Equivalent Stiffness Coefficient Research Articles

Identification of dynamic contact parameters between contact roller and filament package

During the high-speed winding of polyester filament, a contact roller must be applied to press on the filament package’s surface to ensure the filament is placed stably and precisely on the package surface. Thus, a twin-rotor system with contact coupling characteristics between the contact roller and the filament package is formed. Identifying the contact parameters between the contact roller and the package are prerequisite to precisely analyze the dynamic behavior of the winding system, as well as to determine the technical parameters. In this paper, an approach was proposed to identify the equivalent contact stiffness and contact damping coefficients by means of coordination through experiment and simulation. First, based on the forced non-resonance method of a single-degree-of-freedom system, the testing scheme was drawn up in consideration of the winding process parameters. Then, an experimental device for the twin-rotor system was developed, and the dynamic contact parameters just in the working frequency band corresponding to low linear speed of winding were obtained by the experiment, due to the requirement of the forced non-resonance theory and economic limitations of the experimental device. Third, the basic parameters including equivalent radial Young’s modulus and damping ratio of the package were obtained through experimental test. Furthermore, the contact parameters in the working frequency band corresponding to high linear speed of winding were obtained through simulation. Finally, the curve fitting of contact parameters was finished; in addition, the comparative results between the simulation and the experiment are in good agreement. The dynamic contact parameters present nonlinear frequency variation characteristics.

Earthquake dynamic induced by the magma up flow with fractional power law and fractional-order friction.

In this work, we examine the dynamical behaviour of the “single mass-springs” model for earthquake subjected to the strength due to the up flow of magma for the period of volcanism, considering the fractional viscous damping force, the fractional weakening friction and fractional power law of elastic force. The numerical simulation method used in this paper is that of Grünwald-Letnikov based on the generalization of the classical derivative, and the approximately analytical solution obtained by the harmonic balance method. The results have shown that the fractional-order derivative can affect the dynamical properties of fault rock, which is characterized by the equivalent damping coefficient and the equivalent stiffness coefficient. Moreover, the amplitude-frequency equation for the steady-state solution was established. It appears that the resonant amplitude and resonant frequency are strongly dependent on the fractional-order damping r, fractional-order friction q, the fractional deflection 𝛼, the nonlinear stiffness coefficient and the fractional viscous coefficient. We have also shown that, the recurrence time of an event, the duration time of an event and the slip size of an earthquake can be controlled by the fractional-order derivative, the fractional-order deflection and the magnitude of the magma strength. The model allowed us to better interpret the earthquake as a stick-slip motion.

Improving thermomechanical properties of cracked brittle honeycombs by negative Poisson’s ratio effect

This work investigates the effects of cracking on the overall properties of brittle auxetic/non-auxetic honeycombs. The micro numerical model and macro theoretical model are established simultaneously. The analytical expressions of crack opening displacement (COD) are derived and the results agree well with numerical simulations. The fracture toughness of honeycombs is calculated by combining the stress in the numerical model and the stress intensity factor (SIF) in the theoretical model. The reductions in the equivalent stiffness and equivalent thermal stress coefficient (TSC) of the cracked honeycombs are predicted. The negative Poisson’s ratio (NPR) effects on those fracture mechanics parameters and equivalent thermomechanical properties are studied. And considering the orthogonal anisotropic properties of honeycombs, the cracking along two orthogonal directions is examined. It reveals that the significant NPR effects can only be detected in a single direction and the effects in another direction are inconspicuous. In addition, the effects of crack length, medium dimensions, and cell-wall angle of honeycomb cells on the overall performance of the cracked medium are also evaluated by parametric studies and the results are displayed graphically.

Performance of finite bearing under the combined influence of turbulent and non-Newtonian lubrication

The current numerical investigation is used to predict the dynamic performance of finite bearing considering the combined influence of turbulence regime and non-Newtonian flow. With appropriate assumptions, the Navier–Stokes and continuity equation have been revised by the linear turbulence and non-Newtonian fluid model together. The clearance space of the finite bearing has been determined by the finite element method adopting Galerkin’s procedure and robust iteration technique. The cylindrical coordinate forms of momentum and continuity equations are used for the flow field of the finite bearing assuming the turbulent regime and non-Newtonian lubricant. Dynamic performance parameters of a finite bearing have been computed regarding direct and cross-coupled fluid-film coefficients, equivalent stiffness coefficient, whirl ratio, and critical mass at different eccentricity ratios for distinct values of Reynolds numbers preferably up to 13,300 and varied values of non-linear factor of the non-Newtonian fluid model. The obtained results revealed the performance enhancement in the combined regime as compared to pure turbulence and non-Newtonian flow conditions. The stability of finite bearing is significantly improved under the proposed severe flow regime.

Active Control Method Based on Equivalent Stiffness and Damping Coefficient for an Electromagnetic Isolation System

For improving the performance of an electromagnetic isolation system with reasonable parameters and avoid the parameter tuning problem of a PID controller, an active control method is put forward based on equivalent stiffness and damping coefficient. In this paper, the range of equivalent stiffness coefficient and damping coefficient of the electromagnetic force are calculated based on the required range of dynamic performance indexes. According to the nonlinear expression between electromagnetic force and coil current and gap, the relationships between the coil current and equivalent stiffness coefficient and damping coefficient are established. Then, the equivalent stiffness coefficient and damping coefficient can be satisfied by the controlled current in different gaps for meeting the required dynamic performance indexes. For reducing the maximum overshoot and the number of oscillations of the system, the active control method with the piecewise equivalent stiffness and damping coefficient is proposed based on the piecewise control strategy to realize the variable control parameters of the isolation system. Simulation and experimental results verify that the control method based on the equivalent stiffness and damping coefficient can obtain the desired dynamic performance indexes and the proposed control method with the piecewise strategy can not only reduce the setting time of the system, but also ensure the stability of the system.

Numerical investigations of bistable piezoelectric cantilever for enhanced energy harvesting

Piezoelectric energy harvesting applications have been highly impacted research area recently. Numerical investigations for bistable piezoelectric cantilevers have great importance to understand its dynamic performance. This paper aims to develop comprehensive numerical models to simulate the dynamic response of aunimorph piezoelectric bender under bistability effect for enhanced energy harvesting. To this end, the equivalent stiffness, damping, electromagnetic coupling and capacitance coefficients of a bistable piezoelectric cantilever have been numerically developed. Besides, finite element models are developed to determine the bistability repulsion force between magnets. The resulting simulations are then implemented in an electromechanical model to predict the output voltage and power over a range of load resistance.

A novel sensitive piezoelectric mass balance used for weightless environment

A novel sensitive piezoelectric mass balance (PEMB) was developed for using in weightless environment. The mass of the measured object was obtained by detecting the resonant frequency shift of the PEMB. This weighing method was illustrated systematically. In order to build the relationship between the resonant frequency shift and the measured mass, the equivalent stiffness coefficient and the equivalent concentrated mass of the PEMB were analyzed theoretically. The influence of the structural and material parameters on the sensitivity was analyzed, which provided the design reference to improve the sensitivity. The finite-element-method (FEM) static analysis of the PEMB was carried out with ANSYS software to investigate its shock resistance. Furthermore, the vibration test and calibration experiment effectively verified the theoretical analyses results. The developed PEMB holds merits of independence on acceleration field, independence on properties of the measured object and with shock resistance. Consequently, it can be a suitable candidate for measuring mass of solid samples with unknown properties in the weightless environment.

Stochastic Response of SDOF Self-Centering System

As a new type of seismic resisting device, the self-centering system is attractive due to its excellent re-centering capability, but research on such a system under random seismic loadings is quite limited. In this paper, the stochastic response of a single-degree-of-freedom (SDOF) self-centering system driven by a white noise process is investigated. For this purpose, the original self-centering system is first approximated by an auxiliary nonlinear system, in which the equivalent damping and stiffness coefficients related to the amplitude envelope of the response are determined by a harmonic balance procedure. Subsequently, by the method of stochastic averaging, the amplitude envelope of the response of the equivalent nonlinear stochastic system is approximated by a Markovian process. The associated Fokker–Plank–Kolmogorov (FPK) equation is used to derive the stationary probability density function (PDF) of the amplitude envelope in a closed form. The effects of energy dissipation coefficient and yield displacement on the response of system are examined using the stationary PDF solution. Moreover, Monte Carlo simulations (MCS) are used for ascertaining the accuracy of the analytical solutions.

Simulation analysis and experimental evaluation of the transient behaviour of a reluctance magnetic coupling

The aim of this study is to present the dynamic behaviour of two co-axial rotating shafts connected by a reluctance magnetic coupling. The analysis is based on non-linear differential equations of motion. The reluctance magnetic coupling is modelled by an equivalent torsional stiffness coefficient and an additional viscous damping coefficient to account for the effects of induced currents in the salient-pole during the transient. These coefficients are obtained from three-dimensional finite element electromagnetic models. In order to evaluate the accuracy of the proposed model, several transient responses for the shaft line are considered. The simulation results are compared with those obtained from measurements.

A Macro Model for Electroadhesive Contact of a Soft Finger With a Touchscreen.

A contact problem of electroadhesion for a conductive elastic body pressed against a rigid plane surface of a dielectric coating covering a conductive substrate is formulated applying the Johnsen-Rahbek approximation for the attractive surface stresses and the Derjaguin-Muller-Toporov (DMT) hypothesis about the influence of the adhesive stresses on the deformable shape of the elastic body. An approximate solution is obtained using the Winkler-Fuss deformation model with the equivalent (contact load dependent) stiffness coefficient evaluated according to the Xydas-Kao soft finger model. The friction force under applied voltage is evaluated as the product of the coefficient of friction and the integral of the macro contact pressure over the apparent contact area. The upper and lower estimates for the friction force are discussed in the case of absence of any external normal load.

Study on calculation method of new corrugated steel reinforcement structure of highway tunnel

Corrugated steel, a new structure, shows great advantages in many fields, however, it is rarely used in the reinforcement of highway tunnels. Besides, corresponding design method and mechanical properties are still not clear yet. In this study, a full-scale test is carried out to explore the calculation method of corrugated steel as a new reinforcement structure. Combining with numerical simulation and theoretical calculation, the load-deflection law of corrugated steel is revealed, which has a two-stage stiffness characteristic (anti-backlash stage and elastic stage). Equivalent stiffness coefficient is proposed to establish a simplified calculation method of the equivalent stiffness of corrugated steel. And RDP (Ratio of Depth to Pitch) is the main factor affecting the equivalent stiffness coefficient.

Study the Foundation Effect on the Hydrodynamic Bearing Performance.

The hydrodynamic bearings are important components of most of the rotary parts in different applications. The current study examines the performance of the traditional type, which is the most common because they are easy to the manufactured, relatively low cost, but they have low stability compared with other type because they have large values for the cross coupling stiffness coefficients, which are responsible for the whirl phenomenon. The mathematical model was constructed and the equations of the thickness change oil film were presented. In addition to the mathematical formula of Reynolds equation, the numerical solution was adopted to solve it using a (five-nodes) scheme method and it is solved using the (MATLAB) software. The oil film and the foundation were considered as springs that were connected to each other in series and the equivalent stiffness coefficient are calculated. The results showed that taking the foundation effect into account reduces the overall values of the stiffness coefficient. The results showed that the use of different materials in the covering leads to a decrease in the equivalent stiffness coefficient value depending on the layer thickness of the covering. The method of partial covering caused an important of some of stiffness coefficient and decrease..

First assessment on suspension parameter optimization for a solar – powered vehicle

Optimization of suspension parameters with respect to comfort and road holding is a challenging issue for solar–powered cars, due to in–wheel electric engines on very light vehicles, carrying payloads which can exceed their total mass. The solar–powered car considered in this study was designed and manufactured for racing by the University of Bologna; with a mass of 300 kg and a payload of 320 kg due to four occupants, using 5 m2 of monocrystalline silicon photovoltaic panel on the roof, 64 kg of lithium–ion batteries and two electric engines coupled directly to the rear wheels, it can achieve either a range of 600 km at cruising speed, or velocity peaks of 120 km/h. In this contribution, equivalent vertical stiffness and equivalent damping coefficients are optimized for both axles, achieving results that in terms of comfort and road holding are comparable to those of standard passenger cars.

Computational- and experimental-based analysis of the load capacity of dowel-brick structure of graphite component in TMSR

To ensure the structural integrity of graphite reflector and the insertion of the control rod in the seismic event, a finite element analysis (FEA) of the whole graphite core in Thorium-based Molten Salt Reactor (TMSR) is urgently required. The stiffness of the dowel-brick structure is one of the most crucial parameters to verify the finite element model in whole core modelling. In this paper, ten non-failure and ten failure tests have been carried out to study the stiffness and load capacity of the dowel-brick structure and to investigate how the size of the dowel affects these parameters. In addition, two groups of FEA have been performed first, whose results are used to design the above tests. The numerical and experimental results indicate that the load capacity of dowel-brick structure is significantly affected by the height of the dowel and the direction load applied. The failure load in the direction perpendicular to the line connecting two dowels is obviously higher than that in the parallel direction. Meanwhile, due to most of cracks occurring in the lower brick, it is identified as the weakest one in the dowel-brick structure. Furthermore, when the dowel is short, the equivalent stiffness coefficients of the dowel-brick structure in directions parallel and perpendicular to the line connecting two dowels are approximately equal. However, the latter will be much higher than the former when the dowel is long enough. The stiffness coefficients of the structure in two directions increase slightly as the diameter of the dowel increasing. The experimental results have been used in the numerical analysis of the whole graphite core modeling in TMSR.

Equivalent stiffness prediction and global buckling analysis using refined analytical model of composite laminated box beam

Abstract The analytical model applicable to calculate the equivalent stiffnesses of composite box beam has been refined. The calculation of equivalent stiffness coefficients of composite laminated box beam is simplified and the connection between shear-deformable beam theory and classical laminate theory is established. The equivalent stiffness analytic formulas expressed by beam cross-section geometry and laminate stiffness coefficients are obtained. These analytical formulas are suitable for composite laminated box beam with circumferential uniform stiffness, and accounts for bending- transverse shear and torsiontensile coupling effect. The correctness and precision of refined analytical model is verified by test and finite element method, respectively. The influences of the lay-ups on the elastic coupling of composite structures and their causes are studied. The variation of the equivalent stiffnesses of the laminated box beams with different lay-ups is predicted. The global buckling analysis of composite laminated box beam considering the transverse shear deformation is carried out. The formula of the global buckling critical load is obtained combining with the theoretical formulas of equivalent stiffnesses. The influences of the lay-ups, shear deformation and slenderness ratio on the global buckling critical load are studied.

Investigation on dynamic behaviors of thermal protection system using a two degree-of-freedom nonlinear theoretical method

In order to study the nonlinear dynamic behaviors of Thermal Protection System (TPS) and the nonlinear dynamic strength of the strain-isolation-pad (SIP), a two degree-of-freedom nonlinear dynamic theoretical model was presented under the acoustic excitation and base excitation. The tile is simplified as a mass point, a linear spring and a damping element, and the SIP is simplified as a mass point, a nonlinear spring and a damping element. On this basis, the solving process of the nonlinear theoretical model and the iterative process of the equivalent linear stiffness coefficient of SIP were derived by the statistical linearization method. The dynamic responses analyzed by the nonlinear theoretical model and linear theoretical model are compared. The nonlinear stiffness of SIP shows obvious influence on behaviors of TPS and dynamic stress of SIP, and the equivalent linear stiffness of SIP is related to the types of excitations. Finally, the influences on above dynamic responses by the nonlinear stiffness level of SIP were studied. The equivalent linear stiffness coefficient of SIP, acceleration of TPS and dynamic stress of SIP decrease with the increase of the nonlinear level for the stiffness of SIP.

Dynamical response of fractional-order nonlinear system with combined parametric and forcing excitation

A dynamical analysis of a Mathieu-van der Pol-Duffing nonlinear system with fractional-order derivative under combined parametric and forcing excitation is studied in this paper. The approximate analytical solution is researched for 1/2 sub harmonic resonance coupled with primary parametric resonance based on the improved averaging approach. The steady-state periodic solution including its stability condition is established. The equivalent linear stiffness coefficient (ELDC) and equivalent linear damping coefficient (ELSC) for this nonlinear fractional-order oscillator are defined. Then, the numerical simulations are presented in three typical cases by iterative algorithms. The time history, phase portrait, FFT spectrum and Poincare maps are shown to explain the system response. Some different responses, such as quasi-periodic, multi-periodic and single periodic behaviors are observed and investigated. The results of comparisons between the numerical solutions and the approximate analytical solutions in three typical cases show the correctness of the analytical solutions. The influences of the fractional-order parameters on the system dynamical response are researched based on the ELDC and ELSC. Through analysis, it could be found that the increase of the fractional-order coefficient would result in the rightward and downward movements of the amplitude-frequency curves. The increase of the fractional-order coefficient will also move the bifurcation point rightwards and will make the existing range of steady-state solution larger. It could also be found that the ELSC will become larger and ELDC smaller when the fractional order is closer to zero, so that the decrease of the fractional order would make the response amplitude larger. At last, the detailed conclusions are summarized, which is beneficial to design and control this kind of fractional-order nonlinear system.

Development and Analysis of the Control Effect of a Reid Damper with Self‐Centering Characteristics

To improve the recoverability of structures following an earthquake, a Reid friction damper with self‐centering characteristics is proposed and its hysteretic behavior is studied by theoretical analysis and experimental research. The main parameters of the damper are the equivalent stiffness and energy dissipation coefficient. Based on a 10‐story steel frame structure, 10 energy dissipation design schemes using the proposed Reid damper are proposed. The additional equivalent damping ratios of the 10 schemes are equal, whereas the energy dissipation coefficients of the dampers are different. The vibration control effects of the energy dissipation structures are analytically investigated under four earthquake loads. The experimental results of the friction damper are in good agreement with the theoretical results, and the hysteretic behavior of the damper follows that of a typical Reid model. The seismic response and structural damage can be reduced using any of the 10 design schemes; however, the effects are different. When the energy dissipation coefficient is in the range of 0.1–0.3, the control effect on the interstory drift is better; however, the structural acceleration response and damping force of the dampers increase. When the energy dissipation coefficient is in the range of 0.6–1.0, the energy dissipation effect of the dampers is good; however, the self‐centering ability is poor. Therefore, the optimum range of the energy dissipation coefficient of a Reid damper intended for energy dissipation structures should be 0.3–0.6.

Shaking table testing and numerical modeling of continuous welded ballast track on bridges under longitudinal seismic loading

In order to confirm the validity of the ideal elasto-plastic resistance model applied to the ballast track under seismic loading, this paper studies the seismic response of continuous welded ballast track on bridges through the shaking table test and presents a process of updating the model based on the test results. The results indicate that the track constraint can improve the low order natural frequency of bridges significantly, and reduce the displacement response of the bridge. When ballast beds are effectively in a dynamic reciprocating state while under seismic loading, a structural change between the granules will occur, wherein some will flow and redistribute. The dynamic hysteretic change of the ballast longitudinal resistance is complex and quite different from that of the ideal elasto-plastic hysteretic route, and the ballast longitudinal resistance performance degenerates. If ballast longitudinal resistance is assumed to be ideal elastic-plastic resistance, the actual beam displacement response will be underestimated and the calculated rail seismic force will be greater than the test result. Moreover, the equivalent stiffness coefficient Ke and damping coefficient Ce of the ballast dynamic resistance characteristics could be obtained by model updating, and the simulation results coincide well with the test results.

对偶变量块体混合元及其位移元的收敛性和精度分析

The symplectic characteristics of the equivalent stiffness coefficient matrix for the Hamiltonian canonical equations of elasticity and the Hamiltonian mixed element were intuitive, and the symplectic characteristics of the equivalent stiffness coefficient matrix for the dual-variable brick mixed element (DVBME), which was derived based on the Hellinger-Reissner (H-R) variational principle and the symplectic-conservative theory of elasticity, were similarly intuitive. The governing equations of elasticity were established immediately through the DVBME formulation, and the solution of the governing equations was obtained with the mixed method. Meanwhile, the dual-variable brick displacement element (DVBDE) formulation was deduced from the DVBME formulation, which was only related to displacement variables. The solution of the governing equations based on the DVBDE formulation was got with the displacement method. The numerical examples show that the convergence rates of displacement and stress variables of the 8-node DVBDE with reduced integration are balanced and stable with high precision. The convergence rate of stress of the DVBDE is almost equal to that of the translational 20-node displacement element with reduced integration. The DVBDE is universal.