• Advances in nano research
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• v.8 no.1
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• pp.25-36
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• 2020

Rotating systems concern with torsional vibration, and it should be considered in vibration analysis. To do this, the time-dependent torsional vibrations in a single-walled carbon nanotube (SWCNT) under the linear and harmonic external torque, are investigated in this paper. Eringen's nonlocal elasticity theory is considered to demonstrate the nonlocality and constitutive relations. Hamilton's principle is established to derive the governing equation of motion and consequently related boundary conditions. An analytical method, called the Galerkin method, is utilized to discretize the driven differential equations. Linear and harmonic torsional loads, along with determined amplitude, are applied to the SWCNT as the external torques. SWCNT is considered under the clamped-clamped end supports. In free vibration, analysis of small scale effect reveals the capability of natural frequencies in different modes, and this results desirably are in coincidence with another study. The forced torsional vibration in the time domain, especially for carbon nanotubes, has not been done before in the previous works. The previous forced studies were devoted to the transverse vibrations. It should be emphasized that the dynamical analysis of torsion is novel, workable, and at the beginning of the path. The variations of nonlocal parameter, CNT's thickness, and the influence of excitation frequency on time-dependent angular displacement and nondimensional angular displacement are investigated in the context.

• Journal of Power System Engineering
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• v.22 no.6
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• pp.11-19
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• 2018

In this study, the authors examine the propulsion shafting of the training ship SAEDONGBAEK and perform modeling to analyze the torsional free vibration of the shafting. In this paper, the computational algorithm for analyzing the torsional free vibration of the shafting with a reduction gear is formulated by the sylvester-transfer stiffness coefficient method (S-TSCM) that is a recently developed and a powerful method in free vibration analysis. According to the state of the controllable pitch propeller of the shafting and the temperature of the elastic coupling, the torsional free vibration of the shafting is performed by the S-TSCM. The authors examine the changes of the natural frequencies and natural modes which are the results of the torsional free vibration analysis of the shafting.

• Advances in materials Research
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• v.11 no.1
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• pp.59-73
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• 2022

In the construction industry, thin-walled frame elements with very slender open cross-sections and low torsional stiffness are often subjected to a complex loading condition where axial, bending, shear and torsional stresses are present simultaneously. Hence, these often fail in instability even before the yield capacity is reached. One of the most common instability conditions associated with thin-walled structures is Lateral Torsional Buckling (LTB). In this study, a first order Generalized Beam Theory (GBT) formulation and numerical analysis of cold-formed steel lipped channel beams (C80×40×10×1, C90×40×10×1, C100×40×10×1, C80×40×10×1.6, C90×40×10×1.6 and C100×40×10×1.6) subjected to uniform moment is carried out to predict pure Lateral Torsional Buckling (LTB). These results are compared with the Finite Element Analysis of the beams modelled with shell elements using ABAQUS and analytical results based on Euler's buckling formula. The mode wise deformed shape and modal participation factors are obtained for comparison of the responses along with the effect of varying the length of the beam from 2.5 m to 10 m. The deformed shapes of the beam for different modes and GBTUL plots are analyzed for comparative conclusions.

• Structural Engineering and Mechanics
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• v.87 no.6
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• pp.541-554
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• 2023

An unbraced cantilever beam subjected to loads which cause bending about the major axis may buckle in a flexuraltorsional mode by deflecting laterally and twisting. For the efficient design of these structures, design engineers require a simple accurate equation for the elastic flexural-torsional buckling load. Existing solutions for the flexural-torsional buckling of cantilever beams have mainly been derived by numerical methods which are tedious to implement. In this research, an attempt is made to derive a theoretical equation by the energy method using different buckled shapes. However, the results of a finite element flexural-torsional buckling analysis reveal that the buckled shapes for the lateral deflection and twist rotation are different for cantilever beams. In particular, the buckled shape for the twist rotation also varies with the section size. In light of these findings, the finite element flexural-torsional buckling analysis was then used to derive simple accurate equations for the elastic buckling load and moment for cantilever beams subjected to end point load, uniformly distributed load and end moment. The results are compared with previous research and it was found that the equations derived in this study are accurate and simple to use.

• Earthquakes and Structures
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• v.23 no.3
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• pp.283-295
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• 2022

Seismic design codes permit the use of Equivalent Static Analysis of buildings considering torsional eccentricity e with dynamic amplification factors on structural eccentricity and some accidental eccentricity. Estimation of e in buildings is not addressed in codes. This paper presents a simple approximate method to estimate e in RC Moment Frame and RC Structural Wall buildings, which required no detailed structural analysis. The method is validated by 3D analysis (using commercial structural analysis software) of a spectrum of building. Results show that dynamic amplification factor should be applied on torsional eccentricity when performing Response Spectrum Analysis also. Also, irregular or mixed modes of oscillation arise in torsionally unsymmetrical buildings owing to poor geometric distribution of mass and stiffness in plan, which is captured by the mass participation ratio. These irregular modes can be avoided in buildings of any plan geometry by limiting the two critical parameters (normalised torsional eccentricity e/B and Natural Period Ratio 𝜏 =T_𝜃/T, where B is building lateral dimension, T_𝜃 uncoupled torsional natural period and T uncoupled translational natural period). Suggestions are made for new building code provisions.

• Earthquakes and Structures
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• v.8 no.2
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• pp.423-442
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• 2015

The effects of accidental eccentricity on the seismic response of four-storey steel buildings laterally stabilized by buckling restrained braced frames are studied. The structures have a square, symmetrical footprint, without inherent eccentricity between the center of lateral resistance (CR) and the center of mass (CM). The position of the bracing bents in the buildings was varied to obtain three different levels of torsional sensitivity: low, intermediate and high. The structures were designed in accordance with the seismic design provisions of the 2010 National Building Code of Canada (NBCC). Three different analysis methods were used to account for accidental eccentricity in design: (1) Equivalent Static Procedure with static in-plane torsional moments assuming a mass eccentricity of 10% of the building dimension (ESP); (2) Response Spectrum Analysis with static torsional moments based on 10% of the building dimension (RSA-10); and (3) Response Spectrum Analysis with the CM being displaced by 5% of the building dimension (RSA-5). Time history analyses were performed under a set of eleven two-component historical records. The analyses showed that the ESP and RSA-10 methods can give appropriate results for all three levels of torsional sensitivity. When using the RSA-5 method, adequate performance was also achieved for the low and intermediate torsional sensitivity cases, but the method led to excessive displacements (5-10% storey drifts), near collapse state, for the highly torsionally sensitive structures. These results support the current provisions of NBCC 2010.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.776-785
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• 2006

Ship builder's requirement for a higher power output rating has lead to the development of super large two stroke low speed diesel engines. Usually a large-sized bore ranging from 8-14 cylinders, this engine group is capable of delivering power output of more than 100,000 bhp at maximum continuous rating. Other positive aspects of this engine type include higher thermal efficiency, reliability, durability and mobility. This all playa vital role in meeting the propulsion requirement of vessels, specifically for large container ships, of which speed is a primary concern to become more competitive. Consequently, this also resulted in the modification of engine parameters and new component designs to meet the consequential higher mean effective pressure and higher maximum combustion pressure. Even though the fundamental excitation mechanism unchanged, torsional vibration stresses in the propulsion shafting are subsequently perceived to be higher. As such, one important viewpoint in the initial engine design is the resulting vibration characteristic expected to prevail on the propulsion shafting system(PSS). This paper investigated the torsional vibration characteristics of these super large engines. For the two node torsional vibration with a nodal point on the crankshaft, a tuning damper is necessary to reduce the torsional stresses on the crankshaft. Hence, the tuning torsional vibration damper design and compatibility to the shafting system was similarly reviewed and analyzed.

• Journal of Korean Society of Steel Construction
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• v.29 no.5
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• pp.361-368
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• 2017

ASCE 7-10 defines the torsional irregular structure as the one that has large torsional responses caused by the eccentricity. The code requires that these structures should be designed abide by the torsional provisions. This study evaluates the influence of torsional provisions on the performance of the designed multiple steel moment frames with different eccentricity. In this study, 3D response history analyses are performed. The results show that the moment frame design according to the standard with torsional irregularity provisions showed larger performance as the eccentricity increased and the distribution of plastic hinges similarly to orthopedic structures.

• Journal of the Korea Concrete Institute
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• v.25 no.6
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• pp.641-648
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• 2013

Current design codes regulate the minimum torsional reinforcement requirement for reinforced concrete members to prevent their brittle failure. The minimum torsional reinforcement ratio specified in the current national code and ACI318-11, however, have problems in the minimum longitudinal reinforcement ratio for torsion, the equilibrium condition in space truss model, and a marginal strength, etc. Thus, in order to overcome such shortcomings, this study presents a rational equation for minimum torsional reinforcement ratio that can provide a sufficient margin of safety in design. The minimum torsional reinforcement ratio proposed in this study was compared to the test results available in literature, and it was confirmed that it gave a proper margin of safety for all specimens studied in this paper.

• Earthquakes and Structures
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• v.11 no.6
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• pp.1027-1041
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• 2016

Different incident angles of ground motions have been considered to evaluate the relationship between floor rotation and torsional irregularity coefficient. The issues specifically addressed are (1) variability in torsional irregularity coefficient and floor rotations with varying incident angles of ground motion (2) contradictory relationship between floor rotation and torsional irregularity coefficient. To explore the stated issues, an evaluation based on relative variation in seismic response quantities of linear asymmetric structure under the influence of horizontal bi-directional excitation with varying seismic orientations has been carried out using response history analysis. Several typical earthquake records are applied to the structure to demonstrate the relative variations of floor rotation and torsional irregularity coefficient for different seismic orientations. It is demonstrated that (1) Torsional irregularity coefficient (TIC) increases as the story number decreases when the ground motion is considered along reference axes of the structure. For incident angles other than structure's reference axes, TIC either decreases as the story number decreases or there is no specific trend for TIC. Floor rotation increases in proportion to the story number when the ground motion is considered along reference axes of structure. For incident angles other than structure's reference axes, floor rotation either decreases as the story number increases or there is no specific trend for floor rotation and (2) TIC and floor rotation seems to be approximately inversely proportional to each other when the ground motion is considered along reference axes of the structure. For incident angles other than structure's reference axes, the relationship can even become directly proportional instead of inversely proportional.