Concept Of Stiffness Research Articles

A simple and versatile dual-state variable stiffness structure based on microwedge dry adhesives

Abstract The integration of softness and rigidity underpins the concept of variable stiffness, leveraging the distinct advantages of both properties. Inspired by this concept, this paper introduces a stiffness-switchable composite structure achieved through laminar jamming enabled by the inherent dry adhesion force of microwedge adhesives. This mechanism allows for a reversible transition between high flexibility and pronounced rigidity, achieving a remarkable stiffness ratio of 75, with easier implementation and enhanced functionality. Comprehensive modeling and experimentation are conducted to reveal intricate aspects of the structure's mechanical properties, such as interlayer behavior and failure processes. This paper also outlines two potential applications for this multifunctional structure: a robotic gripper with dual modes of rigid pinch and compliant adhesion, and an integrated multifunctional sensing setup. The proposed structure might broaden the scope of dry adhesives and laminar jamming structures, suggesting new possibilities for future research and development.

The use of geometrical nonlinear local resonators to enhance the vibration control performance of metamaterial structures

Abstract Metamaterials has become an exciting solution for structural noise and vibration reduction in many engineering applications. Acoustic metamaterials are structures built using repetitive assemblies of identical elements to explore either Bragg-scattering or localized resonance to control mechanical waves. They present frequency bands in which waves do not freely propagate, named bandgaps, allowing acoustic and vibration attenuation at one or multiple targeted frequency ranges. If properly designed and implemented, the inclusion of a nonlinear stiffness can result in resonance frequency shifts that broaden the attenuation frequency band. This work investigates the influence of an array of lightweight nonlinear local resonators (NLR) realized via additive manufacturing on the low-frequency bandgap formation of a metamaterial beam. The NLR uses the high-static-low-dynamic stiffness (HSLDS) concept, which introduces geometric nonlinearity. The proposed model is validated through simulation and experimental analysis. The NLR results in a broadened and shifted attenuation band to lower frequencies without the necessity of adding extra mass to the resonator. This investigation contributes to understanding improvements provided by nonlinear elements for vibration control in metastructures.

A viscoelastic harvester-absorber for energy generation and vibration control

Abstract A vibration energy harvester harnesses the oscillatory movement and
converts it into electrical energy. On the other hand, a (dynamic) vibration absorber
dissipates the mechanical energy of a host structure (primary system). The proposal for
a harvester-absorber device (HAD), comprinsing a piezoelectric element (conventional
harvester) bonded with a viscoelastic layer and a steel constrained layer, is based on the
dual purpose of generating energy and at the same time reducing the vibratory response
of the primary system. Introducing a viscoelastic dissipative layer in a conventional
harvester, also offers the advantage of simultaneously reducing wear on the piezoelectric
element, thereby extending its lifespan and preventing fatigue-related breakage. The
paper presents a model of a harvester-absorber built from a bimorph piezoelectric
beam, a layer of viscoelastic material (E-A-R C1002-01PSA) and a beam of steel, which
acts as a constrained layer. A lumped parameter model is proposed for the theoretical
description of the HAD which is successfully used to experimentally determine its
parameters. After that, and using the equivalent stiffness concept, the HAD was
coupled to a free-free beam with two masses at its ends to study its perfomance over a
real host structure. The inertance of the composite system and voltage/force frequency
response function of the HAD were obtained and compared with experimental results.
The accuracy of the results justifies and validate the model which has the advantage
of simplicity and can contribute to reducing wear and increasing the lifespan of brittle
piezoelectric structures.

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.

Design of Honeycomb‐Filled End Plate for Proton Exchange Membrane Fuel Cells Based on Topology Optimization

Designing a functional end plate for the proton exchange membrane fuel cell (PEMFC) is a challenging task since the structure that simultaneously satisfies uniform contact pressure and lightweight features must be achieved. To design an end plate for both requirements, a multi‐objective topology optimization model of the PEMFC based on the concept of equivalent stiffness is established with the aim of maximum stiffness and minimum root mean square (RMS) of contact displacement. Based on the final topology, the filled honeycomb‐based end plates with excellent mechanical properties and energy absorption effects are optimized through the particle swarm optimization algorithm (PSO). The results demonstrate that the end plate mass is reduced by 39.5% and the stress distribution is more uniform. The standard deviation of pressure decreases by 30.8% compared to the original model data. The proposed optimization method is helpful in the design of future end plates.

Wake-induced torsional oscillation of two tethered cylinders for energy harvesting

When two cylinders submerged in a uniform flow are arranged in tandem, the downstream cylinder can oscillate in response to the wake from the upstream cylinder. In this investigation, the downstream cylinder is allowed to oscillate freely around the center of a fixed upstream cylinder, mimicking a pendulum-like motion. Our findings suggest that the wake stiffness concept, initially verified for relatively large cylinder spacing (ℓ≥4) and linear transverse cylinder motion, is also relevant for characterizing the wake-induced vibration (WIV) response observed for two tandem tethered cylinders situated in close proximity (2≤ℓ≤4) for Reynolds numbers in the range 1.0×104≲Re≲1.2×105, with tests conducted up to Re≈1.4×105. For small cylinder spacing (ℓ≤2.5), the downstream cylinder attains a maximum oscillation angle amplitude and exhibits consistent vibration, providing reliable potential for energy harvesting. We also explore hysteresis in the WIV response, which is observed to depend on the history of Reynolds number variation. Our findings reveal hysteresis at both the onset and termination of oscillation.

A novel concept of components system stiffness and stiffness model application for VSV adjustment mechanism

In actual engineering practice of the variable stator vane (VSV) adjustment mechanism, it has been found that the deformation beyond design conditions of the kinematic chain formed from the linkage ring to the blades influences the motion accuracy of the mechanism the most. In this paper, the static stiffness model of the components system, formed from the linkage ring to the blades, is developed and then a motion compensation method based on the stiffness model is proposed. The correctness of the stiffness model is verified by the FEA method. With the model, influence factors such as blade quantity on the stiffness are characterized. In order to investigate the engineering applicability of the stiffness model, the motion compensation model is applied to the dynamic analysis and contrasts with the experimental results of two test benches designed based on the real VSV mechanisms. As a result, the validity of the stiffness model and the value of the proposed method are both well affirmed.

Arterial Stiffness: From Basic Primers to Integrative Physiology.

The elastic properties of conductance arteries are one of the most important hemodynamic functions in the body, and data continue to emerge regarding the importance of their dysfunction in vascular aging and a range of cardiovascular diseases. Here, we provide new insight into the integrative physiology of arterial stiffening and its clinical consequence. We also comprehensively review progress made on pathways/molecules that appear today as important basic determinants of arterial stiffness, particularly those mediating the vascular smooth muscle cell (VSMC) contractility, plasticity and stiffness. We focus on membrane and nuclear mechanotransduction, clearance function of the vascular wall, phenotypic switching of VSMCs, immunoinflammatory stimuli and epigenetic mechanisms. Finally, we discuss the most important advances of the latest clinical studies that revisit the classical therapeutic concepts of arterial stiffness and lead to a patient-by-patient strategy according to cardiovascular risk exposure and underlying disease.

The cardiomyocyte origins of diastolic dysfunction: cellular components of myocardial "stiffness".

The impaired ability of the heart to relax and stretch to accommodate venous return is generally understood to represent a state of "diastolic dysfunction" and often described using the all-purpose noun "stiffness." Despite the now common qualitative usage of this term in fields of cardiac patho/physiology, the specific quantitative concept of stiffness as a molecular and biophysical entity with real practical interpretation in healthy and diseased hearts is sometimes obscure. The focus of this review is to characterize the concept of cardiomyocyte stiffness and to develop interpretation of "stiffness" attributes at the cellular and molecular levels. Here, we consider "stiffness"-related terminology interpretation and make links between cardiomyocyte stiffness and aspects of functional and structural cardiac performance. We discuss cross bridge-derived stiffness sources, considering the contributions of diastolic myofilament activation and impaired relaxation. This includes commentary relating to the role of cardiomyocyte Ca2+ flux and Ca2+ levels in diastole, the troponin-tropomyosin complex role as a Ca2+ effector in diastole, the myosin ADP dissociation rate as a modulator of cross bridge attachment and regulation of cross-bridge attachment by myosin binding protein C. We also discuss non-cross bridge-derived stiffness sources, including the titin sarcomeric spring protein, microtubule and intermediate filaments, and cytoskeletal extracellular matrix interactions. As the prevalence of conditions involving diastolic heart failure has escalated, a more sophisticated understanding of the molecular, cellular, and tissue determinants of cardiomyocyte stiffness offers potential to develop imaging and molecular intervention tools.

Is it possible to objectively determine morning stiffness in rheumatoid arthritis?

This study aimed to objectively and quantitatively exhibit morning stiffness by using electrophysiological methods. The prospective, controlled study was conducted with 52 participants between February 2013 and February 2014. Of the participants, 26 were recruited among RA patients (3 males, 23 females; mean age: 55.9±11.2 years; range, 24 to 74 years) followed at the rheumatology clinic, and 26 were healthy subjects (4 males, 22 females; mean age: 54.9±8.3 years; range, 41 to 70 years) for the control group. Duration and severity of morning stiffness were recorded for all participants. Activity of disease and functional status were evaluated by the Disease Activity Score 28 and Health Assessment Questionnaire (HAQ), respectively. Electrophysiological reaction times, severity of pain (Visual Analog Scale), HAQ, and grip strength were measured for each participant twice in 24 h in the morning (08:00-09:00 am) and afternoon (03:00-05:00 pm). In the RA group, motor reaction and response times and severity of pain values were significantly lower in the afternoon compared to the morning (p=0.030, p=0.031, and p=0.002, respectively), and hand grip strengths were significantly higher in the afternoon (p=0.007). In the control group, no change was observed between morning and afternoon measurements in the strength and reaction time variables. Our hypothesis that stiffness would slow down the movements in the morning in RA was supported by the prolonged motor and response times in the morning compared to the afternoon. However, in the control group (no morning stiffness), there was no difference in reaction time variables between the morning and afternoon, objectively demonstrating the concept of morning stiffness in this study.

Simultaneously primary and super-harmonic resonance of a van der Pol oscillator with fractional-order derivative

The dynamic characteristics and stability of a fractional-order van der Pol oscillator under simultaneously primary and super-harmonic resonance are analyzed by the multiscale method. At first, the first-order approximate analytical solution of the system is obtained, and the analytical results are verified by numerical simulation. In addition, the concepts of equivalent linear damping and equivalent linear stiffness of simultaneously primary and super-harmonic resonance are proposed to enhance the comprehension of fractional parameters roles. Based on Lyapunov's stability method, qualitative analysis is performed on the stability region and the type of equilibrium points of the steady-state solution. The influences of fractional order and coefficient on system stability, equivalent damping, and equivalent stiffness are discussed. It is found that the change of fractional order and coefficient will cause a deviation of the vibration curve and affect the multiple solutions, resonant frequency, and stability range of the system, which is useful to design or control the similar dynamic system.

Development of shock absorber with quasi-zero stiffness effect to reduce dynamic effects on pump unit

The article is devoted to the improvement of the vibration isolation and shockproof properties of the shock absorber used in the vibration isolation compensator system of the pumping unit (PU). The set task is to create an elastic damping system with the desired low (quasi-zero) stiffness, which makes it possible to reduce the detrimental effect of pumping unit vibrations both on human health and on the equipment itself. High internal dynamic (vibration) loads are the main causes of early failure of pumping units, which are transmitted to the equipment through pipelines and foundations, mainly due to various operational factors. A promising trend in increasing the operating reliability and efficiency of pumping and power equipment is the use of a vibration-isolating compensator system (VICS). To obtain greater efficiency of vibration isolation, it is proposed to apply a modern method of vibration damping – the use of elastic mechanical systems with quasi-zero stiffness. The damping devices with a quasi-zero stiffness effect were studied. An assessment of the operability and effectiveness of these dampers at oil and gas facilities was given. Based on the information studied, a new concept of a quasi-zero stiffness damping device is proposed. The method of mathematical analysis determined its power curve. A 3D model of the damper device was built using a simulation software. The functional check of the damper was performed with mathematical modeling carried out on the computing device with the help of a specialized Ansys software that allows performing a system analysis of an object using the finite element method. The following results were obtained: the design of the damper with the effect of quasi-zero stiffness allows to widen the range of basement load transmission coefficient reduction towards low frequencies. The low rigidity of the system at the operating point ensures low values of the frequency of natural oscillations, and, consequently, high vibration isolation qualities.

Modular Soft Robotic Actuators from Flexible Perforated Sheets

Soft robotic actuators can be designed to achieve complex and tailored motions while simultaneously leveraging their compliance to interact with complex and often delicate environments. Mechanical metamaterials reveal a route to customizable deformations, force exertion, and mechanical energy efficiency attainable by careful arrangement of local geometric features. Herein, modular soft robotic actuators are developed from soft elastomers and flexible thermoplastic sheets of various unit cell designs. The efforts are focused on center‐symmetric perforated sheets, which are formed into flexible cylindrical skins that surround the soft inflatable actuators. The results demonstrate the influence of perforation geometry on the spatial stiffness of the reinforcement structure and the proposed actuators’ response through several investigations. It is demonstrated that the free‐boundary displacement, maximal force exertion, and mechanical energy efficiency of extensile actuators are dependent on a change of deformation mode in the mesostructure. The spatial stiffness concept is extended to develop soft robotic actuators that can bend, twist, and perform hybrid motions, such as simultaneous bending and twisting. Multisegment soft robotic arms are also developed from the aforementioned actuators. Investigations in this study provide a step toward the development of highly customizable and programmable soft robotic actuators for various applications.

Multi-beam piezoelectric systems by means of dynamically equivalent stiffness concept

Energy harvesting devices allow to obtain forms of energy present in nature and to convert them into electrical energy. One way of generating energy from mechanical vibrations is by using beams of piezoelectric materials. This paper proposes an alternative methodology for characterizing the dynamic behavior of a vibrating composite system composed of a cantilever steel base beam (primary system) and a piezoelectric beam attached to it. The approach involves representing the piezoelectric beam using an equivalent dynamic stiffness at its base. This simplifies the mathematical representation of the compound system and enables the system dynamics to be described solely in terms of the generalized coordinates of the primary system, which is advantageous in optimization environments where a reduced number of equations can facilitate analysis. To determine the equivalent dynamic stiffness, different mathematical models of one and multiple degrees of freedom are presented, including the description of the polyamide base of the piezoelectric sheet. An inverse problem is used to identify system parameters, and the energy generation over a wide range of frequencies is analyzed. Experimental frequency response functions of the voltage–acceleration type are obtained to validate numerical findings, demonstrating that the proposed methodology is a cost-effective alternative for parameter identification or optimal design in energy generation.

The Role of the Vasculature in Heart Failure.

The contribution of the vasculature in the development and progression of heart failure (HF) syndromes is poorly understood and often neglected. Incorporating both arterial and venous systems, the vasculature plays a significant role in the regulation of blood flow throughout the body in meeting its metabolic requirements. A deterioration or imbalance between the cardiac and vascular interaction can precipitate acute decompensated HF in both preserved and reduced ejection fraction phenotypes. This is characterised by the increasingly recognised concept of ventricular-arterial coupling: a well-balanced relationship between ventricular and vascular stiffness, which has major implications in HF. Often, the cause of decompensation is unknown, with international guidelines mainly centred on arrhythmia, infection, acute coronary syndrome and its mechanical complications as common causes of decompensation; the vascular component is often underrecognised. A better understanding of the vascular contribution in cardiovascular failure can improve risk stratification, earlier diagnosis and facilitate earlier optimal treatment. This review focuses on the role of the vasculature by integrating the concepts of ventricular-arterial coupling, arterial stiffness and venous return in a failing heart.

Effect of preloading on vibration and buckling responses of variable stiffness composite cylindrical shells

Composite cylindrical shell has been utilized in marine shipping industry as a reliable auxiliary wind propulsion device that can reduce fuel consumption. However, due to the special boundary constraints and complex loading cases, the vibration and buckling responses of such devices differ significantly from traditional cylindrical shells. The present research deals with the vibration and buckling behavior of composite cylindrical shells utilizing the promising variable stiffness (VS) concept. The effects of the preloading states and the design constraints were analyzed to explore the effectiveness of VS concept in cylindrical shell structures. Compared to constant stiffness (CS) composite cylindrical shells, VS cylindrical shells are less sensitive to variation in preloading states and geometric imperfections, and the buckling strength can be improved under some combination of loading sates. The effect of boundary constraints on stiffness and bucking strength is less prominent own to VS properties, in that stress concentrations near the end of the cylindrical shell structures can be smoothed out, and the strain distributions are spaced more evenly.

Numerical Study on the Buckling Behavior of FG Porous Spherical Caps Reinforced by Graphene Platelets

The buckling response of functionally graded (FG) porous spherical caps reinforced by graphene platelets (GPLs) is assessed here, including both symmetric and uniform porosity patterns in the metal matrix, together with five different GPL distributions. The Halpin-Tsai model is here applied, together with an extended rule of mixture to determine the elastic properties and mass density of the selected shells, respectively. The equilibrium equations of the pre-buckling state are here determined according to a linear three-dimensional (3D) elasticity basics and principle of virtual work, whose solution is determined from classical finite elements. The buckling load is, thus, obtained based on the nonlinear Green strain field and generalized geometric stiffness concept. A large parametric investigation studies the sensitivity of the natural frequencies of FG porous spherical caps reinforced by GPLs to different parameters, namely, the porosity coefficients and distributions, together with different polar angles and stiffness coefficients of the elastic foundation, but also different GPL patterns and weight fractions of graphene nanofillers. Results denote that the maximum and minimum buckling loads are reached for GPL-X and GPL-O distributions, respectively. Additionally, the difference between the maximum and minimum critical buckling loads for different porosity distributions is approximately equal to 90%, which belong to symmetric distributions. It is also found that a high weight fraction of GPLs and a high porosity coefficient yield the highest and lowest effects of the structure on the buckling loads of the structure for an amount of 100% and 12.5%, respectively.

Development of a Bionic Tube with High Bending-Stiffness Properties Based on Human Tibiofibular Shapes.

The human tibiofibular complex has undergone a long evolutionary process, giving its structure a high bearing-capacity. The distinct tibiofibular shape can be used in engineering to acquire excellent mechanical properties. In this paper, four types of bionic tubes were designed by extracting the dimensions of different cross-sections of human tibia-fibula. They had the same outer profiles, but different inner shapes. The concept of specific stiffness was introduced to evaluate the mechanical properties of the four tubes. Finite-element simulations and physical bending-tests using a universal testing machine were conducted, to compare their mechanical properties. The simulations showed that the type 2 bionic tube, i.e., the one closest to the human counterpart, obtained the largest specific-stiffness (ε = 6.46 × 104), followed by the type 4 (ε = 6.40 × 104) and the type 1 (ε = 6.39 × 104). The type 3 had the largest mass but the least stiffness (ε = 6.07 × 104). The specific stiffness of the type 2 bionic tube increased by approximately 25.8%, compared with that of the type 3. The physical tests depicted similar findings. This demonstrates that the bionic tube inspired by the human tibiofibular shape has excellent effectiveness and bending properties, and could be used in the fields of healthcare engineering, such as robotics and prosthetics.

Investigation of elastic properties of solid polymer materials by indentation method

The mechanical properties of solid (crystalline) polymer materials are proposed to be investigated simultaneously using two complementary methods based on controlled indentation of a spherical indenter. The first method consists in the direct analysis of the load curve without using the concept of contact stiffness; the second method is based on measurements of the size of prints depending on the magnitude of the static load. The study shows that the reinforcement of a solid polymer with carbon fibers can lead to a significant increase in its elastic-strength properties. Keywords: polymer composite materials, indentation, Hertz contact theory, spherical stamp, reduced modulus of elasticity, Brinell hardness, ultimate strength.

Strain stiffening elastomers with swelling inclusions.

Inhomogeneously swollen elastomers are an emergent class of materials, comprising elastic matrices with inclusion phases in the form of microgel particles or osmolytes. Inclusion phases can undergo osmotically driven swelling and deswelling over orders of magnitude. In the swollen state, the inclusions typically have negligible Young's modulus, and the matrix is strongly deformed. In that regime, the effective mechanical properties of the composite are governed by the matrix. Laying the groundwork for a generic analysis of inhomogeneously swollen elastomers, we develop a model based on incremental mean-field homogenization of a hyperelastic matrix. The framework allows for the computation of the macroscopic effective stiffness for arbitrary hyperelastic matrix materials. For an in-depth quantification of the local effective stiffness, we extend the concept of elastic stiffness maps to incompressible materials. For strain-stiffening materials, stiffness maps in the swollen state highlight pronounced radial stiffening with a non-monotonic change in stiffness in the hoop direction. Stiffening characteristics are sensitive to the form of constitutive models, which may be exploited in the design of hydrated actuators, soft composites and metamaterials. For validation, we apply this framework to a Yeoh material, and compare to recently published data. Model predictions agree well with experimental data on elastomers with highly swollen embedded microgel particles. We identify three distinct regimes related to an increasing degree of particle swelling: first, an initial decrease in composite stiffness is attributed to particle softening upon liquid intake. Second, dilute particle swelling leads to matrix stiffening dominating over particle softening, resulting in an increase in composite stiffness. Third, for swelling degrees beyond the dilute limit, particle interactions dominate further matrix stiffening.