• Smart Structures and Systems
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• v.26 no.4
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• pp.481-493
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• 2020

The negative stiffness spring and inerter are both characterized by the negative stiffness effect in the force-displacement relationship, potentially yielding an amplifying mechanism for dashpot deformation by being incorporated with a series tuning spring. However, resisting forces of the two mechanical elements are dominant in different frequency domains, thus leading to necessary complementarity in terms of vibration control and the amplifying benefit. Inspired by this, this study proposes a Negative Stiffness Inerter System (NSIS) as an earthquake protection system and developed analytical design formulae by fully utilizing its advantageous features. The NSIS is composed of a sub-configuration of a negative stiffness spring and an inerter in parallel, connected to a tuning spring in series. First, closed-form displacement responses are derived for the NSIS structure, and a stability analysis is conducted to limit the feasible domains of NSIS parameters. Then, the dual advantageous features of displacement reduction and the dashpot deformation amplification effect are revealed and clarified in a parametric analysis, stimulating the establishment of a displacement-based optimal design framework, correspondingly yielding the design formulae in analytical form. Finally, a series of examples are illustrated to validate the derived formulae. In this study, it is confirmed that the synergistic incorporation of the negative stiffness spring and the inerter has significant energy dissipation efficiency in a wide frequency band and an enhanced control effect in terms of the displacement and shear force responses. The developed displacement-based design strategy is suitable to utilize the dual benefits of the NSIS, which can be accurately implemented by the analytical design formulae to satisfy the target vibration control with increased energy dissipation efficiency.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.8
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• pp.977-989
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• 1999

The purpose of this study is to analyze how the human body having more muscles than its degree-of-freedom modulates an effective stiffness using redundant actuation, and to apply this concept to the design and control of advanced machines which requires adaptable spring. To investigate the adaptable stiffness phenomenon due to redundant actuation in the human body, this paper derives a general stiffness model of the Human body. In particular, for a planar 1 DOF human arm model, a planar 2 DOF human arm model, a spherical 3 DOF shoulder model, a 4 DOF human arm model, and a 7 DOF human arm model, the required nonlinear geometry ad the number of required actuator for successful modulation of the effective stiffness are analyzed along with a load distribution method for modulation of the required stiffness of such systems. Secondly, the concept of motion frequency modulation is introduced to show the usefulness of adaptive stiffness modulation. The motion frequency modulation represents a control of stiffness and / or inertia properties of systems. To show the effectiveness of the proposed algorithm, simulations are performed for 2 DOF anthropomorphic robot.

• Proceedings of the KSR Conference
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• 2005.05a
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• pp.504-509
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• 2005

Railway noise and vibration has been recognized as major problems with the speed-up of rolling stock. As a kind of solution to these problems, the decrease of stiffness of track pad have been tried. However, in this case, overturning of rail due to lateral force should be considered because it can have effect on the safety of running train. Therefore, above two things - decrease of stiffness of track pad and overturning of rail due to lateral force - should be considered simultaneously for the appropriate determination of spring coefficient of track pad. With this viewpoint, minimum spring coefficient of track pad is estimated through the comparison between the theoretical relationship about the overturning of rail and 3-dimensional FE analysis result. Two kinds of Lateral force and wheel load are used as input loads. Extracted values from the conventional estimation formula and the Shinkansen design loads are used. It is found that the overturning of rail changes corresponding to the change of the stiffness of track pad and the ratio of lateral force to wheel load. Moreover, it is found that the analysis model can have influence on the results. Through these procedure, minimum spring coefficient of track pad is estimated.

• Korean Journal of Applied Biomechanics
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• v.28 no.1
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• pp.61-67
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• 2018

Objective: The human body is often modelled as a spring-mass system. Lower extremity stiffness has been considered to be one of key factor in the performance enhancement of running, jumping, and hopping involved sports activities. There are several different classification of lower extremity stiffness consisting of vertical stiffness, leg stiffness, joint stiffness, as well as muscle and tendon stiffness. The primary purpose of this paper was to review the literature and describe different stiffness models and discuss applications of stiffness models while engaging in sports activities. In addition, this paper provided a current update of the lower extremity literature as it investigates the relationships between lower extremity stiffness and both functional performance and injury. Summary: Because various methods for measuring lower extremity stiffness are existing, measurements should always be accompanied by a detailed description including type of stiffness, testing method and calculation method. Moreover, investigator should be cautious when comparing lower extremity stiffness from different methods. Some evidence highlights that optimal degree of lower extremity stiffness is required for successful athletic performance. However, the actual magnitude of stiffness required to optimize performance is relatively unexplored. Direct relationship between lower extremity stiffness and lower extremity injuries has not clearly been established yet. Overall, high stiffness is potentially associate risk factors of lower extremity injuries although some of the evidence is controversial. Prospective injures studies are necessary to confirm this relationship. Moreover, further biomechanical and physiological investigation is needed to identify the optimal regulation of the lower limb stiffness behavior and its impact on athletic performance and lower limb injuries.

• Nuclear Engineering and Technology
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• v.30 no.4
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• pp.287-297
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• 1998

The elastic stiffness formula of leaf type holddown spring(HDS) assembly is verified by comparing the values of elastic stiffness with the characteristic test results of the HDS's specimens. The comparisons show that the derived elastic stiffness formula is useful in reliably estimating the elastic stiffness of leaf type HDS assembly. The elastic stiffness sensitivity of leaf type HDS assembly is analyzed using the formula and its gradient vectors obtained from the mid-point formula. As a result of sensitivity analysis, the elastic stiffness sensitivity with respect to each design variable is quantified and design variables of large sensitivity are identified. Among the design variables, leaf thickness is identified as the most sensitive design variable to the elastic stiffness of leaf type HDS assembly. In addition, the elastic stiffness sensitivity, with respect to design variable, is in power-law type correlation to the base thickness of the leaf.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.10
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• pp.140-147
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• 1998

The dynamic behavior of elastically restrained beams under the action of distributed tangential forces is investigated in this paper. The beam, which is fixed at one end, is assumed to rest on an intermediate spring support. The governing equations of motion are derived from the energy expressions, and the finite element formulation is employed to calculate the critical distributed tangential force. Jump phenomena for the critical distributed tangential force and instability types are presented for various spring stiffnesses and support positions. Stability maps are generated by performing parametric studies to show how the distributed tangential forces affect the frequencies and the stability of the system considered. Through the numerical simulations, the following conclusioils are obtained: (i) Only flutter type instability exists for the dimensionless spring stiffness K $\leq$ 97, regardless of the position of the spring support. (ii) For the dimensionless spring stiffness K $\leq$ 98, the transition from flutter to divergence occurs at a certain position of the spring support, and the transition position moves from the free end to the free end of the beam as the spring stiffness increases. (iii) For K $\leq$ 10$^{6}$ the support condition can be regarded as a rigid support condition.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.1
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• pp.110-122
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• 2008

Pneumatic vibration isolator typically consisting of dual-chamber pneumatic springs and a rigid table are widely employed for proper operation of precision instruments such as optical devices or nano-scale equipments owing to their low stiffness- and high damping-characteristics. As environmental vibration regulations for precision instruments become more stringent, it is required to improve further the isolation performance. In order to facilitate their design optimization or active control, a more accurate mathematical model or complex stiffness is needed. Experimental results we obtained rigorously for a dual-chamber pneumatic spring exhibit significantly amplitude dependent behavior, which cannot be described by linear models in earlier researches. In this paper, an improvement for the complex stiffness model is presented by taking two major considerations. One is to consider the amplitude dependent complex stiffness of diaphragm necessarily employed for prevention of air leakage. The other is to employ a nonlinear model for the air flow in capillary tube connecting the two pneumatic chambers. The proposed amplitude-dependent complex stiffness model which reflects dependency on both frequency and excitation amplitude is shown to be very valid by comparison with the experimental measurements. Such an accurate nonlinear model for the dual-chamber pneumatic springs would contribute to more effective design or control of vibration isolation systems.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.7 s.262
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• pp.777-783
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• 2007

Since the performance of the circuit breaker mainly depends on the spring operating mechanism, the analysis of the spring operating mechanism is required. The spring, especially closing spring, stores the deformation energy due to the compression and then accelerates the big loads rapidly in the circuit breaker. To accurately carry out the kinematic and dynamic analysis of the circuit breaker, the precise modeling of the spring behavior is necessary. In this paper, the static stiffness of the spring is captured by using the tester. A simple mechanism similar to the spring operating mechanism was designed to generate the release motion of the spring. A high speed camera was used to capture the behavior of the spring. Three types of spring models such as a linear spring model, modal spring model, and nodal spring model are suggested and compared with the experimental results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.7 s.262
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• pp.725-731
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• 2007

An air spring which is a part of the suspension system of automobiles is used to reduce and absorb the vibration and the noise. Main components of the air spring are a cord reinforced rubber bellows, a canister and a piston. The performance of the air spring are depended on configurations of rubber bellows, the angle and elastic modulus of cord. The finite element analysis are executed to predict and evaluate the load capacity and the stiffness. The design variables of air spring are determined to adjust the required specifications of the air spring. Several samples of the air spring are manufactured and experimented. It is shown that the results by finite element analysis are in close agreement with the test results.

• Proceedings of the KSR Conference
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• 2008.06a
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• pp.2236-2241
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• 2008

To predict the dynamic behaviour of railway vehicle, the complex vehicle structure has been described by mathmatical model such as mass, spring and damper. Air-spring has played a major role to improve dynamic characteristics, vibration isolation and ride comfort. The mechanical behaviour of air spring is very complicated. The behaviour is based on fluid and thermodynamic mechanisms. The main parameters of air spring are stiffness due to compression of the air in the spring and surge reservoir, change of area stiffness and orifice damping. In this paper, we have studied an air-spring modeling method and compared the difference between calculation and test.