• Structural Monitoring and Maintenance
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• v.11 no.2
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• pp.127-148
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• 2024

Estimating cable tension is important in the maintenance of cable structures, such as cable-stayed bridges. In practice, the higher-order vibration method based on natural frequencies is used. In recent years, dampers have been installed onto cables to suppress aerodynamic vibration. Because the higher-order vibration method is suitable to cables without a damper, the damper must be removed before using this method. Because damper removal is time-consuming and labor-intensive, a previous study proposed a tension estimation method for a cable with a damper based on the natural frequencies, which does not require the damper's removal. However, the previous method relies on the modeling accuracy of the damper's complex stiffness. The damper design formula, while intended for design purposes, does not consistently reflect the damper's actual complex stiffness. Therefore, the estimation accuracy deteriorates when the damper's actual complex stiffness deviates from the damper design formula. With this background, this paper introduces a novel tension estimation method based on mode shapes, which circumvents damper modeling errors since mode shapes are independent of the damper's complex stiffness. In the numerical verification using 90 models, the proposed method estimated tension accurately with an estimation error within 0.59%. In the experimental verification, the proposed method estimated tension accurately with an estimation error within 4.17% except for one case, while the previous method had an estimation error of 44% when the damper design formula was used. The proposed method was found to be superior to the previous method in terms of accuracy and practicality by numerical simulation and experiment.

• Structural Engineering and Mechanics
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• v.13 no.4
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• pp.437-453
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• 2002

In this paper, dynamic stiffness and flexibility for circular membranes are analytically derived using an efficient mixed-part dual boundary element method (BEM). We employ three approaches, the complex-valued BEM, the real-part and imaginary-part BEM, to determine the dynamic stiffness and flexibility. In the analytical formulation, the continuous system for a circular membrane is transformed into a discrete system with a circulant matrix. Based on the properties of the circulant, the analytical solutions for the dynamic stiffness and flexibility are derived. In deriving the stiffness and flexibility, the spurious resonance is cancelled out. Numerical aspects are discussed and emphasized. The problem of numerical instability due to division by zero is avoided by choosing additional constraints from the information of real and imaginary parts in the dual formulation. For the overdetermined system, the least squares method is considered to determine the dynamic stiffness and flexibility. A general purpose program has been developed to test several examples including circular and square cases.

• Journal of KSNVE
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• v.9 no.1
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• pp.42-48
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• 1999

In this paper, a computer simulation method for dynamic analysis of the hydraulic engine mount system is proposed. The hydraulic engine mount system controls the damping characteristics using the viscosity of fluid flow The complex stiffness of the main rubber of the hydraulic engine mount system is computed by finite element analysis for the viscoelastic materials and hydro-static elements. A numerical analysis method is presented to solve nonlinear equations of the hydraulic engine mount system. which is composed of an engine mass, fluid in inertia track and a vertical inertia force of reciprocating mass in the engine. Also. dynamic properties of the hydraulic engine mount system are analyzed in the frequency domain. Effects of the hydraulic engine mount system running over the rough road are investigated using a vehicle dynamic model. These results are compared with those of the rubber mount system.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.369-376
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• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.34-39
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• 1998

In order to compute the forces which are transmitted through rubber bushings with a commercial multibody dynamic analysis (MBDA) program, a rubber bushing model is needed. The rubber bushing model of MBDA programs such as DADS or ADAMS is the Voigt model which is simply a parallel spring-viscous damper system, meaning that the damping force of the Voigt model is proportional to the frequency. However, experiments do not necessarily support this proportionality. Alternatively, the viscoelastic characteristics of rubber bushings can be better represented by the complex stiffness. The purpose of this paper is to develop a viscoelastic rubber bushing model for the MBDA programs. Firstly, a methodology is proposed to calculate the complex stiffness of rubber bushings considering static and dynamic load conditions. Secondly, a viscoelastic rubber bushing model developed which uses standard elements provided by DADS. The proposed methods are applied to the rubber bushings of the lower control arms of a rear suspension of a 1994 Ford Taurus model. Then, the forces computed for the rubber bushing model are analyzed and compared with the Voigt model in time and frequency domains.

• Structural Engineering and Mechanics
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• v.45 no.4
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• pp.423-437
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• 2013

Complex structures are usually assembled from several substructures with joints connecting them together. These joints have significant effects on the dynamic behavior of the assembled structure and must be accurately modeled. In structural analysis, these joints are often simplified by assuming ideal boundary conditions. However, the dynamic behavior predicted on the basis of the simplified model may have significant errors. This has prompted the researchers to include the effect of joint stiffness in the structural model and to estimate the stiffness parameters using inverse dynamics. In the present work, structural joints have been modeled as a pair of translational and rotational springs and frequency equation of the overall system has been developed using sub-structure synthesis. It is shown that using first few natural frequencies of the system, one can obtain a set of over-determined system of equations involving the unknown stiffness parameters. Method of multi-linear regression is then applied to obtain the best estimate of the unknown stiffness parameters. The estimation procedure has been developed for a two parameter joint stiffness matrix.

• Journal of KSNVE
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• v.9 no.1
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• pp.141-148
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• 1999

Resilient mounting is effective measures to reduce the structure-borne noise and radiated noise for many applications. The acoustic stiffness (frequency-dependent stiffness) of resilient mounts is an important parameter required in order to model vibration isolation with high accuracy. It is general to use measurement method for obtaining acoustic stiffness of complex resilient mounts under static preload. In this paper, the principles of measuring acoustic stiffness were described and the developed test apparatus was introduced. Also, the feasibility of the test apparatus is illustrated by measurement results of a resilient mount.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.5
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• pp.30-37
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• 1996

The objective of this research is to explore the analysis and test method for the reliable design and fabrication of a high precision dynamically tuned gyroscope. The tuning frequency is decided by the calculation of mass moment of inertia of rotor and gimbal and the stiffness of flexures. Due to the complex geometry of the flexure, calculation of the stiffness of the suspension flexure is difficult. In this paper, three analytical methods for obtaining the stiffness of the flexure are porposed and a special testing method is used for checking the accuracy of the computed results.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.7
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• pp.723-729
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• 2012

Spring-like leg models have been employed to explain various dynamic characteristics in human walking. However, this leg stiffness model has limitations to represent complex motion of actual human gait, especially the behaviors of each lower limb joint. The purpose of this research was to determine changes of total leg stiffness and lower limb joint stiffness with gait speed in knee osteoarthritis. Joint stiffness defined as the ratio of the joint torque change to the angular displacement change. Eight subjects with knee osteoarthritis participated to this study. The subject walked on a 12 m long and 1 m wide walkway with three sets of four different randomly ordered gait speeds, ranging from their self-selected speed to maximum speed. Kinetic and kinematic data were measured using three force plates and an optical marker system, respectively. Joint torques of lower limb joints calculated by a multi-segment inverse dynamics model. Total leg and each lower limb joint had constant stiffness during single support phase. The leg and hip joint stiffness increased with gait speed. The correlation between knee joint angles and torques had significant changed by the degree of severity of knee osteoarthritis.

• Smart Structures and Systems
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• v.15 no.3
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• pp.627-643
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• 2015

Negative stiffness, previously emulated by active or semi-active control for cable vibration mitigation, is realized passively using a self-contained highly compressed spring, the negative stiffness device (NSD).The NSD installed in parallel with a viscous damper (VD) in the vicinity of cable anchorage, enables increment of damper deformation during cable vibrations and hence increases the attainable cable damping. Considering the small cable displacement at the damper location, even with the weakening device, the force provided by the NSD-VD assembly is approximately linear. Complex frequency analysis has thus been conducted to evaluate the damping effect of the assembly on the cable; the displacement-dependent negative stiffness is further accounted by numerical analysis, validating the accuracy of the linear approximation for practical ranges of cable and NSD configurations. The NSD is confirmed to be a practical and cost-effective solution to improve the modal damping of a cable provided by an external damper, especially for super-long cables where the damper location is particularly limited. Moreover, mathematically, a linear negative stiffness and viscous damping assembly has proven capability to represent active or semi-active control for simplified cable vibration analysis as reported in the literature, while in these studies only the assembly located near cable anchorage has been addressed. It is of considerable interest to understand the general characteristics of a cable with the assembly relieving the location restriction, since it is quite practical to have an active controller installed at arbitrary location along the cable span such as by hanging an active tuned mass damper. In this paper the cable frequency variations and damping evolutions with respect to the arbitrary assembly location are then evaluated and compared to those of a taut cable with a viscous damper at arbitrary location, and novel frequency shifts are observed. The characterized complex frequencies presented in this paper can be used for preliminary damping effect evaluation of an adaptive passive or semi-active or active device for cable vibration control.