• Steel and Composite Structures
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• v.52 no.6
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• pp.609-620
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• 2024

The impact problem of imperfect beams is crucial in engineering fields such as water conservancy and transportation. In this paper, the low velocity impact of graphene reinforced metal foam beams with geometric defects is studied for the first time. Firstly, an improved Hertz contact theory is adopted to construct an accurate model of the contact force during the impact process, while establishing the initial conditions of the system. Subsequently, the classical theory was used to model the defective beam, and the motion equation was derived using Hamilton's principle. Then, the Galerkin method is applied to discretize the equation, and the Runge Kutta method is used for numerical analysis to obtain the dynamic response curve. Finally, convergence validation and comparison with existing literature are conducted. In addition, a detailed analysis was conducted on the sensitivity of various parameters, including graphene sheet (GPL) distribution pattern and mass fraction, porosity distribution type and coefficient, geometric dimensions of the beam, damping, prestress, and initial geometric defects of the beam. The results revealed a strong inhibitory effect of initial geometric defects on the impact response of beams.

• Tribology and Lubricants
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• v.24 no.2
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• pp.90-95
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• 2008

An elastic-plastic contact analysis is developed using a semi-analytical method. The elastic contact is solved within a Hertz theorem. The reciprocal theorem with initial strains is then introduced, to express the surface geometry as a function of contact stress and plastic strains. The irreversible nature of plasticity leads to an incremental formulation of the elastic-plastic contact problem, and an algorithm to solve this problem is set up. Closed form expression, which give residual stresses and surface displacements from plastic strains, are obtained by integration of the reciprocal theorem. The distribution of contact stress, residual stress and plastic strain are obtained by the changed surface geometry.

• Tribology and Lubricants
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• v.14 no.4
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• pp.58-63
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• 1998

This paper presents a study of the elastohydrodynamic lubrication of elliptical contacts where lubricant entrainment coincides with the major axis of the Hertzian contact ellipse. A finite difference method and the Newton-Raphson method are applied to analyze the problem. Film contours and pressure distributions are compared with the results for lubricant entrainment coincides with the minor axis. Variations of the minimum and central film thicknesses with the radius ratio are also examined. The results showed that the present numerical scheme can be used generally in the analysis of the EHL of elliptical contacts where the lubricant entraining vector did not coincide with either of the principal axis of the conjunction.

• Tribology and Lubricants
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• v.31 no.5
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• pp.189-194
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• 2015

This paper focuses on the conformal contact problem. A typical example of conformal contact is the contact between a pin and hole. In particular, this paper focuses on the condition for assuming a contact stress field to be a Hertzian pressure profile by using well-known classical solutions associated with Hertzian contact. Persson first developed the conformal contact analysis method around half a century ago, but there have been no significant improvements since then. The present research also adopted this method, but developed new solutions from the viewpoint of application to structural design. The analysis began with a comparison between Persson°Øs conformal contact stress and the Hertzian stress fields. The next step was to check the differences in the normalized stress values of both. This study used the tolerance for the difference in the peak stresses of Persson°Øs solution and the Hertz solution to validate the Hertzian assumption. This gave the range for the difference in radii of the pin and hole when the contact force and mechanical properties of the material are specified. The results showed that, at a tolerance of 5%, the Hertzian assumption is valid if half of the contact angle is less than 35°ý. In addition, the Hertzian assumption holds even for a relatively long contact length, in contrast to the general incomplete contact problem. This paper discusses these results along with other aspects of the application to the design.

• Journal of Advanced Research in Ocean Engineering
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• v.4 no.4
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• pp.146-162
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• 2018

The unsteady problem of a rigid body impact onto a floating plate is studied. Both the plate and the water are at rest before impact. The plate motion is caused by the impact force transmitted to the plate through an elastic layer with viscous damping on the top of the plate. The hydrodynamic force is calculated by using the second-order model of plate impact by Iafrati and Korobkin (2011). The present study is concerned with the deceleration experienced by a rigid body during its collision with a floating object. The problem is studied also by a fully-nonlinear computational-fluid-dynamics method. The elastic layer is treated with a moving body-fitted grid, the impacting body with an immersed boundary method, and a discrete-element method is used for the contact-force model. The presence of the elastic layer between the impacting bod- ies may lead to multiple bouncing of them, if the bodies are relatively light, before their interaction is settled and they continue to penetrate together into the water. The present study is motivated by ship slamming in icy waters, and by the effect of ice conditions on conventional free-fall lifeboats.

• Structural Engineering and Mechanics
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• v.90 no.4
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• pp.357-370
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• 2024

Due to the fact that the mechanism of the effects of temperature and initial geometric imperfection on low-velocity impact problem of axially moving plates is not yet clear, the present paper is to fill the gap. In the present paper, the nonlinear dynamic behavior of axially moving imperfect graphene platelet reinforced metal foams (GPLRMF) plates subjected to lowvelocity impact in thermal environment is analyzed. The equivalent physical parameters of GPLRMF plates are estimated based on the Halpin-Tsai equation and the mixing rule. Combining Kirchhoff plate theory and the modified nonlinear Hertz contact theory, the nonlinear governing equations of GPLRMF plates are derived. Under the condition of simply supported boundary, the nonlinear control equation is discretized with the help of Gallekin method. The correctness of the proposed model is verified by comparison with the existing results. Finally, the time history curves of contact force and transverse center displacement are obtained by using the fourth order Runge-Kutta method. Through detailed parameter research, the effects of graphene platelet (GPL) distribution mode, foam distribution mode, GPL weight fraction, foam coefficient, axial moving speed, prestressing force, temperature changes, damping coefficient, initial geometric defect, radius and initial velocity of the impactor on the nonlinear impact problem are explored. The results indicate that temperature changes and initial geometric imperfections have significant impacts.

• Journal of Drive and Control
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• v.13 no.4
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• pp.45-51
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• 2016

The power train of a hydro-mechanical, continuously variable transmission for forklifts makes use of hydro-static units, hydraulic multi-wet disc brakes & clutches, and complex helical & planetary gears. The complex helical & planetary gears are very important parts of the transmission because of a strength problem. In the present study, we calculated the specifications of the complex helical & planetary gear train, and analyzed the gear bending and compressive stresses of the gears. It is necessary to analyze the gear bending and compressive stresses thoroughly for optimal design of the complex helical & planetary gears with respect to cost and reliability. In this paper, we analyze the actual gear bending and compressive stresses of complex helical & planetary gears using the Lewes & Hertz equation, and we also verify the calculated specifications of the complex helical & planetary gears by evaluating the results of the data of allowable bending and compressive stress using the Stress vrs Number of Cycles curves of gears.

• Journal of Korean Association for Spatial Structures
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• v.11 no.3
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• pp.77-83
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• 2011

Laminated composite plates have shown their superiority over metals in applications requiring high specific strength, high specific modulus, and so on. Therefore, they have used in various industry. However, they have poor resistance to impact compared to typical metal materials. To resolve this problem by many researchers for a variety of studies have been attempted. This study investigates characteristic of impact behavior of laminated composite plates due to initial stress. Using finite element program which involved the indentation law, we investigate characteristic of impact behavior of laminated composite plates due to initial stress.

• Journal of the Korean Society for Precision Engineering
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• v.6 no.3
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• pp.68-77
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• 1989

The surface rolling for cylindrical surface of a grey cast iron was carried out using a lathe with a simple newly-designed tool system. A surface rolling tool used was steel ball whose diameter was 3/8 inch (9.525mm) The effects of rolling feeds and number of rolling on surface rolling were investigated. The contact pressure between ball and workpiece which was considered as Hertz's contact problem was examined and the track of motion of a ball on the cylindrical surface of a work- piece was measured according to the rolling feed. The results obtained were as follows; 1. The roughness of the machined surface which was originally 5.3 .approx. 28 umRz decreased to 1.2 .approx. 5 umRz according to rolling feeds and numbers of rolling. 2. The hardness increased from Hv 260 to Hv 290 .approx. 310 through 2 .approx. 4 rollings according to the roughness of machined surfaces. 3. The reduction of diameter was found to be proportional to the variations of roughness of previous machined surfaces. About 60% to 90% of reduction in diameter was made during the first rolling process. 4. An equation relating the reduction of diameter and the variation of surface roughness after surface rolling was presented using a geometric surface model. 5. An equation for the calculation of dynamic contact area between pressure ball and workpiece according to the rolling feed was presented.

• Proceedings of the KIEE Conference
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• 1997.11a
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• pp.500-504
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• 1997

Current source inverter drives of auto sequentially commutated type are very popular in high power applications, because of simple power circuit configuration with four quadrant operation. But the six-step current output create harmonic problems and the input power factor of such a drive is not always good. In this respect pulse width modulated drives using gate turn off thyristors ( GTO ) are finding application, especially in traction drives. However the switching and snubber loses of a GTO do not permit the inverter switching frequency go beyond a few hundred hertz.This will again introduce low frequency harmonic problems. Multi level inverters of the 3-level and 5-level can be considered as an alternative to overcome the low switching frequency harmonic problem of the 2-level GTO inverters. But with multi level inverters the complexity of the power circuit increases. In this paper a combination of multi level ( 2-level and 3-level ) inverters and multi phase induction motor ( 3-phase and 6-phase) configurations are presented for high power VSI drives for traction applications with reduced inverter switching frequency requirements coupled with reduced voltage rating for the power switch.