Stiffness Coefficients Research Articles

Two-dimensional stiffness identification by inversion of local wavenumbers based on artificial neural network

Impact and fatigue damages in carbon fiber reinforced polymers (CFRP) are unavoidable in severe operating conditions, which will lead to the stiffness properties degrading and redistributing in space. The local wavenumbers of guided waves at a specific point depend on the stiffness at that spatial location. Therefore, the two-dimensional stiffness properties can be determined by inversion of local wavenumbers. In this paper, the relationship between the local wavenumbers and the stiffness coefficients was established by the artificial neural network (ANN) method. For each spatial point, based on the semi-analytical finite element (SAFE) method, the wavenumbers (inputs of ANN) with different frequencies can be obtained at given stiffness coefficients (outputs of ANN). Furthermore, the accuracy of the ANN method was validated by the finite element model. Results show that the predicted two-dimensional stiffness coefficients of the damaged region are close to the true ones, thus demonstrating the accuracy of the two-dimensional stiffness identification method.

Амплитудно-частотные характеристики виброзащитной системы сиденья с трехсегментной статической силовой характеристикой и участком квазинулевой жесткости

Vibration protection for heavy equipment operators is important. Exposure to vibration is harmful to health. Vibration protection seats are used for protection. Reliable passive systems with quasi-zero stiffness are promising. For the developed design of the seat on the basis of parallelogram mechanism, spring, cable and rollers, the study of vibration-protective properties is carried out. The design scheme has been developed, key parameters have been selected, and their study on vibration protection parameters has been carried out. The static force response was approximated by three linear segments with a horizontal mean. The known dynamic model describing forced oscillations of the mass was used. The displacement of the base was given by a harmonic function. Vibration protection systems with three-segment and with one-segment static force response were compared. The comparison was carried out in terms of transmission coefficients, accelerations and suspension displacement. The results of the computational experiment are presented in the form of graphs: amplitude-frequency characteristics in the form of transmission coefficients in acceleration and displacement, at different amplitudes of base vibrations, damp-ing and stiffness coefficients. Dependences of average values of transmission coefficients in the investigated frequency range are given. Vibration damping is effective when the maximum suspension travel does not exceed the middle section of the static characteristic. The most effective vibration damping, according to the average value of the acceleration transfer coefficient, is achieved at minimum, and for a single-segment characteristic — zero values of the stiffness coefficient. The presence of extreme segments in the characteristic significantly increases the average values of the accelera-tion and displacement transfer coefficients of the suspension. Seat vibration protection systems in real conditions should have a limitation of suspension displacement for ergonomic reasons. The values of the stiffness coefficients of the extreme parts of the static force response, according to the criterion of minimizing the average value of the acceleration transfer coefficient, should be minimized. To substantiate the optimal values of the stiffness coefficients of the extreme sections of the characteristic and viscous friction coefficients, it is advisable to conduct additional studies under step and stochastic impacts.

Test-retest reliability and follow-up of muscle magnetic resonance elastography in adults with and without muscle diseases.

We investigated the potential of magnetic resonance elastography (MRE) stiffness measurements in skeletal muscles as an outcome measure, by determining its test-retest reliability, as well as its sensitivity to change in a longitudinal follow-up study. We assessed test-retest reliability of muscle MRE in 20 subjects with (n=5) and without (n=15) muscle diseases and compared this to Dixon proton density fat fraction (PDFF) and volume measurements. Next, we measured MRE muscle stiffness in 21 adults with Becker muscular dystrophy (BMD) and 21 age-matched healthy controls at baseline, and after 9 and 18months. We compared two different methods of analysing MRE data in this study: 'Method A' used the stiffness maps generated by the Philips MRE software, and 'Method B' applied a custom-made procedure based on wavelength measurements on the MRE images. Intraclass correlation coefficients (ICC) of muscle stiffness ranged from good (0.83 for left vastus medialis, P<0.001) to poor (0.19 for right rectus femoris, P=0.212) for the examined thigh muscles with Method A, but we did not find a significant test-retest reliability with Method B (P>0.050 for all). The ICC of muscle PDFF and volume measurements was excellent (>0.90; P<0.001) for all muscles. At baseline, the average stiffness of all thigh muscles was significantly lower in adults with BMD than in controls for both Method A (-0.2kPa, P=0.025) and Method B (-0.6kPa, P<0.001). Regardless of which method was used, there was no significant difference in the evolution of muscle stiffness in patients and controls over 18months. Test-retest reliability of muscle MRE using a simple 2D technique was suboptimal, and did not reliably measure muscle stiffness changes in adults with BMD as compared with controls over 18months. While the results provide motivation for testing more advanced 3D MRE methods, we conclude that the simple 2D MRE implementation used in this study is not suitable as an outcome measure for characterizing thigh muscle in clinical trials.

A novel adaptive trajectory tracking control for complex environments based on accelerated back-propagation neural network

This work addresses the issue of trajectory tracking accuracy degradation for vehicle dynamics parameters and road conditions changing, an adaptive trajectory tracking controller is designed for the intelligent vehicle. Based on the yaw dynamics model, a model predictive controller (MPC) is developed for the trajectory tracking process. Meanwhile, the impacts of different control parameters on trajectory tracking at various speeds are compared. And the change rule between optimal control parameter values and reference speeds is determined by cubic polynomial fitting to ensure minimal error during the trajectory following process. Then, an estimator for vehicle tire cornering stiffness and road adhesion coefficient is designed and tested based on the accelerated back-propagation neural network (ABPNN) model, with its estimation values being compared to those obtained through recursive least square method. Last, a co-simulation platform combining MATLAB/Simulink and CarSim software is established to conduct the trajectory tracking experiment under variable working conditions. Experimental results show that the proposed adaptive controller not only exhibits high accuracy in trajectory tracking but also demonstrates excellent stability and adaptability under medium to low speed conditions, particularly when encountering changing road conditions.

Effect of pocket orientation on PVP lubricated hybrid conical journal bearing system

In a MHCJB (multi-recessed hybrid conical journal bearings), the orientation of the pockets affects the oil film pressure dispersion in the clearance space of bearing thereby it affects the performance of bearing system. This article aims to analyse the influence of pocket orientation on the characteristics of MHCJB operating with PVP (piezo-viscous-polar) lubricant. To analyse the effect of pocket orientation, the study considers two configurations of MHCJB with different pocket arrangement. The modified form of Reynolds equation governing the flow of PVP lubricant in MHCJB is numerically solved by using Galerkin’s technique. The results have been computed for the value of semi-cone angle (γ =10o), piezo viscous parameter (α¯pv= 0.0, 0.3) and polar parameter (l¯cs= 0.0, 0.2). The results indicate that pocket orientation-II offers maximum enhancement of 11.77 % in stiffness coefficient (S¯xx) and 2.45 % in damping coefficient (C¯zz). Further, PVP lubricant offers substantial improvement in stability threshold speed.

Numerical Investigation of Solitary Wave Attenuation by a Vertical Plate-Type Flexible Breakwater Constructed Using Hyperelastic Neo-Hookean Material

This study conducted numerical investigations on solitary wave attenuation by a vertical plate-type flexible breakwater constructed using hyperelastic neo-Hookean material. The wave attenuation performance and elastic behaviors of the flexible breakwater were discussed systematically by considering the effects of three prominent factors: mass coefficient, stiffness coefficient, and Poisson’s ratio. It is indicated that more compressible and flexible materials are beneficial for enhancing efficiency in mitigating solitary wave energy and protecting the structure from damage. In addition, the performance of the hyperelastic neo-Hookean material model was compared with that of a linear elastic isotropic material model coupled with linear and nonlinear geometry analysis (LGEOM and NLGEOM) by evaluating several key targets: wave reflection coefficient, transmission coefficient, horizontal tip displacement, and wave load. Our findings revealed that the hyperelastic neo-Hookean material model showed almost the same predictions as the linear elastic isotropic material model with NLGEOM, but significantly diverged from that with LGEOM. The linear elastic isotropic material model with LGEOM cannot capture the nonlinear variations in structural geometry and stress–strain relationship, resulting in the underestimation and overestimation of horizontal tip displacement under moderate and extreme wave loads, respectively. Moreover, it underestimates the damage inflicted by solitary waves due to inaccurately predicted wave reflection and transmission.

Study on the energy capture spectrum of a two-body hinged-raft wave energy converter

Wave energy converters (WECs) of the hinged-raft type offer flexible arrangements and can be further applied in arrays. This study employs a numerical model to investigate the energy capture spectrum (ECS) of a two-body hinged-raft WEC under random waves utilizing the open-source simulation software WEC-Sim. The model explores in detail the combined effects of random wave parameters and WEC parameters, including the power take-off (PTO) damping coefficient, PTO stiffness coefficient, and horizontal hinge position, on the ECS. The findings revealed that the hinged-raft WEC is highly sensitive to the average wave period and adaptable to varying wave heights. Optimal energy capture under conditions of varying wave heights can be achieved by adjusting a specific PTO coefficient. These findings underscore the complex response of the two-body hinged-raft WEC to wave parameters and emphasize the importance of understanding these sensitivities and adaptabilities to optimize the WEC system, enhance efficiency, and promote its application in arrays.

Research on a Calculation Method for the Horizontal Displacement of the Retaining Structure of Deep Foundation Pits

The precise calculation and effective control of the horizontal displacement of deep foundation pit retaining structures are critical for foundation pit support design and construction. Based on stress–strain linear elastomer theory and considering the deformation coordination between an enclosure wall and its internal support member, a formula for the redundant restraint force acting on the retaining wall was derived through the unit load method and the principle of elastic superposition. Moreover, a method for calculating the horizontal displacement of the retaining structure of a deep foundation pit was formulated, which is convenient for engineering applications. The method can also be used to calculate the horizontal displacement of cantilevered and anchored retaining structures when the loading conditions of the deep foundation pit and the relevant parameters of the enclosure structure are known. A case study was conducted on a standard section with an excavation width H of 19.3 m and an excavation depth h of 17.8 m. The structural parameters of the enclosure wall, along with the elastic support stiffness coefficient and soil layer parameters of the pit, were inputted into a MATLAB calculation code. Then, four internal support constraint forces Fi and the calculated values for the horizontal displacement of the enclosure wall were obtained after running the code. The calculated curve closely matched the curve of values measured in the field. The horizontal displacements of the top of the wall of several cement–soil gravity enclosure structures mentioned in the literature were also calculated. The results of these calculations were then compared with the measured data and corresponding data from the literature. The examples provided clear evidence demonstrating that the proposed method is highly reliable for calculating the horizontal displacement of deep foundation pit enclosure structures.

Characterization of steel T-stub compressing timber parallel to the grain component

Although there are several steel-to-timber joint types, there is still a lack of studies that more precisely characterize the components in the interaction between steel and timber in compression. Thus, this work aims to characterize the steel T-stub compressing the glued laminated timber (GLT) parallel to the grain component, focusing on formulating analytical expressions for design resistance, stiffness coefficient and deformation capacity. In order to validate the analytical models and increase the reliability of the component method, an experimental campaign was conducted through compression tests on 90 specimens composed of steel T-stubs with five different flange thicknesses under full and partial compression. It was identified that although GLT has lower compressive strength and lower stiffness than steel, the main failure mode in specimens studied was T-stub flange yielding. The proposed formulations were consistent with the experimental results and it can be used to predict the structural behavior of this component. The application of the component analytical variable elastic approach to a semi-rigid connection showed an increase in the accuracy for predicting its moment resistance.

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

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

Analysis of micropolar elastic multi-laminated composite and its application to bioceramic materials for bone reconstruction.

The asymptotic homogenization method is applied to characterize the effective behaviour of periodic multi-laminated micropolar elastic heterogeneous composites under perfect contact conditions. The local problem formulations and the analytical expressions for the effective stiffness and torque coefficients are derived for the centrosymmetric case. One of the main findings in this work is the analysis of the rotations effect of the layers' constitutive properties on the mechanical response of bi-laminated composites. The effects of microstructure and interfacial interactions on the composite's mechanical behaviour are captured through the independent effective moduli. Comparisons with the classical elastic case show the approach validation. Some numerical examples are shown. Furthermore, considering the micropolar media's prevalence in bio-inspired systems, the model's applicability is evaluated for reconstructing bone fractures using multi-laminated biocomposites. An important finding in this bio-inspired simulation is related to the analysis of a periodic bi-laminated micropolar composite whose isotropic constituents are a bioceramic material and a compact bone. This artificial bio-inspired material should integrate with host tissue to support cell growth and be stable and compatible. These characteristics are crucial in the enhancement of the fractured bone.

The Effect of Hyperelasticity and Nonlinearity on the Dynamic Behaviors of Hyperelastic Functionally Graded Beams on Nonlinear Elastic Foundation

Hyperelastic functionally graded materials have a wide range of application prospects in soft robotics and biomedical fields. This paper investigates the nonlinear free and forced vibrations of a hyperelastic functionally graded beam (HFGB) based on higher-order shear deformation beam theory. The geometrical nonlinearity is considered by using the von-Kármán’s nonlinear theory. The three-material-parameter free energy function named as Ishihara model is employed to characterize the hyperelastic material. The power-law gradient form along the thickness direction is adopted. The HFGB is resting on the elastic foundation. The Winkler, Pasternak and nonlinear stiffness coefficients are considered. The time-harmonic external force is applied to the HFGB. The nonlinear governing equations for the vibration of the HFGB are derived by using Hamilton’s principle, and are subsequently transformed into ordinary differential equations via Galerkin’s method. The nonlinear free vibration and primary resonance of the HFGB are investigated analytically by employing the extended Hamiltonian method and multiple scales method, respectively. The results indicate that the power-law index, slenderness ratio, material properties, and elastic foundation parameters have significant influences on the nonlinear frequency of free vibration as well as the frequency–response and force–response curves of forced vibration. The phase plane method is employed to analyze the system’s stability states under various excitation amplitudes. The relative error between the results of the current computational model and the published literature is less than 0.1 percent.

Recovering of the Stiffness Coefficients of the Sturm–Liouville Operator on a Star Graph from a Finite Set of Its Eigenvalues

Recovering of the Stiffness Coefficients of the Sturm–Liouville Operator on a Star Graph from a Finite Set of Its Eigenvalues

Dynamic Analysis of the Locomotion Mechanism in Foxtail Robots: Frictional Anisotropy and Bristle Diversity.

This study investigated the locomotion mechanism of foxtail robots, focusing on the frictional anisotropy of tilted bristles under the same friction coefficient and propulsion strategy using bristle diversity. Through dynamic analysis and simulations, we confirmed the frictional anisotropy of tilted bristles and elucidated the role of bristle diversity in generating propulsive force. The interaction between contact nonuniformity and frictional anisotropy was identified as the core principle enabling foxtail locomotion. Simulations of foxtail robots with multiple bristles demonstrated that variations in bristle length, angle, and deformation contribute to propulsive force generation and environmental adaptability. In addition, this study analyzed the influence of major design parameters on frictional anisotropy, highlighting the critical roles of body height, bristle length, stiffness, reference angle, and friction coefficient. The proposed guidelines for designing foxtail robots emphasize securing bristle nonuniformity and inducing contact nonuniformity. The simulation framework presented enables the quantitative prediction and optimization of foxtail robot performance. This research provides valuable insights into foxtail robot locomotion and lays a foundation for the development of efficient and adaptive next-generation robots for diverse environments.

Application of ultrasound shear wave elastography in tumors of head and neck region – a preliminary study and literature review

&lt;b&gt;Introduction:&lt;/b&gt; Ultrasound (US) scanning is one of the primary modalities in diagnostic imaging of the head and neck region. Shear wave elastography (SWE) is an ultrasound technique that facilitates objective measurements of the stiffness of the examined tissues. Additional data obtained from SWE can increase the diagnostic value of ultrasound scans in clinical practice.&lt;b&gt;Materials and methods:&lt;/b&gt; A retrospective analysis of SWE examinations as performed in patients with head and neck tumor in the period of 2021 through 2022 is presented. The obtained SWE measurements were referenced against the results of histopathological or cytological examinations.&lt;b&gt;Results:&lt;/b&gt; SWE scans were acquired in 101 patients. In 62 patients, major salivary gland lesions were examined to reveal 7 malignant neoplasms, 49 benign neoplasms, and 6 inflammatory lesions. Lymph nodes were examined in 31 patients to reveal 11 cases of reactive lymph nodes, 12 metastases of malignant neoplasms, and 8 cases of lymphoma. Eight tumors of other nature and location were also examined to reveal 2 malignant neoplasms, 5 benign neoplasms, and 1 inflammatory infiltrate within the area of large vessels. Based on the results, SWE was concluded to be a useful tool for differentiation between metastatic and reactive lymph nodes. In salivary gland lesions, the measurements of tissue stiffness are particularly useful in the differential diagnosis of the most common non-malignant tumors.&lt;b&gt;Conclusions:&lt;/b&gt; Shear wave elastography is a valuable adjunct to ultrasound imaging. Further studies on a larger group of patients with diverse pathologies are required to identify cutoff points for tissue stiffness coefficients for different types of lesions.

Influence of Physical Parameters of Elastic Rotor on Asymmetric Supports on Frequencies Its Free Oscillations

The problem of finding frequencies of vibrations of the elastic rotor on asymmetric supports is considered. Taking into account the small free vibrations of the rotor, the frequency equation of the direct problem is obtained. According to the equation, the influence on the vibration frequencies of the physical parameters of the rotor and its elastic supports was investigated. It is shown that the increase in the stiffness coefficients of the supports leads to an increase in frequencies, and the increase in the mass of the rotor, on the contrary, to a decrease in the frequencies of its vibrations. Numerical calculations are given with the corresponding results in the form of tables and graphs of dependencies.

Design and optimization of a two-degrees-of-freedom single-sided vibro-impact nonlinear energy sink for transient vibration suppression of a thin plate

To rapidly suppress the transient vibration response of a thin plate, a two-degrees-of-freedom single-sided vibro-impact nonlinear energy sink (TSSVI NES) is proposed in this paper. Based on the Kirchhoff hypothesis, the coupled equations of motion between the plate and the TSSVI NES are established. The system is modeled by the Galerkin technique and numerically solved using the fourth order Runge-Kutta method. To obtain the optimal parameters of the TSSVI NES, a particle swarm optimization method is adopted. The system response with the TSSVI NES is compared with that of the cubic nonlinear energy sink (CNES) and the single-sided vibro-impact nonlinear energy sink (SSVI NES), showing that the vibration suppression ability of the TSSVI NES is better. The mechanism of rapid response suppression of the TSSVI NES is demonstrated by way of simulations. A parametric study is also conducted to determine the effects of damping, the coefficient of restitution, mass, stiffness, and installation position of TSSVI NES on the efficacy of the vibration control device. The numerical results demonstrate that the performance of the TSSVI NES is robust to the damping, coefficient of restitution, and installation position, but sensitive to mass difference and stiffness difference. Finally, the effect of the TSSVI NES is examined when the plate is excited by seismic loads, demonstrating a good response suppression performance.

Dynamic characteristics analysis of multi-link mechanism with clearances considering uncertain parameters

As a typical multi-body system, multi-link mechanisms are widely used in industry. Inevitably, there are joint clearances in multi-link mechanisms. Besides under the conditions of manufacturing, assembly and wear, the parameters of the multi-link mechanism can create uncertainty, and joint clearances and uncertain parameters of the multi-link mechanisms deteriorate the dynamic characteristics, this directly leads to a reduction in working accuracy of the mechanisms. At present, the research focus on multi-link mechanism with clearance considering certain parameters, and relatively few research on the multi-link mechanism with clearance considering uncertain parameters, the existing research on uncertain parameters mainly focus on the uncertainty of single parameter, while the research on the dynamic response of the mechanism with multi-clearances considering the uncertainty of multiple parameters is very less. The main purpose of this article is to provide a novel feasible method for studying the dynamic characteristics of multi-link mechanisms with joint clearances under the consideration of interval uncertain parameters and random parameters. Therefore, the dynamic characteristics of mechanism with multiple clearances considering uncertain parameters, which includes interval parameters and random parameters, are investigated in this article. Taking the 6-bar mechanism as the research object, considering clearances, Poisson’s ratios, stiffness coefficients, and driving speed as the uncertain parameters, the dynamic models of 6-link mechanism with multiple clearances considering interval parameters and random parameters are developed respectively. Using Chebyshev polynomial to solve interval parameters and polynomial chaos to solve random parameters, the effects of uncertain parameters such as clearances, Poisson’s ratios, stiffness coefficients, and driving speed on the dynamic response of the mechanism are analyzed, respectively. This research can not only provide a basis for studying the essential dynamic characteristics of multi-link mechanism with uncertain parameters, but also lay the foundation for dynamic optimization design of the real mechanisms.

GROUPING OF CLONES OF 4-YEAR-OLD Eucalyptus spp. FOR PULP AND PAPER

As in other countries, In Brazil, new genetic materials of Eucalyptus spp. and their hybrids are multiplied through cloning. These materials, currently in experimental trials, must undergo several stages to select the best ones for pulp and paper production. Therefore, new studies on wood quality are essential. Therefore, this study aimed to group 11 clones of Eucalyptus spp. wood, from a clonal plantation in the municipality of Palmital, São Paulo State, for the production of paper and cellulose. For this purpose, four trees of each clone of 4-year-old Eucalyptus spp. were collected. From each tree, a log of 1 m in length was taken from the base of the tree, for the study of the characterization of the basic density and cellular dimensions of the wood. The results showed that there were significant differences between clones for basic density, fiber length, vessel element length and fiber wall thickness. The Runkel ratio, wall fraction and stiffness coefficient did not show significant differences between the different genotypes. From the results obtained, we can conclude that clones can be differentiated only by basic density, fiber length, vessel element length and fiber wall thickness. The Runkel index, flexibility coefficient and wall fraction of Eucalyptus spp. were more efficient to group the clones into two groups.

Non-linear modeling and parameter identification of a bolted joint using substructure synthesis theory

Engineering applications require accurate modeling and parameter identification to anticipate bolted joint behavior under different loading circumstances. Bolted joints are extensively used in civil and mechanical structures. In this research study, cubic stiffness non-linearity is examined and a comprehensive model, which can exhibit the non-linearity of joint behavior, is developed. This is achieved by modeling the bolted joint which is connected at one end of a cantilever beam. Mathematical model is established using concept of sub structure synthesis theory by considering non-linear translational stiffness and non-linear rotational stiffness as a boundary condition. Non-dimensional natural frequencies are estimated by assuming stiffness parameters and joint parameter estimation for translational spring having nonlinear stiffness is calculated using second order curve fitting technique. Furthermore, estimated and exact value of cubic stiffness coefficient are compared. The experimental results shows that the percentage error of estimation for all the modes are less than 8%. The experimentally determined natural frequencies are further contrasted with an analytical results to validate a precision of generated model. Present work contributes in improving the bolted joint analysis by providing a solid non-linear modeling and parameter identification methodology. This methodology enhances design practices and ensures the durability of engineering structures and mechanical systems by improving bolted joint comprehension.