milling stability prediction model is established. Then the robot milling chatter is predicted considering redundant degrees of freedom from the perspective of regenerative chatter prediction theory, and the accuracy of prediction results is verified by milling experiment.

Explicit stabilized multirate methods for the monodomain model in cardiac electrophysiology

Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their improved stability properties. To demonstrate their efficiency for the numerical solution of stiff, multiscale, nonlinear parabolic PDE's, we apply mRKC methods to the monodomain equation from cardiac electrophysiology. In doing so, we propose an improved version, specifically tailored to the monodomain model, which leads to the explicit exponential multirate stabilized (emRKC) method. Several numerical experiments are conducted to evaluate the efficiency of both mRKC and emRKC, while taking into account different finite element meshes (structured and unstructured) and realistic ionic models. The new emRKC method typically outperforms a standard implicit-explicit baseline method for cardiac electrophysiology. Code profiling and strong scalability results further demonstrate that emRKC is faster and inherently parallel without sacrificing accuracy.

The effects of ply clustering positions and orientations on multi‐directional composite laminates' low velocity impact resistance

AbstractIn this paper, nine different carbon fiber laminates containing clusters are designed using the ant colony ACO algorithm, which have similar equivalent bending stiffnesses and B‐matrices, with the differences being the fiber orientation of the clusters and the position of the clusters in the laminates. The dynamic mechanical characterization of laminates for low velocity impact (LVI) at three different energies was carried out by means of a falling weight impact experiment. The experimental results show that the main form of failure of the laminate is delamination failure at low energy impacts, and shear fracture becomes more and more obvious with the elevation of the impact energy, which was observed in detail by the stereo microscope and electron microscope. The damage area of the laminate and the force and displacement curves after 30 J energy impact were compared by x‐ray scanning to derive the effects of the angle of the ply cluster fibers and the different positions of the ply clusters in the laminate on the impact resistance of the laminate. In conclusion, when designing the laminate, consideration should be given to designing 45° clusters on the impacted side and 90° clusters in the middle layer of the laminate to obtain the best impact resistance.Highlights Designed 9 types of laminates with different laminate structures based on ACO algorithm. Different laminates have similar equivalent bending stiffnesses and the B matrix as close to 0 as possible. LVI tests at three energies were performed on 9 types of laminates. The effects of different orientations of the clusters and the position of the clusters in the laminate on the impact resistance of the laminate were investigated.

Stiffly Stable Diagonally Implicit Block Backward Differentiation Formula with Adaptive Step Size Strategy for Stiff Ordinary Differential Equations

Stiffly Stable Diagonally Implicit Block Backward Differentiation Formula with Adaptive Step Size Strategy for Stiff Ordinary Differential Equations

Real-time multibody simulation of vehicle wheel suspensions of different topologies with elastokinematic properties

AbstractDriving simulators are becoming increasingly important in vehicle development, as they allow test drivers to evaluate the driving characteristics of a vehicle at an early stage of the development process. Vehicle dynamics models used for such real-time applications are usually simplified to achieve sufficiently low computation times, especially with respect to the elastokinematic properties of the wheel suspension. This contribution introduces a real-time capable multibody simulation model for wheel suspensions taking into account their elastokinematics. The underlying data model allows the parametrization of different suspension topologies. Linear-implicit integration methods enable real-time capable integration of the underlying numerically stiff equation of motion without major model simplifications. It is shown how the computational effort of linear-implicit integration can be reduced by explicitly taking the suspension topology into account. A versatile process for the analytical online-linearization of the equation of motion of arbitrary suspension topologies is presented. Both a double wishbone and a multilink suspension are simulated with very high accuracy in real-time on a standard PC.

Strength prediction of the notched composite laminates from equivalent un-notched laminates

In this paper, a theoretical failure model is proposed to predict ultimate strength of fiber-reinforced composite laminate with a circular hole. In the failure model, the laminate with a circular hole is modeled by an equivalent intact laminate which contains laminae with the same stacking sequence but with equivalent stiffness and strength derived by micromechanics and point stress formulation, respectively. The ultimate strength of this equivalent intact laminate is calculated by the improved Puck’s failure theory combined with stiffness degradation model. The failure model so formulated is applied to notched laminates with arbitrary stacking sequences. The capability is demonstrated by strength predictions of several multidirectional notched laminates, including [45∘/0∘/−45∘/90∘]2s AS4/3501-6 notched laminates, [45∘/90∘/−45∘/0∘]4s IM7/8552 notched laminates and [0∘/902∘/0∘]4s AS4/3502 cross-ply notched laminates, which are in good agreement with experimental results.

A study of controlling the transverse vibration of a beam-plate system by utilizing a nonlinear coupling oscillator

In the engineering field, prolonged exposure of complex structures to high-strength vibration environments can lead to various engineering challenges. This underscores the importance of effectively managing the vibration of complex structures. Given the extensive utilization of beams and plates in the construction of intricate structures, this study incorporates a nonlinear coupling oscillator into the beam-plate system and formulates a vibration analysis model for this system. The governing equations of the system are derived theoretically and solved numerically using the Galerkin truncation method. This study focuses on the operational modes of the nonlinear coupling oscillator based on accurate numerical results. Meanwhile, the influence of parameters belonging to the nonlinear coupling oscillator on the transverse vibration responses of the beam-plate system is systemically studied. Upon meticulous examination of the numerical results, the operational states of the nonlinear coupling oscillator encompass the normal vibration suppression mode and the quasi-periodic vibration suppression mode. The alteration in the linear elastic coupling stiffness of the beam-plate system impacts the effectiveness of vibration suppression in the nonlinear coupling oscillator. This influence stems from the fact that changes in the linear elastic coupling stiffness directly affect the nonlinear forces exerted on the beam-plate system within a nonlinear coupling oscillator. Within a feasible range, the nonlinear stiffness and viscous damping can be chosen as the adjustable parameters for the nonlinear coupling oscillator to regulate the vibration of the beam-plate system by adjusting the motion mass of the nonlinear coupling oscillator, which presents a challenge. The appropriate utilization of the nonlinear coupling oscillator demonstrates favorable control effectiveness in managing the transverse vibration of the beam-plate system. The study presented in this work offers a method to simultaneously control the vibration of each component within beam-plate coupling systems.

Computer-algebraic approach to first differential approximation: Van der Pol oscillator

First differential approximation has been used to analyze various numerical methods for solving systems of ordinary differential equations. This has made it possible to estimate the stiffness of the ODE system that models the oscillations of the Van der Pol oscillator and the error of the method as well as to propose simple criteria for choosing a calculation step. The presented methods allow one to perform efficient calculations using computer algebra systems.

Kirigami-inspired, three-dimensional piezoelectric pressure sensors assembled by compressive buckling

Piezoelectric sensors whose sensing performances can be flexibly regulated hold significant promise for efficient signal-acquisition applications in the healthcare field. The existing methods for regulating the properties of polyvinylidene fluoride (PVDF) films mainly include material modification and structural design. Compared to material modification, which has a long test period and an unstable preparation process, structural design is a more efficient method. The irigami structure combined with compressive buckling can endow the flexible film with rich macrostructural features. Here, a method is fabricated to modulate the sensing performance by employing distinct 3D structures and encapsulation materials with varying Young’s moduli. The relationship among the aspect ratio (α), pattern factor (η), elastic modulus of encapsulation materials, and equivalent stiffness is obtained by finite element simulation, which provides theoretical guidance for the design of the 2D precursor and the selection of encapsulation materials. In the demonstration applications, the sensor accurately captures pulse waveforms in multiple parts of the human body and is employed for the pressure monitoring of different parts of the sole under various posture states. This method of structure design is efficient, and the preparation process is convenient, providing a strategy for the performance control of piezoelectric pressure sensors.

The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids

The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids

EMI-based monitoring of prestressed concrete beam under chloride-induced corrosion using an embedded piezo sensor

The service life and durability of the prestressed concrete (PC) structures mainly depend on the corrosion resistance of the prestressing strands, wires, or tendons. Once corrosion occurs in the strands, identifying the location and quantifying the phases of corrosion is a very challenging task. Thus, this paper presents a novel way to monitor the corrosion process and identify the deterioration in a PC beam using an embedded piezo sensor (EPS) based on the electro-mechanical impedance (EMI) technique. The accelerated corrosion tests were conducted on a PC beam in which EPS was attached to the prestressing wire inside the beam to monitor the changes in the EMI signature during the corrosion progression. In addition, statistical damage indices such as root mean square deviation is identified to quantify the damage due to corrosion. Further, this study identifies the deterioration in mechanical changes such as stiffness, mass, and damping by extracting the equivalent structural parameters from the raw EMI signatures. Based on qualitative and quantitative results, it is found that the EPS effectively senses the changes at different time intervals during the corrosion process and identifies the damage of corrosion. Also, the equivalent stiffness parameter identified from raw EMI signatures is realistically measuring the material deterioration under corrosion and identifying the corrosion phases. Hence, it is concluded that the EMI technique based on EPS in structural health monitoring of PC beam can accurately assess the deterioration under the effect of corrosion.

A compressible degree of freedom as a means for improving the performance of heaving wave energy converters

A compressible degree of freedom (CDOF) can provide a means of improving wave power capture by adjusting the system stiffness and providing short-term energy storage, reducing or even eliminating the requirement for two-way electrical power flow as is typical in wave energy control systems. With the overarching goal of investigating and facilitating the application of a CDOF within wave energy converter (WEC) design, this paper focuses primarily on the case of heaving buoys, and on using air volumes to provide the compressible spring effect. Analytical formulae for the natural frequencies are used to gain fundamental insights into the main design considerations. Numerical methods are used to augment this understanding, helping to elucidate the effect of geometric parameters and scale on the required compressible volumes and the efficacy of the CDOF. Beginning with the WaveBot WEC, case studies are then used to demonstrate the design drivers in a more applied context, as well as highlighting the benefit of a self-reacting power take-off (PTO) system. The assimilation of these results with the findings of a detailed literature review culminates in a set of recommendations (or guiding principles) for designing a compressible degree of freedom to improve the performance of a heaving wave energy converter. These recommendations apply both to full-scale WECs, and to the design of scale physical modelling studies for validating the analytical and numerical models.

Experiment investigation and theoretical analysis of an improved aluminum alloy gusset joint

This study presents enhancements made to traditional aluminum alloy gusset (AAG) joints, including the integration of a central stiffening (CS) system, an inter-panel stiffening (IS) system, and a peripheral stiffening (PS) system. Three sets of tests on a full-scale specimen are conducted to investigate the improved AAG joint's axial stiffness, in-plane and out-of-plane bending stiffness, as well as ultimate load-bearing capacity. Nonlinear refined finite element models (FEMs) are established and validated through experimental results. Theoretical mechanical models are developed by integrating experiments and FEMs. These models elucidate the contribution of the stiffening systems to the joint's mechanical performance. The CS system is proven to significantly assist in load transfer, particularly in out-of-plane bending conditions. The IS system enhances overall inter-panel integrity, especially during the plastic deformation phase under out-of-plane bending moments. The PS system improves joint stiffness by participating in load transmission under both axial load and in-plane bending moments. Compared to traditional AAG joints, the combined effects of the three stiffening systems enhance overall structural integrity, stiffness, and load-bearing capacity. This enables the full utilization of component material properties and provides excellent ductility before failure occurs.

Study on the Equivalent Stiffness of a Local Resonance Metamaterial Concrete Unit Cell

This paper addresses the pressing scientific problem of accurately predicting the equivalent stiffness of local resonance metamaterial concrete unit cells. Existing theoretical models often fail to capture the nuanced dynamics of these complex systems, resulting in suboptimal predictions and hindering advancements in engineering applications. To address this deficit, this paper proposes a novel two-dimensional theoretical vibration model that incorporates shear stiffness, a crucial yet often overlooked parameter in previous formulations. Motivated by the need for improved predictive accuracy, this paper rigorously validates a new theoretical model through numerical simulations, considering variations in material parameters and geometric dimensions. The analysis reveals several key findings: firstly, the equivalent stiffness increases with elastic modulus while the error rate decreases, holding geometric parameters and Poisson’s ratio constant. Secondly, under fixed geometric parameters and coating elastic modulus, the equivalent stiffness rises with an increasing Poisson’s ratio, accompanied by a decrease in error rate. Importantly, this paper demonstrates that the proposed model exhibits the lowest error rate across all parameter conditions, facilitating superior prediction of equivalent stiffness. This advancement holds significant implications for the design and optimization of metamaterial structures in various engineering applications for vibration isolation, with promising enhancements of performance and efficiency.