Journal articles: 'Linear springs'

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Cadet, Guillaume, Manuel Paredes, and Hervé Orcière. "Improved analytical model for cylindrical compression springs not ground considering end behavior of end coils." Mechanics & Industry 22 (2021): 50. http://dx.doi.org/10.1051/meca/2021048.

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In a context of increased competition, companies are looking to optimize all the components of their systems. They use compression springs with constant pitch for their linear force/length relationship. However, it appears that the classic formula determining the global load-length of the spring is not always accurate enough. It does not consider the effects of the spring's ends, which can induce non-linear behaviour at the beginning of compression and thus propagate an error over the full load-length estimated. The paper investigates the entire behaviour of a cylindrical compression spring, not ground, using analytical, simulation and experimental approaches in order to help engineers design compression springs with greater accuracy. It is built with an analytical finite element method, considering all the geometry and force components of the spring. As a result, the global load-length of compression springs can be calculated with more accuracy. Moreover, it is now possible to determine the effective tri-linear load-length relation of compression springs not ground and thus to enlarge the operating range commonly defined by standards. This study is the first that enables the behaviour to be calculated quickly, by saving time on dimensioning optimisation and on the manufacturing process of compression springs not ground.

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Parise, John J., Larry L. Howell, and Spencer P. Magleby. "Ortho-planar linear-motion springs." Mechanism and Machine Theory 36, no. 11-12 (November 2001): 1281–99. http://dx.doi.org/10.1016/s0094-114x(01)00051-9.

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Kornhauser, A. A. "Dynamic Modeling of Gas Springs." Journal of Dynamic Systems, Measurement, and Control 116, no. 3 (September 1, 1994): 414–18. http://dx.doi.org/10.1115/1.2899236.

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Linear dynamic modeling of gas springs is important for basic design of free piston Stirling engines. The conventional gas spring model, a dashpot in parallel with an ideal spring, gives poor prediction of gas spring performance. The anelastic model presented here consists of two parallel springs, one of which is in series with a dashpot. With proper selection of spring and damping constants, it gives improved prediction of gas spring dynamics.

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Chuanchao, Yan, and Zhao Wen. "The use of pneumatic cylinders with return springs when creating mechanical drives with recuperative energy." MATEC Web of Conferences 287 (2019): 01028. http://dx.doi.org/10.1051/matecconf/201928701028.

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The use of pneumatic cylinders with return springs in mechanical drives with reusable energy for reusable and continuum movements, fixing the output link in the extreme positions are considered. A defined range of work operations can be used by these cylinders. The use of pneumatic actuators with return springs in mechanical drives based on linear spring batteries with two springs is proposed. Algorithms for compensating dissipative losses in mechanical spring drives are considered. The maximum mass values that can be moved by such mechanical drives for each size of the pneumatic cylinder are determined. It is proposed to use pneumatic cylinders with return springs in mechanical drives with energy recovery based on nonlinear spring batteries. A mechanical spring drive for unwinding rolls of packaging materials with discrete modes. In tasks of reciprocating movement of objects with a controlled stand in extreme positions, the reduction of energy costs is achieved when using mechanical spring drives with energy recovery. Energy costs can be reduced several times. Traditionally, a spring-loaded drive contains a linear or non-linear spring-loaded battery, a control system, controlled clips and a motor to compensate for dissipative losses. The use of electric motors to compensate for dissipative losses is also limited by low speed, as compensation for dissipative losses occurs throughout the displacement and with high speed increases engine power and requires transmission with a large gear ratio.

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Badalamenti, J. M., and G. R. Doyle. "Radial-Interradial Spring Tire Models." Journal of Vibration and Acoustics 110, no. 1 (January 1, 1988): 70–75. http://dx.doi.org/10.1115/1.3269483.

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Two radial-interradial spring tire models are developed to predict vertical and drag forces produced by a tire as it rolls over an obstacle. Interradial springs are used to interconnect radial linear or quadratic springs to make each tire element’s deflection dependent upon its adjacent element’s deflections. Forces predicted by these two models are compared with a previously developed quadratic radial spring tire model and test data. The newly developed quadratic radial-linear interradial spring tire model predicts vertical and drag forces that are in close agreement with the test data.

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Ryu, Takahiro, S. Rosbi, K. Matsuzaki, T. Nakae, A. Sueoka, Y. Takikawa, and Y. Ooi. "Effect of Stiffness Ratio of Piecewise-Linear Spring on the Occurrence of Subharmonic Nonlinear Vibration in Automatic Transmission Powertrain." Applied Mechanics and Materials 786 (August 2015): 156–60. http://dx.doi.org/10.4028/www.scientific.net/amm.786.156.

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In the torque converter, a damper with a piecewise-linear spring is used to reduce the forced vibration, and the subharmonic vibration occurs when the spring restoring torque characteristics approach the switching point. This research analyzed the effect of stiffness ratio between the neighboring piecewise-linear springs on the occurrence of the subharmonic nonlinear vibration in automatic transmission powertrain. The powertrain is modeled with multi degree-of-freedom nonlinear system as an actual vehicle. The result shows higher value of the stiffness ratio between the neighboring springs creates larger value of the subharmonic vibration.

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Pedersen, N. L., and P. Pedersen. "Stiffness and design for strength of trapezoidal Belleville springs." Journal of Strain Analysis for Engineering Design 46, no. 8 (September 13, 2011): 825–36. http://dx.doi.org/10.1177/0309324711414337.

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Belleville springs or coned disc springs are commonly used in machine design. The geometric dimensions of the spring and the determination of non-linear force–displacement curve are regulated by different standards. However, the theory behind Belleville spring design standards is founded on a study published in 1936. Furthermore, the common spring design with cross-sections of uniform thickness poses problems in terms of non-uniformity of stress distribution. In view of this, non-linear three-dimensional finite element analyses of spring designs including uniform or variable thickness are carried out in this paper. Finite element results are compared with analytical predictions and critically analysed in terms of the effect of Poisson ratio, overall stiffness, and stress distribution in the spring. This is done in order to verify the range of validity of design standards. Finite element analysis emerges as a powerful and computationally cheap approach to assess the structural behaviour of Belleville springs regardless of their geometry and level of non-linearity.

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Baier-Saip, Jürgen A., Pablo A. Baier, Klaus Schilling, and Jauvane C. Oliveira. "Approximate Artery Elasticity Using Linear Springs." Journal of Medical and Biological Engineering 37, no. 6 (June 17, 2017): 899–911. http://dx.doi.org/10.1007/s40846-017-0254-0.

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Rathi, Vinay Kumar, Shobha Ram, Rohitashw Kumar, Avinash Agarwal, and R. K. Nema. "Hydrological classification and performance of Himalayan springs in climate change scenario – a case study." Water Supply 20, no. 2 (December 27, 2019): 594–608. http://dx.doi.org/10.2166/ws.2019.191.

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Abstract The present study was conducted to evaluate 33 springs' hydrology (discharge and yield estimation) of Chandrabhaga and Danda watersheds of Uttarakhand, India. The springs were classified using Meinzer method and evaluated the relative performance for rejuvenation strategy. It was found that most of springs fall in sixth and seventh class order with flow rate 6.5 to 65.5 and 0.8 to 6.5 m3·day−1, respectively. The relative performance of springs were analyzed based on four methods: (i) spring flow variability, (ii) normalized spring flow (short and long duration), (iii) rainfall spring flow lag and (iv) spring flow gradient. The relative results of springs were analyzed on a scale of 0–5. The Chandrabhaga springs 01, 03, 4B, 05, 06 and 13 were found to be relatively good on a scale value of 4 out of 5 as compared to springs 4A, 07, and 10A with a scale value of 1. For the Danda watershed, the relative performance of springs 4A and 28 found on scale value of 5 and springs 4B, 11 and 20 with a scale value of 4 are relatively good compared to springs 02, 06, 07, 15 and 17. The cumulative flow of spring showed a linear response with cumulative rainfall for the period of June to September (monsoon period). The spring-shed was delineated and evaluated for optimization for the maximum efficiency, spring flow, ratio of area and relief versus maximum spring flow yield. The results revealed that the quantification of water fluxes for water balances, storage of groundwater and development of mathematical models can be used for sustainable water resources development and to revive the mountain springs which helped the adverse impacts of climate change.

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Chaudhury, Arkadeep Narayan, and Debasis Datta. "Analysis of prismatic springs of non-circular coil shape and non-prismatic springs of circular coil shape by analytical and finite element methods." Journal of Computational Design and Engineering 4, no. 3 (February 8, 2017): 178–91. http://dx.doi.org/10.1016/j.jcde.2017.02.001.

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Abstract This paper presents a methodology for designing prismatic springs of non-circular coil shape and non-prismatic springs of circular coil shape using analytical and numerical methods. To start with, simple analytical formulations for obtaining the axial deformation of the springs under axial load have been demonstrated. Next, the processes of obtaining CAD models of the springs and their subsequent finite element analysis (FEA) in commercial softwares have been outlined. In the third part, the different springs have been compared with a common cylindrical spring and their merits compared to a common spring have been demonstrated. Next, a fairly accurate analytical formulation (with maximum error of ∼7–8%) for obtaining the value and location of maximum shear stress for all the springs has been demonstrated. Next, two aspects of non-prismatic springs under dynamic loads, viz. damping introduced in a vibrating system and contribution of the spring to the equivalent mass in a one dimensional vibrating spring mass system due to shape of the spring have been discussed. The last part involves an analytical formulation for the linear elastic buckling of two springs with circular coil shapes. For the majority of the work, emphasis has been on obtaining and using closed form analytical expressions for different quantities while numerical techniques such as FEA have been used for validation of the same. Highlights Analytical formulations of axial deflection different springs under axial load. CAD modeling and FEA of prismatic and non prismatic springs of different coil shapes. Comparison of stress and deflection in mass-equivalent springs of different geometry. Approx. analytical formulation for the location and value of max. stress in springs. Effects of spring shape on damping, vibrational properties in 1D systems and buckling.

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Rahman, M. A., U. Ahmed, and M. S. Uddin. "Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis." International Journal of Applied Mechanics and Engineering 18, no. 3 (August 1, 2013): 793–814. http://dx.doi.org/10.2478/ijame-2013-0048.

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Abstract A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

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Chu, Li, Yi Zhang, and Hua Deng. "Dynamic Modeling and Grasp Characteristics Analysis of an Underactuated Prosthetic Finger." Applied Mechanics and Materials 513-517 (February 2014): 3446–52. http://dx.doi.org/10.4028/www.scientific.net/amm.513-517.3446.

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A dynamic model was established using the virtual spring approach for the underactuated prosthetic finger containing the closed kinematic chains and holonomic constraints. The dynamic model was verified by grasp simulation. The virtual spring is used to approximate the constraint force and differential algebraic equations are converted into ordinary differential equations which are ideal for simulation and real-time control. The grasp characteristics of the underactuated finger were studied based on the model with the stiffness of the linear springs as variables. By properly increasing the stiffness of springs, the grasp stability of underactuated finger could be improved and ejection phenomenon would be reduced. However, self-adaptive capability would be reduced with large stiffness. A characteristic index was used for estimating grasp stability and self-adaptive capability. The simulation results show that setting the stiffness of the linear springs between 1N/mm and 2N/mm is the best choice for the underactuated finger.

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Si, Guo Lei, Feng Yu Yang, Wen Jie Wang, and Yu Hui Liu. "Study on Relief Valve with Permanent Magnetic Spring." Advanced Materials Research 328-330 (September 2011): 224–27. http://dx.doi.org/10.4028/www.scientific.net/amr.328-330.224.

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Based on mechanical phenomena between two fixed magnetic, when the distance is short, the electromagnetic force are linear,therefore,we can make full use of the characters and make it to be permanent magnetic spring replacing the mechanical spring in hydraulic relief valves. Through the use of the Rare-earth magnetic springs in relief valves, we find it is more sensitive to load. Besides these, the rare-earth magnetic springs have a long life and high temperature resistance without failure by fatigue. So the study and design of permanent magnetic spring type relief valve have large application and research value.

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Liang, C., and C. A. Rogers. "Design of Shape Memory Alloy Springs With Applications in Vibration Control." Journal of Vibration and Acoustics 115, no. 1 (January 1, 1993): 129–35. http://dx.doi.org/10.1115/1.2930305.

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Shape memory alloys (SMAs) have several unique characteristics, including their Young’s modulus-temperature relations, shape memory effects, and damping characteristics. The Young’s modulus of the high-temperature austenite of SMAs is about three to four times as large as that of low-temperature martensite. Therefore, a spring made of shape memory alloy can change its spring constant by a factor of three to four. Since a shape memory alloy spring can vary its spring constant, provide recovery stress (shape memory effect), or be designed with a high damping capacity, it may be useful in adaptive vibration control. Some vibration control concepts utilizing the unique characteristics of SMAs will be presented in this paper. Shape memory alloy springs have been used as actuators in many applications although their use in the vibration control area is very recent. Since shape memory alloys differ from conventional alloy materials in many ways, the traditional design approach for springs is not completely suitable for designing SMA springs. Some design approaches based upon linear theory have been proposed for shape memory alloy springs. A more accurate design method for SMA springs based on a new nonlinear thermomechanical constitutive relation of SMA is also presented in this paper.

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Stephens, Andrew D., Rachel A. Haggerty, Paula A. Vasquez, Leandra Vicci, Chloe E. Snider, Fu Shi, Cory Quammen, et al. "Pericentric chromatin loops function as a nonlinear spring in mitotic force balance." Journal of Cell Biology 200, no. 6 (March 18, 2013): 757–72. http://dx.doi.org/10.1083/jcb.201208163.

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The mechanisms by which sister chromatids maintain biorientation on the metaphase spindle are critical to the fidelity of chromosome segregation. Active force interplay exists between predominantly extensional microtubule-based spindle forces and restoring forces from chromatin. These forces regulate tension at the kinetochore that silences the spindle assembly checkpoint to ensure faithful chromosome segregation. Depletion of pericentric cohesin or condensin has been shown to increase the mean and variance of spindle length, which have been attributed to a softening of the linear chromatin spring. Models of the spindle apparatus with linear chromatin springs that match spindle dynamics fail to predict the behavior of pericentromeric chromatin in wild-type and mutant spindles. We demonstrate that a nonlinear spring with a threshold extension to switch between spring states predicts asymmetric chromatin stretching observed in vivo. The addition of cross-links between adjacent springs recapitulates coordination between pericentromeres of neighboring chromosomes.

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Karssen, JG Daniël, and Martijn Wisse. "Running with improved disturbance rejection by using non-linear leg springs." International Journal of Robotics Research 30, no. 13 (September 2, 2011): 1585–95. http://dx.doi.org/10.1177/0278364911408631.

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Most running robots and running models use linear leg springs. Non-linear leg springs have the potential to improve the performance of running robots and models, but it is not clear to what extent. In this paper, the effect of non-linear leg springs on disturbance rejection behavior is investigated. The optimal leg stiffness profile is determined by optimizing the gait sensitivity norm, a measure for disturbance rejection. The results of this optimization show that the optimal leg stiffness profile is strongly non-linear, and that the disturbance rejection is a factor of seven better than it would be with the optimal linear leg stiffness. The cause for this great improvement is that non-linear leg springs allow stable limit cycles that are much further away from the fall modes.

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Sorokin, S. V. "Linear dynamics of elastic helical springs: asymptotic analysis of wave propagation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2105 (February 25, 2009): 1513–37. http://dx.doi.org/10.1098/rspa.2008.0468.

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Helical springs serve as vibration isolators in virtually any suspension system. A variety of theories to describe the dynamic behaviour of these structural elements, which involves interaction of flexural, torsion and longitudinal waves, can be found in the literature. Alongside this, various approximate methods are employed to determine the eigenfrequencies of vibrations of springs. In this paper, the validity ranges of alternative theories are assessed by comparison of the location of the dispersion curves. This paper also contains a rigorous asymptotic analysis of the exact dispersion equation with two small parameters being employed. It allows for the identification of significant regimes of linear wave motion in a helical spring. In each of these regimes, simple formulae for wavenumbers are obtained by the dominant balance method and their validity ranges are checked against direct numerical solution. Mode shapes associated with each wavenumber are also analysed.

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Chen, Xi, Ying Liu, and Hua Zhang. "Finite Element Analysis of Different Flexure Springs." Applied Mechanics and Materials 44-47 (December 2010): 2065–69. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.2065.

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Flexure spring suspensions have demonstrated the ability to provide long operating lifetimes for cryocoolers. The good flexure spring need high radial stiffness and high fatigue life. The profile curves are very important for flexure spring. In this paper, based on the finite element analysis software (ANSYS), geometrically nonlinear static structural analysis and nonlinear dynamics structural analysis were made to several different flexure springs. The fatigue strength, axial and radial stiffness, modal frequency were calculated and listed. The different performance between linear flexure spring and spiral flexure spring were discussed, which would provide an advisory opinion for the design and application of flexure spring in space cryocooler.

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Soulios, G. "SPRINGS (CLASSIFICATION, FUNCTION, CAPTURING)." Bulletin of the Geological Society of Greece 43, no. 1 (January 19, 2017): 196. http://dx.doi.org/10.12681/bgsg.11174.

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Todd, K (1980) proposed the following definition for springs: “a concentrated discharge of groundwater that emerges on the ground as a stream of water that flows freely”. Spring is distinguished from water leak that is a normally diffused but extended (linear or 2D) slower movement of groundwater towards the ground surface. Uprush is every groundwater emergence on the ground surface or through the bed of water bodies (river, lake, sea). In the context of hydrogeology springs and uprushes in general are in fact “overflows” of aquifers; hence they serve as aquifer discharge mechanisms. Springs emerge at the cross section of groundwater level with the topographic relief. Springs are a strong evidence of rich groundwater potential. A big number of small springs emerging at the margins of basins or the hill slopes are an evidence of a shallow aquifer of low hydraulic conductivity. On the contrary, big springs emerging at the bottom of valleys, i.e. the basic geomorphological level, are an indication of a high potential aquifer characterized by considerable values of hydraulic conductivity.

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KETEMA, YOHANNES. "AN OSCILLATOR WITH CUBIC AND PIECEWISE-LINEAR SPRINGS." International Journal of Bifurcation and Chaos 01, no. 02 (June 1991): 349–56. http://dx.doi.org/10.1142/s0218127491000270.

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A system consisting of a mass attached to a nonlinear spring with negative linear stiffness and cubic nonlinearity, (i.e., a spring obeying Duffing's equation with negative linear stiffness) and a linear spring at a certain offset distance is studied. Melnikov's method is applied to determine the existence of homoclinic points for the Poincare map, and preserved resonant orbits and boundaries for these are given in the parameter space. This system is then compared to the system consisting of only the nonlinear spring with regard to the existence of parameter regimes where chaotic motion is possible. It is shown that if the linear spring is of appropriate stiffness the chaotic motion for a given set of parameter values occurring for the system consisting of only the nonlinear spring is replaced by periodic motion and the mechanism of this phenomenon is explained.

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Qiu, Donghai, Manuel Paredes, and Sébastien Seguy. "Variable pitch spring for nonlinear energy sink: Application to passive vibration control." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 2 (March 1, 2018): 611–22. http://dx.doi.org/10.1177/0954406218761485.

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This paper aims to propose a generalized methodology for designing a novel nonlinear energy sink with variable pitch springs. To this end, a generic model of the nonlinear energy sink system providing the nonlinearity of pure cubic stiffness is introduced. Key features of the model include: (i) specifically sizing two variable pitch springs to provide the force polynomial components with only linear and cubic terms; (ii) pre-compressing two springs at the transition point to produce smooth nonlinear force characteristics; (iii) adding a negative stiffness mechanism to counterbalance the linear term. To generate the variable pitch spring, design parametrization is implemented. The type of shape and the pitch distribution adopted for the spring are shown to fit the objective force–displacement function well. To validate the concept, a special sized nonlinear energy sink system is developed. Identification of the force–displacement relation and experiments for the whole system embedded on an electrodynamic shaker are studied. The results show that this nonlinear energy sink can not only output the anticipated nonlinearity, but can also produce energy pumping to protect the primary system in a large band of frequencies, thus making it practical for the application of passive vibration control.

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Yun, Seong Ho, Seong Dae Choi, and Gi Man Kim. "Natural Frequency Sensitivities of Lap Joint on Clamped-Clamped Beam." Advanced Materials Research 694-697 (May 2013): 473–75. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.473.

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This paper deals with the formulation and analysis of dynamic mechanism for joint flexibilities whose relevant magnitudes of stiffnesses are investigated by using linear and torsional springs. The equation of motion is derived by using a generic joint in the middle of clamped-clamped beam. A behavior of natural frequency sensitivities is studied as a function of nondimensional linear and torsional spring stiffnesses.

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Singh, Deep, Rutupurna Choudhury, Manidipto Mukherjee, and Yogesh Singh. "Development of non-linear models to evaluate the NiTi SMA spring actuator." Journal of Mechanical Engineering and Sciences 16, no. 1 (March 23, 2022): 8754–69. http://dx.doi.org/10.15282/jmes.16.1.2022.09.0692.

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The shape memory alloy (SMA) based actuators are replacing huge and bulky actuators because of its ability to provide high work per unit mass and serves as active prismatic joint to develop precise robotic manipulators. It also helps in developing a light weight manipulators with a simple actuation process. Here, the study presents the relationship between the contraction of Nitinol SMA prings and the input variables such as current and time to effectively interpret the behavioural complexity. In addition, the response of two Shape memory alloy springs in series combination has been discussed. The finite element analysis (FEA) of the SMA wire and spring has also been carried out to predict the fatigue life of SMA wire and spring. The result showed that the contraction rate of SMA spring increases with increase in current and vice-versa. Moreover, the range of current is classified based on its significance. The relationship of current, displacement and time parameters, during the actuation of SMA spring, is a second order polynomial regression model. The applied current and time have positive impact on the contractiong rate of SMA. Several polynomial regression models were developed in order to predict the precise amount of spring actuation. This study also predicts the range of current suitable for its actuation based on its application as actuator. The FEA result shows that the SMA springs can have high endurance stress limit which makes it unique as compared to other commercially available actuators. This study enables to predict the rate of contraction and the deflection trend of SMA based actuators for precise positioning applications.

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Gong, Sanpeng, Xinwen Wang, and Sebastian Oberst. "Non-linear Analysis of Vibrating Flip-flow Screens." MATEC Web of Conferences 221 (2018): 04007. http://dx.doi.org/10.1051/matecconf/201822104007.

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Vibrating flip-flow screens provide an effective solution for the screening of highly viscous or fine materials. Apart from other factors, the vibration characteristics of the main and floating screen frames are largely responsible for the flip-flow screen’s sifting performance and its processing capacity. In this paper, the vibration characteristics of a vibrating flip-flow screen with linear and nonlinear springs are compared. Analytical results highlight that increasing the relative amplitude and avoiding undesirable resonances of the main and the floating screen frames can be realised to improve the screen’s performance. The materials on the screen panel have less an effect on the vibration characteristics of the vibrating flip-flow screen with nonlinear springs than using linear springs. Other design parameters which influence the performance of vibrating flip-flow screens are discussed.

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Ju, Young-Hun, Iman Mansouri, and Jong-Wan Hu. "Experimental Study on Recentering Behavior of Precompressed Polyurethane Springs." Materials 15, no. 10 (May 13, 2022): 3514. http://dx.doi.org/10.3390/ma15103514.

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Traditional seismic design has a limitation in that its performance is reduced by significant permanent deformation after plastic behavior under an external load. The recentering characteristics of smart materials are considered to be a means to supplement the limitations of conventional seismic design. In general, the recentering characteristics of smart materials are determined by their physical properties, whereas polyurethane springs can regulate the recentering characteristics by controlling the precompression strain. Therefore, in this study, 160 polyurethane spring specimens were fabricated with compressive stiffness, specimen size, and precompression strain as design variables. The compression behavior and precompression behavior were studied by performing cyclic loading tests on a polyurethane spring. The maximum stress and maximum strain of the polyurethane spring showed a linear relationship. Precompression and recentering forces have an almost perfect linear relationship, and the optimal level of precompression at which residual strain does not occur was derived through regression analysis. Additionally, a prediction model for predicting recentering force based on the linear relationship between precompression and recentering force was presented.

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Dornelles, Rodrigo de Faria Valle, Vera Lúcia Nocchi Cardim, Marília Trierveiler Martins, Ana Carolina Brandão de Campos Fonseca Pinto, and Nivaldo Alonso. "Spring-mediated skull expansion: overall effects in sutural and parasutural areas. An experimental study in rabbits." Acta Cirurgica Brasileira 25, no. 2 (April 2010): 169–75. http://dx.doi.org/10.1590/s0102-86502010000200009.

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PURPOSE: The use of springs in cranial expansion has proven to be effective in the treatment of craniosynostosis. Spring-mediated expansion has been studied both in the sagittal and in parasagittal regions, especially in scaphocephaly. A rabbit model was used in the present study to analyze the effects of springs on the cranial vault and sutures. METHODS: Thirteen 4-week-old New Zealand rabbits were divided into 4 groups: in group I, only amalgam markers were used as control; in group II, amalgam markers were used and sagittal suturectomy was performed; in group III, amalgam markers were used, a sagittal suturectomy was performed and an expansible spring was fitted in the interparietal region and in group IV, markers were used and linear parasagittal craniectomy was carried out with springs. Animals were sacrificed after 2, 4, 8 and 12 weeks. Radiological control and histological analysis were performed in the area of spring implantation. RESULTS: In the groups using springs distraction of the craniectomy borders was greater than in those that did not use springs. New bone formation was observed in all groups, and was faster in group II. Bone growth started from the borders and depth. Bone regeneration presented a similar histological pattern in the groups with spring in the sagittal and parasagittal region. CONCLUSION: The rabbit model proved to be adequate for the analysis proposed by the study. The use of springs in the groups with sagittal and parasagittal osteotomy led to a similar distraction of amalgam markers and both groups had similar ossification histological pattern.

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Sotiropoulos, Dimitrios A. "Dynamic Stiffness of Cracked Interfaces." Journal of Applied Mechanics 57, no. 2 (June 1, 1990): 476–78. http://dx.doi.org/10.1115/1.2892017.

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Quantitative relationships are derived between the dynamic macromechanical stiffness and microparameters of planar interfaces containing distributed cracks. The derivation is based on the solution of the problem of elastic wave reflection by a plane with a continuous distribution of springs to model the cracked interface at the macrolevel. The dynamic spring stiffness is then, through averaging, related to crack-opening volumes and other microparameters. For linear springs and periodic crack distributions, numerical examples are presented for plain strain. The stiffness is shown to strongly depend on frequency.

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Mofidian, S. M. Mahdi, and Hamzeh Bardaweel. "Theoretical study and experimental identification of elastic-magnetic vibration isolation system." Journal of Intelligent Material Systems and Structures 29, no. 18 (July 10, 2018): 3550–61. http://dx.doi.org/10.1177/1045389x18783869.

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A vibration isolation system featuring a combination of elastic and magnetic springs and viscous and magnetic damping is presented. A mechanical flat spring houses a permanent magnet that is levitated between two stationary magnets. A prototype of the isolator is manufactured. COMSOL models are developed for the mechanical and magnetic springs. Measured data and model simulations show that the magnets arrangement results in nonlinear magnetic spring with negative linear stiffness. The mechanical spring exhibits linear behavior with positive stiffness. Experiments are performed and a nonlinear dynamic model is developed. The fabricated isolator is characterized at low and high acceleration levels. Results from model show good agreement with measured data at lower acceleration levels. Slight mismatch between model and experiment is evident at higher accelerations. This mismatch is due to the existence of lateral vibrations that are not accounted for in the unidirectional model. Results show that the combination of mechanical flat spring and magnetic spring reduces the resonant frequency of the isolator. In addition, results confirm the ability of the isolator to attenuate vibrations higher than 11.91 Hz when excited at 2.4525 [m s−2].

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Curti, G., and F. A. Raffa. "Material Nonlinearity Effects in the Stress Analysis of Conical Disk Springs." Journal of Mechanical Design 114, no. 2 (June 1, 1992): 238–44. http://dx.doi.org/10.1115/1.2916937.

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The influence of material nonlinearity on the behavior of conical disk springs (Belleville springs) is investigated by means of finite element models. Both the load-deflection curve and the stress field of this kind of spring are shown to be significantly affected by the elastic-plastic behavior of the material. In particular, as far as the actual stress field is concerned, consideration of the material nonlinearity explains some apparent contradictions of well-known analytical formulations, such as the Almen-La´szlo´ theory, based on the usual assumption of linear elastic behavior of the material.

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30

Zhao, Wen, and Victor Leonidovich Zhavner. "The use of pneumatic cylinders with a return spring to compensate for balance losses in mechanical regenerative drives for reciprocating movements." MATEC Web of Conferences 287 (2019): 01027. http://dx.doi.org/10.1051/matecconf/201928701027.

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Mechanical spring drives with energy recovery are designed to produce return-rotational movements in various technological equipment and reduce energy costs by several times compared with traditional electromechanical, hydraulic and pneumatic drives. The use of pneumatic motors in spring drives to compensate for dissipative losses, fixing the drive in extreme positions and the primary charging of spring batteries is considered. The class of tasks in which spring drives with energy recovery are created using only pneumatic cylinders with return springs is highlighted. This study examines mechanical spring drives with energy recovery, based on nonlinear spring batteries with spring preload in the middle position of the output link. The use of pneumatic actuators with return springs in mechanical drives based on linear spring batteries with two springs is proposed. Mechanical spring drives with energy recovery are designed to produce return-rotational movements in various technological equipment and reduce energy costs by several times compared with traditional electromechanical, hydraulic and pneumatic drives. The amount of energy expended in spring recuperative drives is actually determined by the energy expended on compensating for dissipative losses in kinematic pairs. The results of the study allow the designers of such drives to consciously approach the choice of their schemes and design parameters.

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31

Xie, Xinwu, Gaofeng Wei, Rui Liu, Qiuming Sun, Aijuan Ni, Xiaoli Qin, and Feng Tian. "A NOVEL METHOD TO SIMULATE FORCE-CHEST DISPLACEMENT RELATIONSHIP DURING CARDIOPULMONARY RESUSCITATION." Biomedical Engineering: Applications, Basis and Communications 23, no. 06 (December 2011): 519–26. http://dx.doi.org/10.4015/s1016237211002852.

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Survival from cardiac arrest is dependent on timely cardiopulmonary resuscitation (CPR). Experimental and modeling work had shown that the relationship between compression force and sternal displacement had a tendency of hysteresis curve, which in manikins was rather lineal. A novel method was introduced to improve the mechanical characteristics of the manikins using a variable-stiffness springs group-damper structure, in which the spring's group and the damper simulate the elastic and damping of human chest respectively. To do the simulation, the model of the human chest's mechanical during CPR based on Gruben's pre-result was modified and the elastic part was fitted by piecewise linear function to get the springs' stiffness. The variable-stiffness springs group system was designed accordingly to simulate the human chest' stiffness during CPR, and a damper was designed to simulate the damping of chest. The damper and the variable-stiffness springs group were paralleling combined, forming a mechanical system. A sample system was realized and the test results showed that there were nonlinear elasticity and adequate viscosity in this system, whose coefficients were adjacent to Gruben's 'typical' human. According to the method, the mechanical system could be changed to accurately simulate different models, and its stiffness could be easily adjusted by varying the interval between the nest springs' top. The simulation method could be used directly in manikin, whose mechanical character would be improved and then more adequate training would be provided.

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32

Zhang, B., and Z. Y. Chen. "General Winkler Model for Kinematic Responses of Shafts in Linear Soil." International Journal of Computational Methods 17, no. 05 (February 25, 2019): 1940004. http://dx.doi.org/10.1142/s0219876219400048.

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A simplified model for calculating the seismic responses of the shaft is proposed in this paper. Based on the theory of Winkler elastic foundation beam, the urban shaft is simplified as a vertical beam. The horizontal soil reaction and vertical shear tractions between the shaft circumference and the surrounding soils are considered through horizontal springs and rotating springs on the sidewall of the shaft. The translation and rocking motion of the shaft are considered through horizontal springs and rotating springs at the bottom of the shaft. Then, the dynamic analysis model of the shafts under seismic motion is established, and the control equation of the dynamic response of the shaft in frequency domain is deduced. The analytical solution of the steady state response of the shaft is obtained. Considering the randomness of the earthquake motion, this method can get the shaft kinematic responses under different ground motions efficiently in conceptual design process.

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Şcedilakar, Gürkan. "The Effect of Axial Force on the Free Vibration of an Euler-Bernoulli Beam Carrying a Number of Various Concentrated Elements." Shock and Vibration 20, no. 3 (2013): 357–67. http://dx.doi.org/10.1155/2013/735061.

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In this study, free vibration analysis of beams carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and spring-mass systems subjected to the axial load was performed. All analyses were performed using an Euler beam assumption and the Finite Element Method. The beam used in the analyses is accepted as pinned-pinned. The axial load applied to the beam from the free ends is either compressive or tensile. The effects of parameters such as the number of spring-mass systems on the beam, their locations and the axial load on the natural frequencies were investigated. The mode shapes of beams under axial load were also obtained.

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Zhang, Zhongwei, Xiyan Zhang, Bohui Ma, Mengyao Ding, Bowen Zhu, and Dezheng Tong. "Measurement of Linear Springs’ Stiffness Factor Using Ultrasonic Sensing." Sensors 22, no. 15 (August 5, 2022): 5878. http://dx.doi.org/10.3390/s22155878.

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We designed an ultrasonic testing instrument that consisted of a single-chip microcomputer module, a digital display module, and an ultrasonic sensor module, which conveniently eliminated the troubles faced by the traditional Jolly’s scale. For comparison purpose, three linear springs’ stiffness factors were measured by Jolly’s scale and by our ultrasonic testing instrument. We found that our instrument could more conveniently and in real time display the distance values between the ultrasonic ranging module and the horizontal bottom plate when loading different weights. By processing these distance data, we found that our instrument was more convenient for obtaining the linear springs’ stiffness factors and that the results were more accurate than those of Jolly’s scale. This study verified that our instrument can accurately realize the performance of Jolly’s scale under diverse temperatures and humidity levels with high data reliability and perfect stability.

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35

Chen, Jie, Ken Chen, Thomas R. Katona, James J. Baldwin, and Gordon R. Arbuckle. "Non-linear large deformation FE analysis of orthodontic springs." Bio-Medical Materials and Engineering 7, no. 2 (1997): 99–110. http://dx.doi.org/10.3233/bme-1997-7202.

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36

Poltschak, Florian, and Peter Ebetshuber. "Design of Integrated Magnetic Springs for Linear Oscillatory Actuators." IEEE Transactions on Industry Applications 54, no. 3 (May 2018): 2185–92. http://dx.doi.org/10.1109/tia.2018.2800681.

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37

Stoychev, Stefan. "USING A TWO-MASS FLYWHEEL ON DRIVE SEWING MACHINES." Knowledge International Journal 31, no. 3 (June 5, 2019): 753–58. http://dx.doi.org/10.35120/kij3103753s.

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In the drive of modern machines depending on the engine used, driven mechanisms, frequency and magnitude of transient processes, vibrations with varying frequency and amplitude occur. In most cases, they are unacceptable, result in damage to the machine's component mechanisms, need for repair, worsen operating conditions. One of the ways to reduce harmful vibrations from the drive of the machine is by using screw-spring systems in the design of clutches, dual-mass flywheels and more. In machine-building constructions, the springs can be operated either individually or as components of spring loaded systems with a common load. Thus, for a given load, a desired value of the deformation, stiffness or a special, e.g. broken or non-linear characteristic can be achieved. There are two main ways of connecting springs to systems - parallel (with the same or different lengths) and consistently, combinations of these modes are possible. In many cases, the screw springs are required to withstand very high loads, this leads to larger dimensions of the spring and therefore incompatibility with the dimensions of the assembled node. In these cases, parallel (multi-directional) cylindrical screw springs are used, in this way load and small size requirements are provided. The springs are located one at the other, and in order to remove the twisting of the end supports, they are in a different direction of the turns. The load is absorbed by all the springs and distributed proportionally according to their stiffness. Upon deformation of the spring, potential deformation energy is accumulated, but can’t be fully returned to the mechanical system. Losses in a cycle of loading and unloading of the spring determine its absorbing (damping) capability, which is important for spring buffers and vibro-insulators. With properly selected and dimensioned spring systems, the large torsional vibrations generated by the engine are largely neutralized, which protects the machine's mechanisms against damage, prolongs the period of operation, improves operating comfort. The proposed method is to determine the basic parameters of a system of springs in the form of a dual-mass flywheel. The flywheel can be successfully used to reduce the harmful impact of vibrations when driving sewing machines directly.

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Medai, Nagi, Naoyuki Okamoto, Yu Ogasawara, and Katsuya Hihara. "Factors contributing to tourism demand at major Japanese hot springs." PLOS ONE 17, no. 9 (September 15, 2022): e0274681. http://dx.doi.org/10.1371/journal.pone.0274681.

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Hot springs are a major tourism resource in nature-based tourism, and the hot springs market is one of the biggest sectors in wellness tourism markets. In the present study, we examine factors contributing to tourism demand for major hot spring resorts in Japan using ordinary least squares regression models and generalized linear mixed models, and compare the estimation results. The results show that significant factors in most of our models are quality of accommodations and the degree of dependence on inbound demand. Furthermore, the number of non-Japanese languages supported on websites of hot spring resorts has a significant impact on inbound demand. Since the results of the present study cover more than 80 hot spring sites, the results highlight common important factors for hot spring resorts. Such widely applicable factors have been missing in previous studies, and the present study fills this research gap.

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39

Takino, Fumiya, Takahiro Ryu, Takashi Nakae, Kenichiro Matsuzaki, and Risa Ueno. "Fundamental study on countermeasures against subharmonic vibration of order 1/2 in automatic transmissions for cars." MATEC Web of Conferences 211 (2018): 13004. http://dx.doi.org/10.1051/matecconf/201821113004.

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In automatic transmissions for cars, a damper is installed in the lock-up clutch to absorb torsional vibrations caused by combustion in the engine. Although a damper with low stiffness reduces the torsional vibration, low-stiffness springs are difficult to use because of space limitations. To address this problem, dampers have been designed using a piecewise-linear spring having three different stages of stiffness. However, a nonlinear subharmonic vibration of order 1/2 occurs because of the nonlinearity of the piecewise-linear spring in the damper. In this study, we experimentally and analytically examined a countermeasure against the subharmonic vibration by increasing the stages of the piecewise-linear spring using the one-degree-of-freedom system model. We found that the gap between the switching points of the piecewise-linear spring was the key to vibration reduction. The experimental results agreed with results of the numerical analyses.

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40

Radomirovic, Dragi, and Ivana Kovacic. "On the equivalent systems for concurrent springs and dampers – Part 1: Small in-plane oscillations." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 14 (January 9, 2014): 2520–31. http://dx.doi.org/10.1177/0954406213519616.

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In this work, concurrent linear springs placed in the system that performs small in-plane oscillations around the stable equilibrium position are considered. New theorems defining how they can be replaced by two mutually orthogonal springs are provided. The same concept is applied to find two mutually orthogonal linear viscous dampers that can replace a system of concurrent linear viscous dampers. The directions of such springs and dampers correspond to the principal stiffness and damping axes, respectively. So far unknown invariants related to the sum of stiffness coefficients and damping coefficient of the original and equivalent systems are presented. A few examples are given to illustrate the use and benefits of this approach. In addition, it is shown how the concept of two mutually orthogonal springs can be beneficially used for analysing problems concerned with oscillations of a particle on elastic frames.

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Su, Hai-Jun, and J. Michael McCarthy. "A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms." Journal of Mechanical Design 128, no. 4 (October 4, 2005): 776–86. http://dx.doi.org/10.1115/1.2202137.

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This paper formulates the inverse static analysis of planar compliant mechanisms in polynomial form. The goal is to find the equilibrium configurations of the system in response to a known force/moment applied to the mechanism. The geometric constraint of the linkage defines a set of kinematics equations which are combined with equilibrium equations obtained from partial derivatives of the potential-energy function. In order to apply polynomial homotopy solver to these equations, we approximate the linear torsion spring torque at each joint by using sine and cosine functions. The results obtained from the homotopy solver are then refined using Newton-Raphson iteration. To demonstrate the analysis steps, we study two example planar compliant mechanisms, a four-bar linkage with two torsional springs, and a parallel platform supported by three linear springs. Numerical examples are provided together with plots of the potential energy during a movement between selected equilibrium positions.

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42

Vuong, Ngoc-Dung, Renjun Li, Chee-Meng Chew, Amir Jafari, and Joseph Polden. "A novel variable stiffness mechanism with linear spring characteristic for machining operations." Robotica 35, no. 7 (June 9, 2016): 1627–37. http://dx.doi.org/10.1017/s0263574716000357.

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SUMMARYVariable stiffness mechanisms are able to mechanically reconfigure themselves in order to adjust their system stiffness. It is generally accepted that only antagonistic designs, featuring quadratic springs, can produce linear spring-like behaviour (i.e., a linear relationship between the displacement and its resultant force). However, these antagonistic designs typically are not as energy efficient as series-based designs. In this work, we propose a novel variable stiffness mechanism that can achieve both linear-spring behaviour whilst maintaining an energy efficient characteristic. This paper will present the working principle, mechanical design and characterization of the joints stiffness properties (verified via experimental procedure). The pros and cons of this novel design with reference to the other Variable Stiffness Actuator (VSA) designs will be discussed based on experimental results and in the context of general machining tasks.

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Cao, Hao, Yaopeng Chang, Jiaxi Zhou, Xuhui Zhao, Ling Lu, Fei Chen, and Xiaowen Wu. "High-Efficiency Vibration Isolation for a Three-Phase Power Transformer by a Quasi-Zero-Stiffness Isolator." Shock and Vibration 2021 (April 20, 2021): 1–11. http://dx.doi.org/10.1155/2021/5596064.

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The vibrations generated by a three-phase power transformer reduce the comfort of residents and the service life of surrounding equipment. To resolve this tough issue, a quasi-zero-stiffness (QZS) isolator for the transformer is proposed. This paper is devoted to developing a QZS isolator in a simple way for engineering practices. The vertical springs are used to support the heavy weight of the transformer, while the oblique springs are employed to fulfill negative stiffness to neutralize the positive stiffness of the vertical spring. Hence, a combination of the vertical and oblique spring can yield high static but low dynamic stiffness, and the vibration isolation efficiency can be improved substantially. The dynamic analysis for the QZS vibration isolation system is conducted by the harmonic balance method, and the vibration isolation performance is estimated. Finally, the prototype of the QZS isolator is manufactured, and then the vibration isolation performance is tested comparing with the linear isolator under real power loading conditions. The experimental results show that the QZS isolator prominently outperforms the existing linear isolator. This is the first time to devise a QZS isolator for three-phase power transformers with heavy payloads in engineering practices.

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Wan, Peng, Jun Jie Guo, Pei Lin Wu, and Zhi Gen Fei. "Research on the Method of the Calibration of 3D Linear Scanning Probe System." Applied Mechanics and Materials 121-126 (October 2011): 1073–79. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.1073.

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3D scanning probe is a kind of measuring instrument that is an indispensable part of Gear Measuring Center. It’s used for obtaining micro-displacement in three directions through the deformation of the three mutually vertical parallel springs. The accuracy of the probe system has critical influence on Gear Measuring Center. Because of the limitation of the structure of parallel spring, the installation errors of the probe and the influence of environmental factors, the parallel springs in three directions are not always strictly vertical, the interference and coupling among X,Y,Z directions exist. This problem is very difficult to be solved by adjusting the mechanical structure of 3D scanning probe system. However, the accuracy of probe system can be improved by adopting software-compensation through calibration. In the paper, the calibration matrix of the probe system is generated by fitting the points sampled on the standard ball with the method of the least square. The points are sampled through controlling the probe to touch standard ball in several given directions. The experimental results show that the measurement errors caused by the coupling among the three perpendicular directions can be effectively decreased by the coefficient matrix mentioned above. The method of calibration is practical and effective for improving the measurement accuracy of 3D scanning probe.

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45

Lee, Gun-Myung, and Hong Seok Park. "Characteristics of a Vibration Isolation System with Non-linear Springs." Transactions of the Korean Society for Noise and Vibration Engineering 27, no. 7 (December 31, 2017): 844–49. http://dx.doi.org/10.5050/ksnve.2017.27.7.844.

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46

Aghamohammadi, Amir, M. Ebrahim Foulaadvand, Mohammad Hassan Yaghoubi, and Amir Hossein Mousavi. "Normal modes of a defected linear system of beaded springs." American Journal of Physics 85, no. 3 (March 2017): 193–201. http://dx.doi.org/10.1119/1.4972176.

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47

Huang, Heyuan, Meiying Zhao, Xiaopeng Wan, and Chi Hou. "A Composite Bolted Joints Non-Linear Stiffness Model and its Application." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 1 (February 2018): 66–73. http://dx.doi.org/10.1051/jnwpu/20183610066.

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The paper presents a nonlinear stiffness model on the bearing damage and bolt-load distribution rule of composite bolted joints. Based on the experimental stress-strain curves of composite single-bolted joints, the bearing damage process of structures can be divided into:linear non-damage stage; nonlinear damage propagation stage and linear degeneration stage. In this paper, the composite bolted joints are represented by a system of springs in which the static friction effects between laminates are considered in the linear stage, the non-linear interlaminate shear behavior and the nonlinear damage function for composite are defined and failure behavior based on the energy abortion principle is simulated in the linear degeneration stage. At last, the multi-fasters spring model is analyzed by importing the single-faster spring model.Comparing with the experimental data of multi-fasters shows the numerical result is in good agreement with experimental curves and has little error on the bolt-load distribution, which satisfies to the requirements in the engineering.

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48

Angeli, P., F. De Bona, and M. G. Munteanu. "Flexural stiffness of leaf springs for compliant micromechanisms." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 12 (December 1, 2008): 2505–11. http://dx.doi.org/10.1243/09544062jmes1022.

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Von Kármán equations have been used to evaluate the flexural behaviour of rectangular leaf springs with constant thickness. A closed form solution is obtained, showing that flexural stiffness varies continuously from that obtained by considering a beam model to the value given by the linear plate theory. This behaviour depends on section geometry, Poisson's ratio, and main curvature. A new characterizing parameter, whose relation with flexural stiffness allows a typical non-linear behaviour to be emphasized, is introduced in this work. In particular, for a given geometry and material, the flexural stiffness increases with the deflection and consequently with the load.

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Jeong, Seung-hee, Jeong-hwan Kim, Seung-ik Choi, Jung-keun Park, and Tae-sam Kang. "Platform Design and Preliminary Test Result of an Insect-like Flapping MAV with Direct Motor-Driven Resonant Wings Utilizing Extension Springs." Biomimetics 8, no. 1 (December 23, 2022): 6. http://dx.doi.org/10.3390/biomimetics8010006.

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In this paper, we propose a platform for an insect-like flapping winged micro aerial vehicle with a resonant wing-driving system using extension springs (FMAVRES). The resonant wing-driving system is constructed using an extension spring instead of the conventional helical or torsion spring. The extension spring can be mounted more easily, compared with a torsion spring. Furthermore, the proposed resonant driving system has better endurance compared with systems with torsion springs. Using a prototype FMAVRES, it was found that torques generated for roll, pitch, and yaw control are linear to control input signals. Considering transient responses, each torque response as an actuator is modelled as a simple first-order system. Roll, pitch, and yaw control commands affect each other. They should be compensated in a closed loop controller design. Total weight of the prototype FMAVRES is 17.92 g while the lift force of it is 21.3 gf with 80% throttle input. Thus, it is expected that the new platform of FMAVRES could be used effectively to develop simple and robust flapping MAVs.

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Sin, V. W. T., and M. Wiercigroch. "A symmetrically piecewise linear oscillator: Design and measurement." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 213, no. 3 (March 1, 1999): 241–49. http://dx.doi.org/10.1243/0954406991522617.

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A simple piecewise linear system with symmetrical flexible constraints was designed and manufactured to carry out a wide range of experimental dynamic analysis and ultimately to validate piecewise models. The design choice was based on the following criteria: accuracy in representing the mathematical model, manufacturing simplicity, flexibility in terms of parameter changes and cost effectiveness. The system consists of a block mass attached to two leaf springs, the stiffness of which can easily be varied by changing their length. The secondary stiffness in the form of cantilever beams can be widely varied in the same way. The clearance between the mass and secondary springs can also be varied by adjusting the screws at the ends of the beams. A variable pneumatic damper is mounted on the upper surface of the mass and provides a means of changing the viscous damping coefficient. The experimental set-up, calibration procedures and typical results are discussed.

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Journal articles on the topic 'Linear springs'

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