• Structural Engineering and Mechanics
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• v.89 no.1
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• pp.33-46
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• 2024

The present research delves into the analysis of nonlinear free and forced vibrations of porous functionally graded (FG) shallow shells reinforced with oblique stiffeners, which are embedded in a nonlinear elastic foundation (NEF) subjected to external excitation. Two distinct types of PFG shallow shells, characterized by even and uneven porosity distribution along the thickness direction, are considered in the research. In order to model the stiffeners, Lekhnitskii's smeared stiffeners technique is implemented. With the stress function and first-order shear deformation theory (FSDT), the nonlinear model of the oblique stiffened shallow shells is established. The strain-displacement relationships for the system are derived via the FSDT and utilization of the von-Kármán's geometric assumptions. To discretize the nonlinear governing equations, the Galerkin method is employed. The model such developed allows analysis of the effects of the stiffeners with various angles as desired, in addition to the quantitative investigation on the influence of the surrounding nonlinear elastic foundations. To numerically solve the problem of vibrations, the 4th-order P-T method is used, as this method, known for its enhanced accuracy and reliability, proves to be an effective choice. The validation of the present research findings includes a comprehensive comparison with outcomes documented in existing literature. Additionally, a comparative analysis of the numerical results against those obtained using the 4th Runge-Kutta method is performed. The impact of stiffeners with varying angles and material parameters on the vibration characteristics of the present system is also explored. The researchers and engineers working in this field may use the results of this study as benchmarks in their design and research for the considered shell systems.

• Journal of the Korea institute for structural maintenance and inspection
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• v.25 no.6
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• pp.12-18
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• 2021

The purpose of this study is to effectively mitigate the bending displacement that occurs in the bridge due to forced vibration. We developed CTMD (Combine Tuned Mass Damper) that combines the relationship between spring and mass to control the bending behavior of simple beams. The experiment was conducted to confirm the control effect according to the change in the mass ratio of the developed CTMD. The developed CTMD is designed and manufactured so that the mass ratio can be adjusted according to the characteristics of the bridge. The maximum load of the spring applied to CTMD was fixed at 33.15 N. In order to evaluate the performance of the developed CTMD, a simple beam composed of hinges and rollers as boundary conditions was fabricated. In the experimental method, a CTMD was installed in the center of a simple beam and the deflection displacement according to the mass ratio was measured. The shaking condition was shaken at 3 Hz to induce the maximum bending behavior of the simple beam. As a result of the experiment, it was confirmed that when the optimal mass ratio was 2.1, the damping rate of the bending behavior displacement was about 71.2 %, indicating the best control effect.

• Structural Engineering and Mechanics
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• v.73 no.2
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• pp.123-132
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• 2020

Steel spherical hinged bearings have high loading capacity, reliable load transfer, flexible rotation with universal hinge and allowance of large displacement and rotation angle. However, bearings are in complex forced states subject to various load combinations, which lead to the significant influence on integral structural safety. Taking the large-tonnage complex steel spherical hinged bearings of Terminal 2 of Guangzhou Baiyun International Airport as an example, full-scale rotation and shear behaviour tests of the bearings subject to axial tensile load are carried out, and the corresponding finite element simulation analyses are conducted. The results of experiments and finite element simulations are in good agreement with the coincident development tendency of stress and deformation. In addition, the measured rotational moment is less than the calculated moment prescriptive by the code, and the relationship between horizontal displacement and horizontal shear force is linear. Finally, based on these results, the rotation and shear stiffness models of bearings subject to axial tensile load are proposed for the refinement analysis of integral structure.

• Wind and Structures
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• v.9 no.2
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• pp.109-124
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• 2006

This paper describes the characteristics of the fluctuating lift forces when a circular cylinder vibrates in the cross-flow direction. The response characteristics on elastically supported the circular cylinder was first examined by a free-vibration test. Next, flow-induced vibrations obtained by the free-vibration test were reproduced by a forced-vibration test, and then the characteristics of the fluctuating lift forces, the work done by the fluctuating lift, the behavior of the rolling-up of the separated shear layers were investigated on the basis of the visualized flow patterns. The main findings were that (i) the fluctuating lift forces become considerably large than those of a stationary circular cylinder, (ii) negative pressure generates on the surface of the circular cylinder when the rolling-up of separated shear layer begins, (iii) the phase between the fluctuating lift force and the cylinder displacement changes abruptly as the reduced velocity $U_r$ increases, and (iv) whether the generating cross-flow vibration becomes divergent or convergent can be described based on the work done by the fluctuating lift force. Furthermore, it was found that the generation of cross-flow vibration can be perfectly suppressed when the small tripping rods are installed on the surface of the circular cylinder.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.2
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• pp.117-126
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• 2016

In this paper, a numerical procedure for the natural vibration analysis of plates with openings and carlings based on the assumed mode method is extended to assess their forced response. Firstly, natural response of plates with openings and carlings is calculated from the eigenvalue equation derived by using Lagrange's equation of motion. Secondly, the mode superposition method is applied to determine frequency response. Mindlin theory is adopted for plate modelling and the effect of openings is taken into account by subtracting their potential and kinetic energies from the corresponding plate energies. Natural and frequency response of plates with openings and carlings subjected to point excitation force and enforced acceleration at boundaries, respectively, is analysed by using developed in-house code. For the validation of the developed method and the code, extensive numerical results, related to plates with different opening shape, carlings and boundary conditions, are compared with numerical data from the relevant literature and with finite element solutions obtained by general finite element tool.

• Current Applied Physics
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• v.18 no.11
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• pp.1368-1374
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• 2018

In this paper, forced vibration was used to regulate the droplet migration, fully recording the transient migration of droplets on a micro-textured substrate under the resonance frequency by a high-speed camera. The influence of resonance frequency and dynamic migration characteristics of droplets on the solid micro-texture surface under lateral vibration were researched. The experiment demonstrates that the driving force is caused by the difference between the left and right contact angles made the droplet oscillate and migrate, and as time t increases, the left and right contact points are periodically shifted and the amplitude of migration increases. Therefore, based on the droplet migration behavior and its force balance mechanism, a spring vibration model of migration behavior of the vibrating droplet micro unit was set up to predict the complete trajectory of its migration on a solid surface. The calculation results show that the theoretical displacement is less than the experimental displacement, and the longer the time, the larger the difference. Affected by the vibration, part of the droplet permeates through the micro-texture, resulting in the droplet losing height and the contact angle becoming smaller as well. While the other part of droplet overcomes the internal surface tension to migrate.

• Smart Structures and Systems
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• v.25 no.1
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• pp.57-64
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• 2020

The nonlinear dynamics of a directly forced clamped-clamped-free-free magneto-rheological elastomer (MRE) sandwich shell has been experimentally investigated. Experiments have been conducted on an aluminium shallow shell (shell A) and an MRE-aluminium sandwich shallow shell with single curvature (shell B). An electrodynamic shaker has been used to directly force shells A and B in the vicinity of their fundamental resonance frequency; a laser displacement sensor has been used to measure the vibration amplitude to construct the frequency-response curves. It was observed that for an aluminium shell (shell A), that at small forcing amplitudes, a weak softening-type nonlinear behaviour was observed, however, at higher forcing amplitudes the nonlinear dynamical behaviour shifted and a strong hardening-type response occurred. For the MRE shell (shell B), the effect of forcing amplitude showed softening at low magnetic fields and hardening for medium magnetic fields; it was also observed the mono-curved MRE sandwich shell changed dynamics to quasiperiodic displacement at some frequencies, from a periodic displacement. The presence of a magnetic field, initial curvature, and forcing amplitude has significant qualitative and quantitative effects on the nonlinear dynamical response of a mono curved MRE sandwich shell.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.551-562
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• 2019

In the present study, a suitable mathematical model considering parabolic transverse shear strains for dynamic analysis of laminated composite skew plates under different types of impulse and spatial loads was presented for the first time. The proposed mathematical model satisfies zero transverse shear strain at the top and bottom of the plate. On the basis of the cubic variation of thickness coordinate in in-plane displacement fields of the present mathematical model, a 2D finite element (FE) model was developed including skew transformations in the mathematical model. No shear correction factor is required in the present formulation and damping effect was also incorporated. This is the first FE implementation considering a cubic variation of thickness coordinate in in-plane displacement fields including skew transformations to solve the forced vibration problem of composite skew plates. The effect of transverse shear and rotary inertia was incorporated in the present model. The Newmark-${\beta}$ scheme was adapted to perform time integration from step to step. The $C^0$ FE formulation was implemented to overcome the problem of $C^1$ continuity associated with the cubic variation of thickness coordinate in in-plane displacement fields. The numerical studies showed that the present 2D FE model predicts the result close to the analytical results. Many new results varying different parameter such as skew angles, boundary conditions, etc. were presented.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.10
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• pp.52-58
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• 2020

Bellows are corrugated mechanical elements used to absorb displacements or vibrations caused by temperature changes, pressure, earthquakes, waves, etc., which are welded to flanges or directly connected to pipes. Expansion joint bellows must not only be designed to sufficiently withstand the internal pressure of the pipes but also accommodate axial, transverse, and rotational deformations to minimize the transfer of forces to the sensitive components of the system. Bellows have various types of corrugations, but U-type bellows are most commonly used in general piping systems. In this study, the behavior of U-shaped one-, two-, and three-ply bellows with the same inner diameter under pressure and forced displacement was analyzed using the finite element method. The results were compared with the design formula in the Expansion Joint Manufacturers Association (EJMA)'s code. Manufacturer data were used for the applied pressure and force displacement. The behavioral characteristics of the three cases were compared via structural analysis because the stress levels will be different for each model, even if they have the same inner diameter. Since the analytical model has an axisymmetric shape but displacement occurs in the transverse direction, the finite element model was composed of 1/2 of the whole model, and ANSYS Workbench 17.2 was employed for the analysis.

• Earthquakes and Structures
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• v.1 no.1
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• pp.1-19
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• 2010

It has been known that one-dimensional rod theory is very effective as a simplified analytical approach to large scale or complicated structures such as high-rise buildings, in preliminary design stages. It replaces an original structure by a one-dimensional rod which has an equivalent stiffness in terms of global properties. If the structure is composed of distinct constituents of different stiffness such as coupled walls with opening, structural behavior is significantly governed by the local variation of stiffness. This paper proposes an extended version of the rod theory which accounts for the two-dimensional local variation of structural stiffness; viz, variation in the transverse direction as well as longitudinal stiffness distribution. The governing equation for the two-dimensional rod theory is formulated from Hamilton's principle by making use of a displacement function which satisfies continuity conditions across the boundary between the distinct structural components in the transverse direction. Validity of the proposed theory is confirmed by comparison with numerical results of computational tools in the cases of static, free vibration and forced vibration problems for various structures.