Spring Coefficient Research Articles

Research on Static and Dynamic Characteristics of Shear Spring of the Vibrating Flip-Flow Screen

The vibrating flip-flow screen (VFFS) is a high-efficiency device currently used for deep screening of moist fine-grained materials. During VFFS operation, the normal operation of the screen is affected by fatigue damage to the shear springs arranged symmetrically on both sides of the screen, leading to equipment failures and disruption production. In this paper, the shear spring’s static and dynamic characteristics in different operation conditions were studied using the INSTRON 8801 fatigue test system and Dynacell dynamic sensors. Using an experimental test of shear spring stiffness and damping coefficients, the effects of some factors, i.e., temperature, hardness, amplitude and frequency, were studied. The results show that the temperature of the shear spring on the left side of the flip-flow screen was higher than that of the right side (driving side). With an increase in temperature, the stiffness of the shear spring decreased. With the increase in amplitude, the dynamic stiffness decreased and the damping coefficients did not change; with the increase in frequency, the dynamic stiffness increased and the damping coefficient decreased. At the same amplitude, with the increase in hardness of the shear spring, the dynamic stiffness increased. Finally, the stiffness and damping coefficients of the shear spring before and after tearing were obviously reduced. These research results reveal the relationship of the characteristics of a shear spring with operational conditions, and could provide a theoretical reference for the design of the VFFS and the selection of the shear spring.

Effect of material damping on the impedance functions of an embedded circular foundation under vertical and horizontal excitation

Machine foundations are generally affected by the vibratory shocks from different machines. The behavior of these foundations is influenced by the properties of underlying soil and the excitation frequency of the applied dynamic load. The influence of material damping on the dynamic impedance functions of a circular disk embedded in homogeneous elastic half space is analyzed using one-dimensional wave propagation in cones (cone model) and the results are presented in the form of dimensionless plots to observe the more realistic response of machine foundations. Three different types of material damping models viz., Hysteretic, Voigt and Kelvin model are introduced in the above elastic solutions using correspondence principle. The spring and damping coefficients of the embedded foundation are then computed in a wide range of frequency of excitation under vertical and horizontal mode of vibration varying the influencing parameters namely dimensionless frequency (a0), Poisson’s ratio (ν), embedment ratio (e/r0) and damping ratio (ξ). The outcomes from the present analysis suggest that the spring coefficient is nonlinearly affected by the dimensionless frequency and embedment ratio, for both the modes of vibration. The effect of material damping on spring coefficient is only significant for a0> 2, irrespective of the damping model used.

Thermo-viscous acoustic modeling of perforated micro-electro-mechanical systems (MEMS)

An analytical model based on the low reduced-frequency method is developed for the damping and spring force coefficients of micro-electro-mechanical systems (MEMS) structures. The model is based on a full-plate approach that includes thermal and viscous losses and hole end effects, as well as inertial and compressibility effects. Explicit analytical formulas are derived for damping and spring forces of perforated circular MEMS with open and closed edge boundary conditions. A thermo-viscous finite-element method (FEM) model is also developed for the numerical solution of the problem. Results for the damping and spring coefficients from the analytical models are in good agreement with the FEM results over a large range of frequencies and parameters. The analytic formulas obtained for the damping and spring coefficients provide a useful tool for the design and optimization of perforated MEMS. Specifically, it is shown that for a fixed perforation ratio of the back-plate the radius of the holes can be optimized to minimize the damping.

Model updating‐based automated damage detection of concrete‐encased composite column‐beam connections

This paper presents a comparative study about the numerical and experimental system identification and model updating-based automated damage detection of concrete-encased composite column-beam connections. Four different column-beam connection types named as CBC#A, CBC#B, CBC#C, and CBC#D were considered without any changes in geometrical configuration. Numerical and experimental dynamic characteristics were extracted by initial finite element analysis and nondestructive experimental measurements for undamaged condition. Enhanced frequency domain decomposition (EFDD) method was used for experimental modal extractions. A good agreement was observed between experimental natural frequencies but not enough correlation between damping ratios for all connection types. Maximum differences between initial finite element and undamaged experimental results were calculated as 34.68% for CBC#A, 40.78% for CBC#B, 33.15% for CBC#C, and 47.13% for CBC#D type connection details. The differences were reduced to 0.24%, 0.24%, 0.16%, and 0.15%, respectively, by automated model updating procedure using spring coefficient, modulus of elasticity and weight per unit volume. In the case of the damaged condition, lateral forces were applied to simulate the effect of an earthquake. Cracks strongly affected the natural frequencies. The mode shapes were not broken evidently after damaged conditions. The mode shapes definitely deviated a bit, but generally the same after damages. The natural frequencies have decreased non-monotonically due to the decrease in the rigidity of the column and beam at the cracked section. Maximum differences were calculated as 14.96% for CBC#A, 41.08% for CBC#B, 31.35% for CBC#C, and 45.93% for CBC#D type connection details. After automated model updating the above-mentioned differences were reduced to 0.35%, 0.78%, 0.73%, and 0.85% respectively. Contour diagrams of changes of updating parameters were plotted for damage identification. The regions with high difference rates indicated the location of the damage.

Detection of Contact-type Failure Based on Non-linear Wave Modulation Utilizing Self-Excited Ultrasonic Vibration: Evaluation of Failure Development Focusing on Frequency Modulation

This research concerns the detection method of contact-type failure based on nonlinear wave modulation utilizing ultrasonic vibration driven by self-excitation. When the structure is vibrating by environmental force or forced excitation, the contact area is fluctuated by vibration. In this condition, the vibration transfer characteristics of ultrasonic vibration have fluctuated in synchronization with vibration (non-linear wave modulation). The detection method based on non-linear wave modulation can detect contact-type failure. In this paper, the novel detection method based on nonlinear wave modulation is presented. Firstly, the self-excitation method using local feedback control is introduced. Local feedback control can oscillate at the natural frequency automatically. Secondly, the concept of a novel detection method is introduced. When the structure with contact-type failure is vibrating, the frequency of the ultrasonic vibration excited by local feedback control will fluctuate in synchronization with natural frequency fluctuation. To explain the detection method, non-linear wave modulation is expressed 1 degree of freedom model. In this model, the local stiffness fluctuation is modelled by the spring element of which spring coefficient is fluctuated in synchronization with structural vibration. We regard the transfer function of this model as a linear time-varying system. The amplitude of the fluctuation of natural frequency caused by stiffness fluctuation can be the novel index of failure level. Lastly, the result of the experiment using the uniform beam specimen is shown. From the relationship between forcing pressure of the contact-type failure and the amplitude of the frequency modulation, it is proved that the novel index is associated with failure level.

Elastic-slip interface effect on dynamic response of underwater convey tunnel in saturated poroelastic soil subjected to plane waves

In engineering construction, the elastic-slip interface often exists around the tunnel. An elastic-slip interface model is proposed to analyze the dynamic response of underwater convey tunnel, and the surrounding soil is assumed to be saturated poroelastic medium. The reflected, refracted and scattered waves in the free surface water, the surrounding soil medium and the tunnel are expressed by wave function expansion method. Based on Biot’s dynamic theory, an elastic-slip interface is developed to analyze the scattering of P and SV waves around the tunnel. The interface coefficients (normal and tangential spring coefficients and slip coefficient) are introduced to analyze the elastic-slip interface effect on the dynamic stresses under different wave frequencies. It can be concluded that the effect of normal spring coefficient is greater than that of tangential spring coefficients. The interface effect in the region of low frequency is greater than that of high frequency. The interface effect under different surface water depths and embedded depths of tunnel is also examined. Comparison with existing numerical results validates this dynamic model.

Esforços de um edifício em alvenaria estrutural calculados com fundação rígida e elástica

Este trabalho avalia a influência da rigidez da fundação em um prédio de alvenaria estrutural de quatro pavimentos nas tensões de compressão das paredes. Os resultados foram obtidos a partir de modelos estruturais, levando-se em conta ações verticais e horizontais, fundação rígida e base elástica. O edifício analisado é simétrico nas duas direções e foi desenvolvido para demonstrar, de modo simplificado, o que normalmente ocorre em prédios usuais. Para esse estudo de caso, foram modeladas paredes com e sem aberturas (janelas e portas), com o objetivo de possibilitar a interação e distribuição dos esforços resultantes das várias hipóteses de cálculo. Para a construção dos modelos estruturais foi utilizado o software SAP2000, usando elementos lineares de pórtico e de placas. As análises foram realizadas por meio de ações classificadas em permanentes (D), variáveis (L) e vento (W “90º” e W “0º”), gerando várias combinações e interações entre elas. As premissas de modelagem para o edifício são: estrutura - lajes/paredes em elementos de placas; fundação - radier com estacas sendo utilizados elementos de placas e barras respectivamente. Foram abordados no trabalho dois tipos de solução para as fundações. No primeiro modelo, o apoio da ponta da estaca é considerado rígido (indeslocável), sem interação solo-estrutura. No segundo, o apoio da ponta da estaca é considerado flexível, ocorrendo interação solo-estrutura. Para ambos os modelos, não foi considerado neste estudo a interação do solo com o radier. Na representação do apoio flexível, o coeficiente de mola foi obtido a partir de uma análise geotécnica de uma prova de carga realizada no solo de uma cidade situada no Distrito Federal, Brasil. Comparando o comportamento estrutural do edifício em fundações com apoios rígido ou elástico, observou-se que, para as mesmas combinações de ações aplicadas nos dois modelos, não foram verificadas diferenças significativas nem nas tensões de compressão das paredes, e nem mesmo nos momentos fletores das lajes. Os valores das tensões atuantes, obtidos pelos modelos estruturais, foram superiores às tensões resistentes dos blocos de alvenaria em alguns pontos próximos as extremidades, aberturas e encontros das paredes. Esse fato comprovou a necessidade de se avaliar criteriosamente os encontros de paredes e onde há aberturas (janelas e portas). Conclui-se que as ações do vento não interferem significativamente em um edifício de alvenaria estrutural de 4 pavimentos. As diferenças entre as tensões com fundação rígida e elástica nas paredes, para este caso, são muito pequenas não tendo influência no dimensionamento. A maioria dos pontos de tensão máxima estão localizados nos cantos inferiores das paredes. Surgem tensões de tração nas alvenarias próximas às aberturas. Faz-se necessário, portanto, realizar o grauteamento e armação nos blocos situados nos encontros de paredes e também nos blocos contíguos às aberturas (janelas e portas). Nas partes inferiores e superiores das aberturas se faz necessário a utilização de vergas/contravergas, para combater as tensões de tração na alvenaria. Os procedimentos indicados garantirão maior segurança do edifício em virtude do aumento na resistência dos blocos reforçados por graute/armação, corroborando os entendimentos técnicos sobre o tema.

Axial vibration analysis of a Rayleigh nanorod with deformable boundaries

In this study, the free axial vibration of Rayleigh nanorods with axial restraints is studied via Eringens’ nonlocal elasticity theory. This higher order elasticity theory takes into account the size effect into the formulation due to dealing with micro and nanostructures. The boundary conditions and equation of motion are obtained using Hamilton’s principle. Two symmetrical axial elastic springs are attached to a nanorod at both ends. The novelty of the present study is that it seeks to obtain a general eigen value algorithm for the angular frequencies subjected to the rigid or restrained boundary conditions in a nanorod for the first time. A Fourier sine series is used to work Stokes’ transformation for the Rayleigh nanorods with elastic springs at the ends. Afterward, the effect of the spring coefficient on the the eigen-frequency is investigated. Also, the effects of the nonlocal parameter and the elastic springs on the eigen-frequency is reported.

Design of a Haptic Feedback System for Flight Envelope Protection

Several modern aircraft use a passive control manipulator: a spring–damper system that generates command signals to the flight control computers in combination with a flight envelope protection system that limits pilot inputs when approaching the aircraft limits. This research project aims to increase pilot awareness of this protection system through the use of force feedback on the control device, that is, haptics. This paper describes in detail how the haptic feedback works and when it triggers; another paper will discuss the results of an experimental evaluation. With the current haptic design, pilots can get five cues: first, a discrete force cue when approaching the limits; second, an increased spring coefficient for control deflections that bring the aircraft closer to its limits; third, a stick shaker for low velocities; fourth, if a low-velocity condition requires an input, the stick is moved forward to the desired control input; and finally, the stick follows the automatic Airbus “pitch-up” command during an overspeed condition. This novel system is expected to help pilots correctly assess the situation and decide upon the right control action. It will be evaluated in two scenarios close to the flight envelope limits: a windshear and an icing event.

A variational approach for free vibrating micro-rods with classical and non-classical new boundary conditions accounting for nonlocal strengthening and temperature effects

Transverse vibration of a circular cross sectional micro-rod subjected to a new kind of boundary constraints with elastic torsional springs is presented based on nonlocal elasticity. A nonlocal strengthening beam model is utilized and the effect of temperature changing is taken into consideration. The variational method and Hamilton’s principle are applied to derive the governing equation of motion and corresponding boundary conditions. A higher-order partial differential equation that is a typical characteristic of nonlocal strengthening model is developed, and the boundary conditions contain not only classical conditions but also non-classical higher-order conditions. Unlike previous studies which were only concerned with some conventional boundary constraints, we consider more general boundary conditions named elastic torsional spring supports. Such boundary conditions are between the simply supported and clamped ones, and they are closer to the actual constraints of existing engineering structures. Natural frequencies of micro-rods with new boundary constraints are determined via an eigenvalue method and compared with other results in the literature. It is shown that the nonlocal scale factor, thermal parameter, rigidity parameter and torsional spring coefficient play significant roles in free vibration of micro-rods. The research can provide a reference for a large class of boundary conditions ranging from simply supported to clamped micro-rods.

Nonlinear primary responses of a bilateral supported X-shape vibration reduction structure

The nonlinear forced vibration responses of a bilateral supported X-shape vibration reduction structure are researched. The vertical and rotational displacements of the upper and lower platforms of the structure are taken into account and the nonlinear dynamic model of the structure with four degrees of freedom is established by applying the Lagrange’s equation. The validate experimental study of the structure is carried out and the acceleration response measured from the experiment is compared with the numerical result to verify the correctness of the dynamic model. The steady state amplitude-frequency responses of the system are obtained via the incremental harmonic balance (IHB) method and validated by using the Runge-Kutta numerical simulation. From the analysis, it can be seen that the primary responses of the vertical and rotational displacements of the structure exhibit softening type of nonlinearity. The coupled resonance of the vertical and the rotational displacements of the system can be observed when the system resonances around the fundamental and second natural frequencies. Besides, parametric investigations are performed to analyze the effects of the viscous damping coefficient, the external excitation amplitude, the angle between the rod and the platform, and the stiffness coefficient of the support spring on the resonance properties of the X-shape vibration reduction structure.

Optimization of elastic spring supports for cantilever beams

In this study,a new approach of optimization algorithm is developed. The optimum distribution of elastic springs on which a cantilever Timoshenko beam is seated and minimization of the shear force on the support of the beam is investigated.The Fourier transform is applied to the beam vibration equation in the time domain and transfer function, independent from the external influence, is used to define the structural response. For all translational modes of the beam, the optimum locations and amounts of the springs are investigated so that the transfer function amplitude of the support shear force is minimized. The stiffness coefficients of the springs placed on the nodes of the beam divided into finite elements are considered as design variables. There is an active constraint on the sum of the spring coefficients taken as design variables and passive constraints on each of them as the upper and lower bounds. Optimality criteria are derived using the Lagrange Multipliers method. The gradient information required for solving the optimization problem is analytically derived. Verification of the new approach optimization algorithm was carried out by comparing the results presented in this paper with those ones from analysis of the model of the beam without springs, with springs with uniform stiffness and with optimal distribution of springs which support a cantilever beam to minimize the tip deflection of the beam found in the literature. The numerical results show that the presented method is effective in finding the optimum spring stiffness coefficients and location of springs for all translational modes.The proposed method can give designers an idea of how to support the cantilever beams under different harmonic vibrations.

Identification of nonlinear spring coefficient in asymmetric nonlinear system using auto-regressive time series analysis

Identification of nonlinear spring coefficient in asymmetric nonlinear system using auto-regressive time series analysis

Detailed modelling of packed-bed gas clogging due to thermal-softening of iron ore by Eulerian–Lagrangian approach

Abstract Eulerian–Lagrangian numerical scheme is applied for analysing packed-bed-structure constructions involving non-spherical solids, such as metallurgical cokes and ferrous ores, and the high-temperature softening characteristics of such beds. 3D scanning is applied for determining the coke and ore shapes, and a multi-sphere discrete element method is used as the functional scheme for non-spherical solid-particle motion tracking. The transient deformation behaviour of the softening ore is simulated using the advanced discrete element method, and the gas permeability characteristics exhibited by the ore shapes in the ironmaking process are discussed. Based on this model, cases with varied softening behaviour represented by the joint spring coefficient are investigated and the effect of the ore-softening behaviour on the gas permeability is evaluated. It is established that the pathway of the passing rivulet depends upon the softening-ore deformation behaviour.

Research on the differential settlements of mat foundations

Mat foundation is a very commonly used foundation type. There are many advantages in adopting mat foundations including the effects of loading compensation, full utilization of underground space, lowering foundation settlements and increasing the factor of safety of bearing capacity for foundations etc. In addition, because of the high stiffness of the mat foundation and foundation girders the differential settlements could be effectively decreased, which would in turn increase the safety of structures. The differential settlements of the foundation will produce extra stresses in the structure. At the worst it will make the structure members failure. There are many factors which would affect the differential settlements of the foundation, which include the uneven distribution of structure column loading, the subgrade reaction of foundation soils (or so called soil spring coefficient), the combined stiffness of the foundation plate and foundation girders, the shape and size of the mat plate etc. The main objective of this research is to use the finite element method to simulate the interactions between the mat foundation and the underneath soils. It will focus on the systematic research on all possible factors affecting the differential settlements of mat foundations. The influence of each factor on the differential settlements will be studied and identified. The influence charts for the differential settlements for each individual factor will be proposed. Finally a reliable method using these influence charts to predict the differential settlements of mat foundations will be developed, which will be verified by practical examples.

Constitutive modelling of compression and stress relaxation in pine pellets

The increasing pellet production and a demand for making high quality biofuel pellets call for tools that can facilitate producers to meet these requirements and help understanding the effect feedstock and process parameters. In this study, mechanical and rheological properties of pine pellets made of different particle sizes and compression speeds were studied via pelleting tests and numerical simulations. Single pelleting tests were performed with six different particle size samples, ranging between 0.25 and 2.8 mm, and pelleted at compression speeds of 1, 5, and 10 mm min−1. The experimental results of specific compression and extrusion energy showed a positively linear correlation between particle size and energy consumption. The highest pellet durability was observed for pellets produced from small and mixed particle sizes. Eight different constitutive models were evaluated on their ability to simulate compression and stress relaxation, and their level of complexity. A non-linear Maxwell representation of the Standard Linear Solid (SLS) model was setup and fitted to the experimental compression data. The model coefficient of spring 1 composes the asymptotic stress level of the relaxed pellet, and the coefficient of spring 2 was found to be positively correlated with particle size. The viscosity of the dashpot is also found to be positively correlated with particle size, likewise it depends on the compression speed, where higher compression speed resulted in lower viscosities. The results of the study elucidate new insight into mechanical behavior of biomass particle compression, and the resultant simulations have utility for predicting the pressure requirements to produce pellets.

Force sensing in hybrid Bose-Einstein-condensate optomechanics based on parametric amplification

In this paper, the scheme of a force sensor is proposed which has been composed of a hybrid optomechanical cavity containing an interacting cigar-shaped Bose-Einstein condensate (BEC) where the \textit{s}-wave scattering frequency of the BEC atoms as well as the spring coefficient of the cavity moving end-mirror (the mechanical oscillator) are parametrically modulated. It is shown that in the red-detuned regime and under the so-called impedance-matching condition, the mechanical response of the system to the input signal is enhanced substantially, which leads to the amplification of the weak input signal while the added noises of measurement (backaction noises) can be suppressed and lowered much below the standard quantum limit (SQL). In this way, such a hybrid system operates as an ultra-sensitive force sensor which can amplify the input signal and simultaneously suppress the added noises by controlling the amplitudes of modulation and the system cooperativities. The advantage of the presented nonlinear hybrid system accompanied with the mechanical and atomic modulations in comparison to the bare optomechanical cavities is the enhancement of signal amplification as well as the extension of amplification bandwidth.

Elastic–slip interface effect on the diffraction of plane waves around a saturated lining structure in saturated soil

By combining Biot's dynamic wave theory with the elastic and slip interface theory, the scattering of plane waves around a saturated lining structure embedded in saturated soil is studied. The lining structure is assumed to be arbitrary shape. Separating variable method of Helmholtz equations leads to the semi-analytical solutions of the potentials. By using the conformal mapping method, the lining structures of arbitrary shape can be mapped to the cirque at the same centre with different radii. The elastic and slip material constants of interface are introduced to analyze the effect of interfacial properties. The dynamic stress and pore pressure are solved by applying the displacement and stress boundary conditions with interface effect. In numerical examples, the dynamic stress and pore pressure under different interface coefficients (normal and circumferential spring coefficients and slip coefficient) are analyzed. It is found that the effect of normal spring coefficient is larger than that of circumferential spring coefficients. The imperfect interface effect on the dynamic stress and pore pressure is also related with the wave frequencies.

Manufacture and Testing of Air Springs Used in Railway Vehicles

In this study, the mechanical properties of the air spring used in secondary suspension systems in railway vehicles have been experimentally determined. Firstly, rubber recipes with different components were determined for the production of rubber material, the main raw material of the air spring. Afterward, the mechanical properties of the elastomer material to be used in the manufacture of the air spring were determined by uniaxial tensile tests and RPA (rubber process analyzer) tests were applied to the samples obtained from different types of rubber compound. The machines used for the production of air spring and the test machines used for determining the mechanical properties of the air springs were specially produced and commissioned within the scope of the study. Blasting, airtightness, lifting–expansion, vertical spring coefficient, horizontal spring coefficient and lifetime tests were carried out by using these test machines.

Investigation of viscous fluid flow and dynamic stability of CNTs subjected to axial harmonic load coupled using Bolotin’s method

Purpose The dynamic stability of nano-tubes is an important issue in engineering applications. Dynamic stability of anti-symmetric coupled-carbon nanotubes (C-CNTs)-systems in thermal environment is presented in this paper. In this system, the top and bottom CNTs are subjected to axial harmonic load and action of the viscous fluid, respectively. Design/methodology/approach The coupling and surrounding mediums of the CNTs are simulated by visco-Pasternak foundation containing the spring, shear and damper coefficients. Based on the Timoshenko beam theory and Hamilton’s principle, the coupled motion equations are derived considering size effects using Eringen’s nonlocal theory. Using the exact solution in conjunction with Bolotin’s method, the dynamic instability region (DIR) of the coupled structure is obtained. The effects of various parameters such as small scale parameter, Knudsen number, fluid velocity, static load factor, temperature change, surrounding medium and nanotubes aspect ratio are shown on the DIR of the coupled system. Findings Results indicate that considering parameters such as small scale effects, static load factor, Knudsen number and fluid velocity shifts the DIR of C-CNTs to a lower frequency zone. Originality/value To the best of our knowledge, analyses of anti-symmetric coupled CNTs have not received enough attentions so far. In order to optimize the nanostructures designing, the main purpose of the present paper is to investigate nonlocal dynamic stability of CNTs subjected to axial harmonic load coupled with CNTs conveying fluid.