Dynamic Stiffness Research Articles

Equivalent modeling of LSTS and frequency calculation based on dynamic stiffness method

Large space truss structures (LSTS) are quickly becoming a vital type of space structure due to the fast expansion of the outer space field. The equivalent modeling approach has recently attracted the attention of researchers and engineers due to the finite element method’s limitations. In order to solve the equivalent beam model (EBM) in terms of frequency, the Wittrick-Williams algorithm based on dynamic stiffness matrix and the equivalent modeling procedure of large space truss structure are introduced in this study. The frequencies obtained by the equivalent model are good agreement with that obtaied by the finite element model, demonstrating the efficiency of the frequency solution method and equivalent modeling.

Identification of dynamic coefficients of gas foil bearings by simulated excitation based on coupled fields

The dynamic coefficients (dynamic stiffness coefficient and dynamic damping coefficient) of gas foil bearings (GFBs) are important for transient dynamics calculation and stability analysis of the GFBs-rotor system. Although the perturbation method can be used to calculate the dynamic coefficients, it can only consider a single whirl ratio. Moreover, the whirl ratio is assumed and not practical. Therefore, this paper proposes an identification method of dynamic coefficients of GFBs by simulated excitation. Firstly, based on single journal-single GFB model considering gas-structure interaction by coupled fields, harmonic excitations were applied to the rotor to obtain the shaft orbit. Next, frequency response function method and equivalence coefficient method were used to identify dynamic coefficients. The former method is suitable for the case where response and excitation are same frequency, namely linear problem. The latter method is fit for the situation in which the response has multiple frequency components, namely nonlinear problem. Finally, examples were carried out, and the results from different methods were compared and analyzed. This research work lays a theoretical foundation for the design of the GFBs-rotor system.

Fatigue behavior of pultruded fiberglass tubes under tension, compression and torsion

This work is devoted to an experimental investigation of fatigue behavior of pultruded fiberglass tubes under uniaxial tension, compression and torsion. Static tests were carried out; a presence of postcritical deformation stage during torsion is noted. Regularities of inhomogeneous strain fields evolution are analyzed using digital image correlation method. Fatigue curves are built for four cyclic loading modes: tension-tension, compression-compression, tension-compression and torsion. An analysis of specimens' fractures is carried out, typical damaging mechanisms are revealed. Residual dynamic stiffness data is obtained and studied using a previously proposed fitting model. Results demonstrate model's high descriptive capability and its flexibility to describe two-staged and three-staged stiffness degradation curves. An influence of loading mode on a shape of these curves is found out. Model parameters' dependence on maximum stress value during the loading cycle is studied using the Pearson's correlation coefficient. The necessity of multiaxial fatigue behavior investigation of pultruded fiberglass tubes is concluded.

Wide quasi-zero stiffness region isolator with decoupled high static and low dynamic stiffness

Quasi-zero stiffness (QZS) isolators can achieve the two goals of relatively high static and low dynamic stiffness (HSLDS). However, the static and dynamic stiffness of most QZS isolators remains coupled, causing conflicts in optimizing these dual objectives, especially in the case of large displacement excitations and heavy loads, leading to limited performance. To overcome these limitations, this paper presents an isolator with an extended QZS region that allows for the independent design of HSLDS. The positive stiffness provided by the cantilever beam with curve fixture (CBCF) precisely counteracts the negative stiffness offered by a pair of inclined springs, thereby achieving continuous and extensive QZS characteristics from a point to a region. Dynamic equations are established based on the Lagrangian principle and swiftly solved utilizing the Runge-Kutta-4 method. The proposed isolator exhibits a low resonance frequency, and superior performance when exposed to large displacement excitations compared to alternative isolators. Both static and dynamic experiments confirm a QZS region of 0.023 m and resonance frequencies of below 1 Hz. The proposed isolator facilitates effective vibration isolation for ultra-low-frequency and large displacement excitations.

Influence of Prestress on Vibration Frequency of Beam String Structures Based on Exact Matrix Stiffness Method

Beam string structures (BSS) are frequently employed in large-span spatial structures due to their high load-carrying efficiency and elegant appearance. Owing to the neglect of the influence of prestress, the natural frequency of the BSS is often overestimated which could be crucial to the dynamic behavior of BSS. This paper presents an exact matrix stiffness analysis method (MSM) for investigating the relationship between prestress and the natural frequency of the planar BSS. A novel dynamic stiffness matrix of beam–columns considering the natural frequency and axial force is used to develop the MSM. The dynamic analysis of the structural vibration stability of BSS is performed by using the global structural stiffness matrix which is assembled from the element stiffness matrices in the global coordinate system. The proposed MSM with the exact dynamic element stiffness matrix for the dynamic analysis of the BSS is verified by comparing with previous results based on the finite element method. The illustrative examples demonstrate that the prestress in the cable has a negative effect on the natural frequency of the BSS and should be considered in the dynamic analysis. As the axial force increases from zero to the buckling load [Formula: see text], the natural frequency of the BSS decreases from the maximum vibration frequency to zero. The influence of prestress on the vibration frequencies of BSS is particularly significant when the prestress to balance the loads is large, especially in the case of large dead and live loads (e.g. floor slabs).

Gas-Spring Quasi-Zero Stiffness Air Damping Isolator for Vertical Vibration Control of Indoor Substation Excited by Metro Loads

To mitigate the metro-induced vertical vibration of the indoor substation structure, this study proposes a gas-spring quasi-zero stiffness air damping isolator (AD-QZSI) with excellent low dynamic stiffness and high-static stiffness characteristics. The working principle and mechanical properties of the AD-QZSI are introduced and studied through theoretical and numerical methods. A model for substation considering soil–structure–equipment interaction is established using the software ABAQUS, its accuracy is validated based on a series of measured data from actual projects, and the AD-QZSI’s simulation method and parameter design method are described in detail. The air damper’s stiffness [Formula: see text] is integrated into the isolator’s mechanical model, theoretically and numerically achieving an accurate simulation of AD-QZSI’s nonlinear mechanical properties. The numerical results have an error of less than 5% with the measured data, indicating that the model is able to better capture the actual structure’s dynamic characteristics and is reasonable to be employed for subsequent analysis. Numerical results show that AD-QZSI can significantly reduce the structural vertical vibration, and its control effect is better in the whole frequency band, in particular, the effect is also visible in the low-frequency band, indicating that its vibration isolation frequency band is wider than that of traditional QZS isolator. With the vibration source distance increasing, the control effect of AD-QZSI presents a tendency to decrease and then level off, and its vibration isolation gain is weakened by the continuous increase of the damping ratio greater than 0.01. Moreover, the equipment’s dynamic amplification factor of the isolated structure decreases significantly. Finally, the proposed AD-QZSI can obtain ideal quasi-zero stiffness characteristics by adjusting the air pressure, and the adopted air damper belongs to the green low-carbon components, featuring great practical value and application prospects.

Nonlinear dynamic meshing force analysis of PEEK-based polymer composite involute spline coupling system

The dynamic meshing force affects the stability and wear life of PEEK polymer composite involute spline couplings, but most of the dynamic meshing force is obtained by empirical formula, and there is no effective calculation method in practice. Aiming at the viscoelasticity and nonlinear behavior of PEEK material, this work established a nonlinear dynamic model of the drive system of PEEK-based polymer composite involute spline pair by using the concentrated mass method, taking into account time-varying meshing stiffness, tooth side gap, and comprehensive transmission error, and obtained a dimensionless dynamic matrix that eliminates rigid body displacement. Aiming at the thermal stability of PEEK material, the dynamic meshing stiffness and dynamic meshing force of the involute spline of PEEK-based polymer composite were calculated by considering the thermal effect of misalignment and meshing deformation. The influence of misalignment on the dynamic characteristics of the system under dynamic and static loads was studied. The results show that the dynamic meshing stiffness and dynamic meshing force of involute spline coupling of PEEK-based polymer composite materials under misalignment represent complex nonlinear characteristics; Vibration, load, and viscoelastic deformation have an impact on transmission accuracy and efficiency; And the optimal selection range for friction coefficient, Poisson's ratio, and Young's modulus were determined within the parameter range of involute spline coupling of PEEK-based polymer composite materials as the matrix. It provides a theoretical foundation for designing high-performance, high-precision, and highly reliable PEEK-based polymer composite components.

A Design Optimization Process of Improving the Automotive Subframe Dynamic Stiffness Using Tuned Rubber Mass Damper

A Design Optimization Process of Improving the Automotive Subframe Dynamic Stiffness Using Tuned Rubber Mass Damper

Vibration response of in-vacuo tuneable structured fabrics

This paper presents a first survey on the vibration response of beam-like specimens formed by a vacuum plastic bag with single-layer or double-layer 3D-printed structured fabrics encompassing spherical-octahedra, octahedra and cubes truss-like rigid elements. The study reports a comprehensive analysis of the bending stiffness and energy dissipation properties with respect to the level of vacuum as well as the type and number (single or double) of overlapped fabrics. In this context, it first presents a quasi-static analysis of the bending stiffness and energy dissipation of the specimens. Then, it provides a comprehensive overview of the specimens dynamic properties with respect to measurements of the dynamic stiffness frequency response function and with reference to measurements of hysteresis loops at three characteristic frequencies, namely below, at and above the fundamental bending resonance frequency of the beam-like specimens. The study shows that the bending stiffness and thus the fundamental bending resonance frequency of the specimens can be suitably varied by increasing the level of vacuum in the bags. The specimens made with cubic mails show the highest bending stiffness and fundamental resonance frequency. Also, the specimens with double layer mails show much higher bending stiffness and fundamental resonance frequency. The level of vacuum has little effect on the energy loss, which, in general, is characterised by rather low loss factors. This suggests that once the fabric jams, there is little friction between the particles and the principal damping mechanism is offered by the material energy dissipation in the unit particles.

Vibration analysis of cylindrical shell discontinuously coupled with annular plate with arbitrary boundary conditions

Discontinuously coupled cylindrical shell-plates or plate-like structures are common components of underwater vehicles, and their vibration characteristics change significantly due to modal coupling. The vibration of discontinuously coupled annular plate-cylindrical shell structures is analyzed based on the wave propagation method(WPM) and virtual spring(VS). Taking uniform annular plates and cylindrical shells as spectral elements, the displacement solutions are described by the trigonometric function and Bessel function respectively, and the vibration responses of the annular plate-cylindrical shell with arbitrary boundaries are obtained. Based on VS and weighted least square norm least square method(WLSNLSM), the discontinuous coupling between the annular plate and cylindrical shell is described as the non-uniform distribution of stiffness of virtual spring by continuity condition, and the dynamic stiffness matrices of continuously and discontinuously coupled structure can be obtained simultaneously. The reason for vibration characteristic change under discontinuous coupling is explained from the perspective of modal superposition. Finally, a finite element model is established to verify the accuracy of the proposed method. The influence of general discontinuous coupling on the dynamic behavior of shell structure is analyzed by numerical examples, which provides useful guidance for structural vibration analysis with discontinuous coupling.

Pressure and stiffness of a new air-inflated compression wrap.

To report pressure and stiffness, in healthy volunteers, of a new compression device with an air bladder inflated by a pump to regulate pressure. The device was applied to 60 legs of 30 volunteers and set to exert different pressures of 20-50mmHg. The exerted pressure was measured in supine and standing positions and during simple physical exercises; static stiffness index, dynamic stiffness index, and walking pressure amplitudes were calculated. The exerted pressure showed a good correlation with the expected pressure at each pressure range. The stiffness indices were >10mmHg in the range of inelastic materials. The device was considered very easy to apply and use by the testing researchers. The device stiffness is in the same range as the inelastic bandages. Consequently, similar hemodynamic effectiveness could be expected but must be proved. Unlike inelastic bandages, this device was easy to apply and use.

Perspectives on the generalized modeling of six beam theories: A unified dynamic stiffness matrix

High-precision, efficient and streamlined methods for the dynamic modeling and analyzing of engineering structures have consistently captured attention of designers and researchers. This paper addressed this increasing demand by presenting a generalized modeling and analyzing method. Specially, a unified model was proposed to integrate six beam theories into a single formula. Upon this model, a unified dynamic stiffness matrix was derived, serving as an elemental building block for formulating the transfer matrix, frequency-dependent mass and stiffness matrices as well as further integrating finite element method, dynamic stiffness matrix method and transfer matrix method. Through this transition, challenges associated with transcendental eigenvalue in dynamic stiffness matrix method and transfer matrix method was effectively resolved and the advantages of transfer matrix method in handling complex structure were maximized. Given the widespread utilization of curved beams in buildings, bridges, robotics and sensors, the proposed method was validated through comparative analysis with other methods, focusing on both curved and straight beams. Furthermore, this study delineated applicability scopes of different beam theories and provided the strategic approach for curved and straight beams. The feasibility of this strategy was demonstrated through an investigation involving a corrugated structure comprising both straight and curved beams.

Effective dynamic properties of multi-segment beam lattices: a dynamic stiffness formulation

Effective dynamic properties of multi-segment beam lattices: a dynamic stiffness formulation

Influence of gear modification on dynamic characteristics of star gearing system in geared turbofan (GTF) gearbox based on a closed-loop dynamic analysis method

The star gearing transmission system is a key component of a geared turbofan (GTF) aero-engine. Accurate prediction of the dynamic characteristics of the star gearing transmission system, especially after gear modification, is important for the design of high-performance engines. Firstly, this paper establishes a dynamic time-varying mesh stiffness (TVMS) and a comprehensive transmission error (TE) calculation model for herringbone gear pair considering changes in the meshing state. Then, the dynamic internal excitation calculation model is combined with the lumped parameter dynamic model of the system to form the “excitation–response–feedback” closed-loop coupling dynamic analysis method of the GTF star gearing system. Compared with traditional analysis methods, this method takes into account the effect of contact state changes on internal excitation during the calculation process and corrects internal excitation in real time. Finally, the effect of different topology modification schemes on the system's dynamic characteristics is investigated based on this method. The results show that the closed-loop coupled dynamics analysis method is able to capture contact state changes of the same gear pair at different moments and between different gear pairs at the same moment. Modified #2 is only to modify the planet gear. This scheme can effectively reduce the vibration displacement of the ring gear, and reduce the peak-to-peak value of the ring gear's vibration displacement in all directions by more than 70%. At the same time, the scheme also reduces the load-sharing coefficient of the internal and external meshing pairs of the system by 1.92% and 2.01%, respectively, and the peak-to-peak value of the dynamic factor of the internal and external meshing pairs can be reduced by 57.91% at most.

A Dynamic Gradient Stiffness Material Platform to Manipulate Cardiac Fibroblasts' Spatio‐Temporal Behavior

AbstractAfter myocardial infarction, there exists a spatiotemporal variation of cardiac tissue stiffness across the infarcted border region outward to remote regions, influencing adverse remodeling and cardiac fibrosis, and this stiffness gradient changes over time. Here, a platform with dynamic, tunable, and reversible gradient stiffness can recapitulate in vitro the time‐dependent stiffness range across the infarction border that occurs as part of the remodeling process is presented. This platform enables the observation of time‐dependent interaction between cardiac fibroblasts and their mechanical microenvironment in a spatiotemporal manner. Specifically, the competition and cooperation of a chemical cue (antifibrotic drug) and mechanical cue (gradient softening) in tandem to attenuate the fibrotic responses of cardiac fibroblasts is examined. Applying a combined intervention showed either additive or antagonistic effects on fibrosis‐related gene regulation compared to separate interventions of drug or softening. This work reveals the spatiotemporal variation of fibrotic response in cardiac fibroblasts as well as the complexity of antifibrotic drug dosing with stiffness changes and their combinatory effect on cardiac fibroblasts. This platform provides a unique in vitro tool to study disease progression mechanisms in a more clinically relevant microenvironment and also serves as a cost‐effective model for potential therapeutic screening.

Influence of the Dynamic Stiffness of Shells on the Critical Detonation Thickness of a Low-Sensitivity Explosive

Influence of the Dynamic Stiffness of Shells on the Critical Detonation Thickness of a Low-Sensitivity Explosive

Dynamic stiffness formulation for vibration characteristics analysis of bi-dimensional functionally graded annular plate of variational thickness

Dynamic stiffness formulation for vibration characteristics analysis of bi-dimensional functionally graded annular plate of variational thickness

Dynamic Manipulation and Stiffness Modulation of Cooperative Continuum Robots: Theory and Experiment

Abstract Cooperative continuum robots (CCRs) are composed of multiple coupled continuum arms to cooperatively conduct manipulation tasks. They can highly enhance the performance of individual continuum arms by providing extra stiffness, leading to increased accuracy, payload capacity, and dynamic stability of the robot. This study aimed to investigate the stiffness analysis of tendon-driven supportive-type CCRs (S-CCRs). For this purpose, first, a generalized framework for the dynamic mathematical formulation and numerical solution of S-CCRs was proposed, their dynamic response to complex scenarios was obtained, and the accuracy of the model was experimentally evaluated. Then, the capability of stiffness modulation of S-CCRs was studied. Tendon-driven S-CCRs are potentially capable of changing the stiffness with structural configuration, providing active stiffness control at the design level. Hence, in this study, the effects of the connection point location/angle of the supportive arms to the operative arm, as well as the imposed tendon limitations of the supportive arm on the stiffness of the robot, and consequently on the dynamic payload manipulation, were studied and practical solutions were proposed to develop a simple but effective stiffness control mechanism. This study showed that a typical S-CCR can increase its stiffness, just by a modular connector design up to 84% during manipulation, bringing a novel opportunity for stiffness modulation of CCRs.

Free vibration analysis of composite beams and laminated reinforced panels by refined dynamic stiffness method and CUF-based component-wise theory

This paper presents a comprehensive analysis of the free vibration behavior of composite beams and laminated reinforced panels. Employing high-order theories with displacement variables only, the investigation combines dynamic stiffness method (DSM) and the Carrera unified formulation (CUF). The 3D displacement field can be expanded in the framework of CUF as any order of generic unknown variables over the cross-section, in the case of beam theories. Specifically, Lagrange expansions (LE) of cross-sectional displacement variables are considered, enabling the refinement modeling of complex cross-sections with different layers (layer-wise) and components (component-wise). The governing differential equations and natural boundary conditions are derived using the principle of virtual displacements. Subsequently, an exact dynamic stiffness matrix is developed by establishing a relationship between the amplitudes of harmonically varying loads and the corresponding responses. The Wittrick–Williams algorithm is employed to solve the transcendental eigenvalue problem resulting from this approach. The Lagrange-based CUF(LE)-DSM outperforms other polynomials (such as Taylor)-based CUF in analyzing composite structures, enabling detailed analysis with various geometries, lamination schemes and boundary conditions. It delivers accurate results in reinforced panel analysis, requiring only 13% of the DOFs compared to 3D FE models, thereby reducing computational costs significantly, as confirmed by comparative studies and validations.

Dynamic property evaluation of pipeline clamp based on analyzing the propagation characteristics of flexural wave in pipeline

The external clamp of hydraulic pipeline plays an important role in strengthening pipeline stiffness and improving vibration attenuation ability. In this study, wave propagation method is proposed to evaluate the translational and rotational stiffness and their loss factors of the clamp by analyzing the flexural wave propagation characteristics of pipeline. In order to validate the measured dynamic properties, experimental modal analysis was performed on the two-end elastically-supported pipeline. By modelling the pipeline with translational and rotational edge restraints, the analytical modal frequency parameters, wave numbers, and waveform coefficients were obtained. By comparing of the first-order flexural mode frequencies between experiment and analysis, the dynamic stiffness predicted by the wave propagation method was validated. The effects of the magnitude of torque, direction, clamping torque cycle, and clamp size on the complex dynamic properties of pipeline clamp were investigated. The proposed wave propagation method allows non-destructive continuous monitoring of a clamp stiffness, provides additional information about the vibration attenuation feature. It has advantages in clamp applications and is an effective methodology for measuring the dynamic properties of viscoelastic materials.