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

• Journal of the Korean Society of Safety
• /
• v.29 no.3
• /
• pp.64-71
• /
• 2014

The generalized tangential stiffness matrix of semi-rigid frame element with shear deformations based on Haringx's shear theory is newly derived and compared with the previous study based on Engesser's shear theory. Also, linearized elastic and geometric stiffness matrices are newly presented from the exact tangential stiffness matrix. In oder to obtain the inelastic system buckling load of shear flexible semi-rigid frame structure, the Ef method by tangential modulus theory is adopted and the FE analysis programs are developed. Finally, the shear and semi-rigid effects of system bucking are investigated by two numerical examples.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2008.04a
• /
• pp.856-860
• /
• 2008

Wire-suspensions in the conventional actuators mechanically support the moving part and guarantee the accuracy of the actuator without tangential tilt actuation. However, such a suspension configuration has considerable stiffness in the tangential tilt direction with two additional wire beams for the tangential tilt. Thus, we performed a design sensitivity analysis for the wire-suspension stiffness of 4-axis actuator and controlled the main parameters such as distance among wire-suspensions and wire-suspension length to allow tangential tilt flexibility. The elasticity of frame PCB that supports the moving part by wire-suspensions was also exploited to improve the flexibility of wire-suspension in the tangential tilt direction. A novel suspension structure was devised by establishing eight wire-suspensions at both sides of the moving part for electrical connection to coils. The magnetic circuit according to the proposed 4-axis actuator using multi-polar magnet and coils was also suggested for the generation of electromagnetic forces in the focusing, tracking, radial and tangential tilt directions.

• Computational Structural Engineering
• /
• v.8 no.4
• /
• pp.159-171
• /
• 1995

The parameters describing a complete hysteresis loop include pinch force, drift offset, effective stiffness, unloading and reloading trangential stiffness. Analytical equations proposed to quantify the nonlinear, inelastic behavior of reinforced shear walls can be used to predict these parameters as a function of axial load and drift ratio. For example, drift offset, effective stiffness, and first and second unloading and reloading tangential stiffness are calculated using equations obtained from test data for a desired drift ratio or ductility level. Pinch force can also be estimated for a given drift ratio and axial load. The effective virgin stiffness at the first yield and its post yield reduction can be estimated. The load deflection response of flexural reinforced concrete shear walls can now be estimated based on the effective wall stiffness that is a function of axial force and drift ratio.

• Structural Engineering and Mechanics
• /
• v.16 no.2
• /
• pp.195-217
• /
• 2003

This paper, which is an extension of a previous work by Viola et al. (2002), deals with the dynamic stability of beams under a triangularly distributed sub-tangential forces when the effect of an elastically restrained end is taken into account. The sub-tangential forces can be realised by a combination of axial and tangential follower forces, that are conservative and non-conservative forces, respectively. The studied beams become unstable in the form of either flutter or divergence, depending on the degree of non-conservativeness of the distributed sub-tangential forces and the stiffness of the elastically restrained end. A non-conservative parameter ${\alpha}$ is introduced to provide all possible combinations of these forces. Problems of this kind are usually, at least in the first approximation, reduced to the analysis of beams according to the Bernoulli-Euler theory if shear deformability and rotational inertia are negligible. The equation governing the system may be derived from the extended form of Hamilton's principle. The stability maps will be obtained from the eigenvalue analysis in order to define the divergence and flutter domain. The passage from divergence to flutter is associated with a noticeable lowering of the critical load. A number of particular cases can be immediately recovered.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.33 no.2
• /
• pp.409-422
• /
• 2013

For stability design and P-${\Delta}$ analysis of steel frames with semi-rigid connections, the explicit form of the exact tangential stiffness matrix of a generalized semi-rigid frame element having rotational and translational connections is firstly derived using the stability functions. And its elastic and geometric stiffness matrix is consistently obtained by Taylor series expansion. Next depending on connection types of semi-rigidity, the corresponding tangential stiffness matrices are degenerated based on penalty method and static condensation technique. And then numerical procedures for determination of effective buckling lengths of generalized semi-rigid frames members and P-${\Delta}$ and shortly addressed. Finally three numerical examples are presented to demonstrate the validity and accuracy of the proposed method. Particularly the minimum braced frames and coupled buckling modes of the corresponding frames are investigated.

• Geomechanics and Engineering
• /
• v.25 no.4
• /
• pp.341-345
• /
• 2021

1D sand compression response to ko-loading experiences volume contraction from low to high effective stress regimes. Previous study suggested compressibility model with physically correct asymptotic void ratios at low and high stress levels and examined only for both remolded clays and natural clays. This study extends the validity of Enhanced Terzaghi model for different sand types complied from 1D compression data. The model involved with four parameters can adequately fit 1D sand compression data for a wide stress range. The low stress obtained from fitting parameters helps to identify the initial fabric conditions. In addition, strong correlation between compressibility and the void ratio at low stress facilitates determination of self-consistent fitting parameters. The computed tangent constrained modulus can capture monotonic stiffening effect induced by an increase in effective stress. The magnitude of tangent stiffness during large strain test should not be associated with small strain stiffness values. The use of a single continuous function to capture 1D stress-strain sand response to ko-loading can improve numerical efficiency and systematically quantify the yield stress instead of ad hoc methods.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
• /
• 1997.04a
• /
• pp.111-121
• /
• 1997

The stability of a rotor-bearing system supported by swirl-controlled hybrid journal bearing with pair-type angled injection orifices is investigated for improvement of the whirl frequency ratio by allowing effective control of the tangential flow inside the bearing clearance, i.e., by achieving more freedom in controlling strength and direction of the supply tangential flow inside the bearing clearance. It is suggested that the system instability can be improved through the change of bearing dynamic characteristic parameters with the swirl control. The orifice diameter d$_0$ and recess injection angle $\alpha$ along with combinations of swirl/anti-swirl supply pressures and directions (3.0-3.0MPa, 4.0-2.0MPa, 2.0-4.0MPa) are selected for design parameters for swirl-controlled effective factors dependent on journal speeds (3000, 9000, 15000, 21000 rpm). It has been found that the orifice diameter do shows strong effects on effective maneuverability of direct-stiffness and direct damping values, while recess injection angle $\alpha$ results in substantial magnitude and direction of cross-stiffness. Specifically, recess injection parameters which are functions of angle of orifice feeding flow and recess dimensions showed very feasible effect on the stability of swirl-controlled rotor-bearing system.

• Journal of Korean Association for Spatial Structures
• /
• v.14 no.3
• /
• pp.47-56
• /
• 2014

This paper investigates the characteristics of unstable behaviour and critical buckling load by joint rigidity of framed large spatial structures which are sensitive to initial conditions. To distinguish the stable from the unstable, a singular point on equilibrium path and a critical buckling level are computed by the eigenvalues and determinants of the tangential stiffness matrix. For the case study, a two-free node example and a folded plate typed long span example with 325 nodes are adopted, and these adopted examples' nonlinear analysis and unstable characteristics are analyzed. The numerical results in the case of the two-free node example indicate that as the influence of snap-through is bigger; that of bifurcation buckling is lower than that of the joint rigidity as the influence of snap-through is lower. Besides, when the rigidity decreases, the critical buckling load ratio increases. These results are similar to those of the folded-typed long span example. When the buckling load ratio is 0.6 or less, the rigidity greatly increases.

• Tribology and Lubricants
• /
• v.13 no.3
• /
• pp.63-72
• /
• 1997

The stability of a rotor-bearing system supported by swirl-controlled hybrid journal bearing with pair-type angled injection orifices is investigated for improvement of the whirl frequency ratio by allowing effective control of the tangential flow inside the bearing clearance, i.e., by achieving more freedom in controlling strength and direction of the supply tangential flow inside the bearing clearance. It is suggested that the system instability can be improved through the change of bearing dynamic characteristic parameters with the swirl control. The orifice diameter $d_0$ and recess injection angle $\alpha$ along with combinations of swirl/anti-swirl supply pressures and directions (3.0~3.0 MPa, 4.0~2.0 MPa, 2.0~4.0 MPa) are selected for design parameters for swirl-controlled effective factors dependent on journal speeds (3000, 9000, 15000, 21000 rpm). It has been found that the orifice diameter $d_0$ shows strong effects on effective maneuverability of direct-stiffness and direct damping values, while recess injection angle $\alpha$ results in substantial effects on the magnitude and direction of cross-stiffness. Specifically, recess injection parameters which are functions of angle of orifice feeding flow and recess dimensions showed very feasible effect on the stability control of swirl-controlled rotor-bearing system.