• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.9
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• pp.1486-1491
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• 2003

A modeling method for the modal analysis of a composite trapezoidal plate undergoing in-plane translational acceleration is presented in this paper. The equations of motion for the plate are derived and transformed into a dimensionless form. The effects of the inclination angles, fiber orientation angle and the acceleration on the modal characteristics of the plate are investigated.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.5
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• pp.414-420
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• 2014

In this paper, the vibration characteristics of the trapezoidal corrugated plate with axial stiffeners and lumped masses are investigated by the analytical method. The corrugated plate can be treated as an equivalent orthotropic plate as this plate has different flexure properties in two perpendicular directions; flexible in the corrugation direction and stiff in the transverse direction. The effective extensional and flexural stiffness of the equivalent plate are considered to obtain the precise solution in the analysis. The plate is stiffened by concentric stiffeners horizontally to the corrugation direction. The discrete stiffener theory is adopted to consider the position of stiffener. To demonstrate the validity of the proposed approach, the comparison is made with the results of 3D ANSYS finite element solutions. Some numerical results are presented to check the effect of the geometric properties.

• Steel and Composite Structures
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• v.48 no.3
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• pp.275-291
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• 2023

This paper has focused on presenting vibration analysis of trapezoidal sandwich plates with 3D-graphene foam reinforced polymer matrix composites (GrF-PMC) core and FG wavy CNT-reinforced face sheets. The porous graphene foam possessing 3D scaffold structures has been introduced into polymers for enhancing the overall stiffness of the composite structure. Also, 3D graphene foams can distribute uniformly or non-uniformly in the plate thickness direction. The effective Young's modulus, mass density and Poisson's ratio are predicted by the rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The First-order shear deformation theory of plate is utilized to establish governing partial differential equations and boundary conditions for trapezoidal plate. The governing equations together with related boundary conditions are discretized using a mapping-generalized differential quadrature (GDQ) method in spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained using GDQ method. Validity of the current study is evaluated by comparing its numerical results with those available in the literature. It is explicated that 3D-GrF skeleton type and weight fraction, carbon nanotubes (CNTs) waviness and CNT aspect ratio can significantly affect the vibrational behavior of the sandwich structure. The plate's normalized natural frequency decreased and the straight carbon nanotube (w=0) reached the highest frequency by increasing the values of the waviness index (w).

• Wind and Structures
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• v.19 no.4
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• pp.405-420
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• 2014

This paper examines the nonlinear behaviour of corrugated steel plate shear walls under lateral pushover load. One of the innovations in these types of walls which have used in recent years is the use of the corrugated steel shear walls rather un-stiffness plates. In the last decades many experimental studies have been done on the on the corrugated steel shear walls. A finite element analysis that includes both material and geometric nonlinearities is employed for the investigation. A comparison is made between the behaviour of steel shear walls with sinusoidal corrugated plate and trapezoidal corrugated plate. The effects of parameters such as the thickness of the corrugated plate, the corrugation depth in the corrugated plates and the corrugation length of the infill of the corrugated plates, are investigated. The results of this study have demonstrated that in the wall with constant dimensions, the trapezoidal plates have higher energy dissipation, ductility and ultimate bearing than sinusoidal waves, while decreasing the steel material consumption.

• Steel and Composite Structures
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• v.51 no.1
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• pp.73-91
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• 2024

This paper has focused on presenting vibration analysis of trapezoidal sandwich plates with a damaged core and FG wavy CNT-reinforced face sheets. A damage model is introduced to provide an analytical description of an irreversible rheological process that causes the decay of the mechanical properties, in terms of engineering constants. An isotropic damage is considered for the core of the sandwich structure. The classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The First-order shear deformation theory of plate is utilized to establish governing partial differential equations and boundary conditions for the trapezoidal plate. The governing equations together with related boundary conditions are discretized using a mapping-generalized differential quadrature (GDQ) method in spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained using GDQ method. Validity of the current study is evaluated by comparing its numerical results with those available in the literature. After demonstrating the convergence and accuracy of the method, different parametric studies for laminated trapezoidal structure including carbon nanotubes waviness (0≤w≤1), CNT aspect ratio (0≤AR≤4000), face sheet to core thickness ratio (0.1 ≤ ${\frac{h_f}{h_c}}$ ≤ 0.5), trapezoidal side angles (30° ≤ α, β ≤ 90°) and damaged parameter (0 ≤ D < 1) are carried out. It is explicated that the damaged core and weight fraction, carbon nanotubes (CNTs) waviness and CNT aspect ratio can significantly affect the vibrational behavior of the sandwich structure. Results show that by increasing the values of waviness index (w), normalized natural frequency of the structure decreases, and the straight CNT (w=0) gives the highest frequency. For an overall comprehension on vibration of laminated trapezoidal plates, some selected vibration mode shapes were graphically represented in this study.

• Journal of Korean Association for Spatial Structures
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• v.21 no.4
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• pp.57-64
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• 2021

This paper conducted a comparative analysis of the shear buckling characteristics of trapezoidal and sinusoidal corrugated steel plates considering of their initial imperfection. Initial imperfection refers to the state where the shape of the corrugated plate is initially not perfect. As such, an initially imperfect shape was assumed using the eigen buckling mode. To calculate the buckling stress of corrugated steel plates, the linear buckling analysis used a boundary condition which was applied to the plate buckling analysis. For the comparison of trapezoidal and sinusoidal corrugation, the shape parameters were assumed using the case where the length and slope of each corrugation were the same, and the initial imperfection was considered to be from 0.1% to 5% based on the length of the steel plate. Here, for the buckling analysis, ANSYS, a commercial FEA program, was used. From the results of buckling analysis, the effect of overall initial imperfection showed that the larger the initial imperfection, the lower the buckling stress. However, in the very thin model, interaction or local buckling was dominant in the perfect shape, and in this case, the buckling stress did not decrease. Besides, the sinusoidal model showed higher buckling stress than the trapezoidal one, and the two corrugation shapes decreased in a similar way.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.7
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• pp.787-794
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• 2016

In this study, the exact rigidity and the free vibration of trapezoidal corrugated plate are analyzed by being based on the Kirchhoff's plate theory and the Ritz method. The previous rigidity of corrugated plate analyzed by considering just a geometric characteristic, a basic assumption and an equivalent idea can cause large errors in practical behaviors. Accordingly, the exact rigidity supplemented by correction factors of the theoretical rigidity is needed. Therefore an analysis on the exact rigidity and the free vibration using the rigidity for the plate is performed in this paper.

• Magazine of the Korean Society of Agricultural Engineers
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• v.19 no.4
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• pp.4533-4543
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• 1977

The purpose of this study was to investigate and compare flow discharges of rectangular, V-notch and trapezoidal type of cutthrooat flumes, and the published data for trapezoidal parshall flumes. And the trapezoidal cutthroat flumes were also compared in their accuracy of discharge measurements for various convergence ratios in the inlet section and divergence ratios in the outlet section. Five flumes were studied, and all the flumes were 45cm long with flat-bottom and were made of well-finished transparent acryl plate of 3mm thickness. One rectangular, one V-notch and three trapezoidal types were numbered 1 to 5 as shown in Fig. III-1. The measured depth of water was ranged from 5 to 20cm. The results obtained in this study are summarized as follows: 1. The general discharge equations for tested prototypes are listed for free flow in Table IV-1 and for submergence flow in Table IV-4. 2. In both free and submerged flow, the accuracy of the discharge formula obtained by this test is highly significant at 1% level as shown in Table IV-2 and Table IV-6. The accuracy of disharges measured depends upon the convergence and divergence ratios in the trapezoidal types: the less the ratios of convergence as well as divergence, the lower the accuracy. 3. Submergence ratios tend to increase in the order of flume number except flume No. 4. This implies that trapezoidal cutthroat flumes are more acceptable than rectangular or V-notch ones for free flow. 4. The transition submergence for the trapezoidal Parshall flumes ranges from 80-85 percent, which is slightly higher than the tested flume. However, the trapezoidal cutthroat flume No. 5 has higher transition submergence ratio, ranging from 73-78 percent, than other trapezoidal ones. The difference between the trapezoidal Parshall flumes and the trapezoidal cutthroat flumes in transition submergence seems small enough to be ignored in their field use. 5. Trapezoidal cutthroat flume is simple and economical to construct in existing openchannels whose shapes are generally trapezoidal. In order to obtain the best rating accuracy, flume No. 3 among the tested trapezoidal types is recommended, because it shows the highest accuracy for both free and submerged flow.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.513-520
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• 2003

As a trapezoidal corrugated steel plate has the sufficient stiffness out of plane direction without shear stiffener or thick plate, a use in the web of bridge structure is on the increase. However, there are no domestic design guides for shear buckling strength of corrugated plates. Therefore, foreign design specifications are analyzed about application methods and a numerical parametric study is used to get the relationship of the shear strength and geometric boundary conditions for corrugated plates. Elastic buckling finite element analysis is executed through eigenvalue analysis using the eight nodes five freedoms thin shell element. Parameters such as the width and height of panel and the thickness and height of web, are determined considering the factors to influence on the buckling of corrugated plate. Accuracy of shear buckling analysis is evaluated with theory of foreign buckling equations.

• Journal of the Korea institute for structural maintenance and inspection
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• v.18 no.6
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• pp.11-20
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• 2014

This paper aims at comparing and analyzing shear buckling characteristics between sinusoidal corrugation shape and trapezoidal one. For this, I adopted the equal-length trapezoidal corrugation and sinusoidal one for the analytical models, and analyzed their shear buckling characteristics through linear buckling analysis and on its theory. Generally, the shear buckling shapes of corrugated steel plates are classified into local buckling, global buckling, and interactive buckling from the two buckling modes. Sinusoidal corrugation shape, unlike trapezoidal corrugation, does not have flat sides, which causes another tendency in shear buckling mode. Especially, the changes and different aspects of shear buckling on the boundary between local buckling and global buckling appear in different corrugation shapes. According to the analysis results, interactive buckling mode appeared on the boundary of local buckling and global bucking in trapezoidal corrugation. However, in the case of corrugated steel plates with sinusoidal configuration, interactive buckling mode appeared in the part where global bucking takes place. Besides, trapezoidal shapes are of advantages on shear buckling resistance in the local buckling section, and so are sinusoidal shapes in the global buckling section.