• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2009.10a
• /
• pp.321-321
• /
• 2009

This paper presents quasi-zero-stiffness (QZS) characteristic of a passive isolator using flexures under compression force. The passive isolator consists of a positive stiffness element (a vertical coil spring) and a negative stiffness element (flexures under compression force), and their proper combination of the positive and negative stiffness elements can produce both substantial static and zero dynamic stiffness, so called QZS. Firstly, a nonlinear dimensionless expression of a flexure under compression force is derived. A dynamic model of the passive isolator is developed and numerical simulations of its time and frequency response are performed. Then, undesirable nonlinear vibration is quantified using a period doubling bifurcation diagram and a Poincare's map of the isolator under forced excitation. Finally, experiments are performed to validate the QZS characteristic of the passive isolator.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2007.11a
• /
• pp.1259-1265
• /
• 2007

This paper presents nonlinear vibration characteristics of a vertical passive zero stiffness isolator. The passive isolator can achieve zero stiffness through buckling of notched flexure caused by a compressive force. First, a simulation model of the isolator was built based on elastic beam theory. As increasing the compression force, time and frequency responses of the isolator were simulated. In addition, further nonlinear vibration characteristics were investigated through a bifurcation diagram and a Poincare's map, which shows that even chaostic vibration could happen. The simulations show that as the compressive force increases, the stiffness goes close to zero and the nonlinear characteristic becomes stronger to have a great effect on the isolation performance.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2009.06a
• /
• pp.681-682
• /
• 2009

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2012.05a
• /
• pp.1097-1098
• /
• 2012

• Smart Structures and Systems
• /
• v.31 no.3
• /
• pp.213-227
• /
• 2023

A passive prismatic-shaped isolation platform (PIP) is proposed to realize enhanced quasi-zero stiffness (QZS) effect. The design concept uses a horizontal spring to produce a tunable negative stiffness and installs oblique springs inside the cells of the prismatic structure to provide a tunable positive stiffness. Therefore, the QZS effect can be achieved by combining the negative stiffness and the positive stiffness. To this aim, firstly, the mathematical modeling and the static analysis are conducted to demonstrate this idea and provide the design basis. Further, with the parametric study and the optimal design of the PIP, the enhanced QZS effect is achieved with widened QZS range and stable property. Moreover, the dynamic analysis is conducted to investigate the vibration isolation performance of the proposed PIP. The analysis results show that the widened QZS property can be achieved with the optimal designed structural parameters, and the proposed PIP has an excellent vibration isolation performance in the ultra-low frequency due to the enlarged QZS range. Compared with the traditional QZS isolator, the PIP shows better performance with a broader isolation frequency range and stable property under the large excitation amplitude.

• Proceedings of the KSME Conference
• /
• 2007.05a
• /
• pp.688-693
• /
• 2007

Most frame structures cannot be manufactured in a single-piece form. Ideally, when a structure is built up by assembling multi pieces, assembly at the joints should be rigidly performed enough to have almost full stiffness, which is difficult for practical reasons such as manufacturing cost and time. In this research, we aim to develop a manufacturability-oriented compliance-minimizing topology optimization using a ground beam model incorporating additional zero-length elastic joint elements. In the present formulation, design variables control the stiffness of zero-length elastic joints, not the stiffness of beams. Because joint stiffness values at the converged state can be utilized to select candidate assembly locations and their strengths, the technique is extremely useful to design multi-piece frame structures. An optimal layout is also extracted based on the stiffness values.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2006.04a
• /
• pp.589-596
• /
• 2006

An improved numerical method to obtain the exact element stiffness matrix is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric thin-walled beam-columns with two-types of elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column. This numerical technique is firstly accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Then exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions.

• Smart Structures and Systems
• /
• v.25 no.5
• /
• pp.543-557
• /
• 2020

This paper presents a series of experimental and numerical investigations on a vertical isolation system with quasi-zero stiffness (QZS) property. The isolation system comprises a linear helical spring and disk spring. The disk spring is designed to provide variable stiffness to the system. Orthogonal static tests with different design parameters are conducted to verify the mathematical and mechanical models of the isolation system. The deviations between theoretical and test results influenced by the design parameters are summarized. Then, the dynamic tests for the systems with different under-load degrees are performed, including the fast sweeping tests, harmonic excitation tests, and half-sine impact tests. The displacement transmissibility, vibration reduction rate, and free vibration response are calculated. Based on the test results, the variation of the transmission rule is evaluated and the damping magnitudes and types are identified. In addition, the relevant numerical time history responses are calculated considering the nonlinear behavior of the system. The results indicate that the QZS isolation system has a satisfactory isolation effect, while a higher damping level can potentially promote the isolation performance in the low-frequency range. It is also proved that the numerical calculation method accurately predicts the transmission character of the isolation system.

• Journal of Korean Society of Steel Construction
• /
• v.14 no.4
• /
• pp.509-518
• /
• 2002

In order to perform the spatial buckling and static analysis of the nonsymmetric thin-walled beam-column element, improved exact static stiffness matrices were evaluated using equilibrium equation and force-deformation relationships. This numerical technique was obtained using a generalized linear eigenvalue problem, by introducing 14 displacement parameters and system of linear algebraic equations with complex matrices. Unlike the evaluation of dynamic stiffness matrices, some zero eigenvalues were included. Thus, displacement parameters related to these zero eigenvalues were assumed as polynomials, with their exact distributions determined using the identity condition. The exact displacement functions corresponding to three loadingcases for initial stress-resultants were then derived, by consistently combining zero and nonzero eigenvalues and corresponding eigenvectors. Finally, exact static stiffness matrices were determined by applying member force-displacement relationships to these displacement functions. The buckling loads and displacement of thin-walled beam were evaluated and compared with analytic solutions and results using ABAQUS' shell element or straight beam element.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1996.04a
• /
• pp.182-189
• /
• 1996

The focus of this study is on the problem of the design of structure of undetermined topology. This problem has been regarded as being the most challenging of structural optimization problems, because of the difficulty of allowing topology to change. Conventional approaches break down when element sizes approach to zero, due to stiffness matrix singularity. In this study, a novel nonlinear Programming formulation of the topology Problem is developed and examined. Its main feature is the ability to account for topology variation through zero element sizes. Stiffness matrix singularity is avoided by embedding the equilibrium equations as equality constraints in the optimization problem. Although the formulation is general, two dimensional plane elasticity examples are presented. The design problem is to find minimum weight of a plane structure of fixed geometry but variable topology, subject to constraints on stress and displacement. Variables are thicknesses of finite elements, and are permitted to assume zero sizes. The examples demonstrate that the formulation is effective for finding at least a locally minimal weight.