• Structural Engineering and Mechanics
• /
• 제21권6호
• /
• pp.713-735
• /
• 2005

Due to the complexity of mathematical expressions, the literature concerning the free vibration analysis of plates carrying multiple three-degree-of-freedom (dof) spring-mass systems is rare. In this paper, the three degrees of freedom (dof's) for a spring-mass system refer to the translational motion of its lumped mass in the vertical ($\bar{z}$) direction and the two pitching motions of its lumped mass about the two horizontal ($\bar{x}$ and $\bar{y}$) axes. The basic concept of this paper is to replace each three-dof spring-mass system by a set of equivalent springs, so that the free vibration characteristics of a rectangular plate carrying any number of three-dof spring-mass systems can be obtained from those of the same plate supported by the same number of sets of equivalent springs. Since the three dof's of the lumped mass for each three-dof spring-mass system are eliminated to yield a set of equivalent springs, the total dof of the entire vibrating system is not affected by the total number of the spring-mass systems attached to the rectangular plate. However, this is not true in the conventional finite element method (FEM), where the total dof of the entire vibrating system increases three if one more three-dof spring-mass system is attached to the rectangular plate. Hence, the computer storage memory required by using the presented equivalent spring method (ESM) is less than that required by the conventional FEM, and the more the total number of the three-dof spring-mass systems attached to the plate, the more the advantage of the ESM. In addition, since manufacturing a spring with the specified stiffness is much easier than making a three-dof spring-mass system with the specified spring constants and mass magnitude, the presented theory of replacing a three-dof spring-mass system by a set of equivalent springs will be also significant from this viewpoint.

• 대한기계학회논문집A
• /
• 제31권12호
• /
• pp.1165-1172
• /
• 2007

The spacer grid set is a part of a nuclear fuel assembly. The set has a spring and the spring supports the fuel rods safely. Although material nonlinearity is involved in the deformation of the spring, nonlinearity has not been considered in design of the spring. Recently a nonlinear response structural optimization method has been developed using equivalent loads. It is called nonlinear response optimization equivalent loads (NROEL). In NROEL, the external loads are transformed to the equivalent loads (EL) for linear static analysis and linear response optimization is carried out based on the EL in a cyclic manner until the convergence criteria are satisfied. EL is the load set which generates the same response field of linear analysis as that of nonlinear analysis. Shape optimization of the spring is carried out based on EL. The objective function is defined by minimizing the maximum stress in the spring while mass is limited and the support force of the spring is larger than a certain value. The results are verified by nonlinear response analysis. ABAQUS is used for nonlinear response analysis and GENESIS is employed for linear response optimization.

• Structural Engineering and Mechanics
• /
• 제28권6호
• /
• pp.659-676
• /
• 2008

The reports regarding the free vibration analysis of uniform beams carrying single or multiple spring-mass systems are plenty, however, among which, those with inertia effect of the helical spring(s) considered are limited. In this paper, by taking the mass of the helical spring into consideration, the stiffness and mass matrices of a spring-mass system and an equivalent mass that may be used to replace the effect of a spring-mass system are derived. By means of the last element stiffness and mass matrices, the natural frequencies and mode shapes for a uniform cantilever beam carrying any number of springmass systems (or loaded beam) are determined using the conventional finite element method (FEM). Similarly, by means of the last equivalent mass, the natural frequencies and mode shapes of the same loaded beam are also determined using the presented equivalent mass method (EMM), where the cantilever beam elastically mounted by a number of lumped masses is replaced by the same beam rigidly attached by the same number of equivalent masses. Good agreement between the numerical results of FEM and those of EMM and/or those of the existing literature confirms the reliability of the presented approaches.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2007년도 춘계학술대회A
• /
• pp.694-699
• /
• 2007

The spacer grid set is a part of a nuclear fuel assembly. The set has a spring and the spring supports the fuel rods safely. Although material nonlinearity is involved in the deformation of the spring,nonlinearity has not been considered in design of the spring. Recently a nonlinear response structural optimization method has been developed using equivalent loads. It is called nonlinear response optimization equivalent loads (NROEL). In NROEL, the external loads are teansformed to the equivalent loads (EL) for linear static analysis and linear response optimization is carried out based on the EL in a cyclic manner until the convergence criteria are satisfied. EL is the load set which generates the same response no EL. The objective function is defined by minimizing the maximum stress in the spring while is limited and the support force of the spring is larger than a certain value. The results are verified by nonlinear. ABAQUS is used for nonlinear response analysis and GENESIS is employed for linear response optimization.

• 한국기계가공학회지
• /
• 제10권4호
• /
• pp.22-30
• /
• 2011

This study analyzes harmonic vibration with natural frequency according to the configuration of damper clutch. In the case of double spring, equivalent stress at same direction of the revolution at inner and outer coil spring is over 30% as compared with at its opposite direction. Natural frequency or harmonic response with maximum deformation in case of the less coil pitch is below 3Hz as compared with in case of the more coil pitch. As the coil pitch of damper spring as the case 2 or 4 becomes smaller, its mass and deformation can be large. In these cases, spring constant and natural frequency become smaller. In the case 5 or 6 of double spring at natural vibration or harmonic response, the frequency becomes over 300Hz. As the result of this study is applied by the design of damper spring, the damage at its connected part is prevented and the durability can be predicted.

• Structural Engineering and Mechanics
• /
• 제16권3호
• /
• pp.341-360
• /
• 2003

The goal of this paper is to determine the eigenvalues of a uniform rectangular plate carrying any number of spring-damper-mass systems using an analytical-and-numerical-combined method (ANCM). To this end, a technique was presented to replace each "spring-damper-mass" system by a massless equivalent "spring-damper" system with the specified effective spring constant and effective damping coefficient. Then, the mode superposition approach was used to transform the partial differential equation of motion into the matrix equation, and the eigenvalues of the complete system were determined from the associated characteristic equation. To verify the reliability of the presented theory, all numerical results obtained from the ANCM were compared with those obtained from the conventional finite element method (FEM) and good agreement was achieved. Since the order of the property matrices for the equation of motion obtained from the ANCM is much lower than that obtained from the FEM, the CPU time required by the ANCM is much less than that by the FEM.

• Structural Engineering and Mechanics
• /
• 제47권3호
• /
• pp.443-454
• /
• 2013

A leaf spring, especially the longitudinal type is liable and persistent element in automotive suspension system. In the present scenario the composite materials are widely used in the automobile industries has shown a great interest in the replacement of steel spring due to high strength by weight ratio. Previous investigations focused on stresses and displacement analysis of single leaf spring for different materials. The present work aims to design and analysis of leaf spring for two different cases by considering the Young's modulus to yield strength ratio. In the first case the analysis deals with the design and analysis of a single cantilever solid triangle beam which is an equivalent beam of a spring with three leaves having uniform strength. In the second case a 3-beams of rectangular cross section has been considered which is equivalent to a spring with three leaves. The analysis was carried out based on contact mechanics approach. The results were compared, that the fiberglass composite leaf spring is suitable for high loading capacity, reliability and efficiency.

• 한국자동차공학회논문집
• /
• 제7권9호
• /
• pp.89-96
• /
• 1999

This paper presents the optimization design technique on the joint stiffness and section characteristic factors of chassis frame, by using beam and spring elements in a given design package. Two correction methods are used for the optimization design of chassis frame. First is the equivalent inertia of moment method in relation to the section characteristic factors of joint zones, which are thickness , width and height of frame channel section. Second is the rotational spring element with joint stiffness of joint zones. The CAE example shows that the relationship of section characteristic factors and joint stiffness can effectively be used in designing chassis frame. In this point, if static and dynamic targets are given, the joint-zone and section characteristic factors of chassis frame intended may be designed and defined by using beam and rotational spring elements.

• 소음진동
• /
• 제5권4호
• /
• pp.537-542
• /
• 1995

In this paper the method of modeling and optimization for the joint of the vehicle structure is proposed. First it is described that the method of substituting equivalent beam elements to spring elements for the joint. The stiffnesses of the spring elementsare calculated using the section properties of equivalent beam elements. To get required dynamic characteristics section properties of equivalent beam element are set to design variables and optimized. The study shows that joint stiffnesses can be effectively determined in designing vehicle structure.

• 대한전기학회논문지:전기기기및에너지변환시스템부문B
• /
• 제51권7호
• /
• pp.370-378
• /
• 2002

As resent trends in structural construction have been to build taller and larger structures than any time in the past, they have had high flexibility and low damping that can cause large vibration response under severe environmental loading such as earthquakes, winds, and mechanical excitations. The damper with mass and spring is one approach to safeguarding the structure against excessive vibrations. In this paper, the lumped electrical circuit approach of mass/spring system is used to model the mechanical aspects according to the frequency. Therefore, the mass/spring system can be dealt with here and linked with the equivalent circuit of electric linear oscillatory actuator(LOA). Analysis models are two types of vibration control system, active mass damper(AMD) and hybrid mass damper(HMD). AMD consists of the moving coil LOA with mass only The LOA of HMD with mass and spring is composed of the fixed coil and the movable permanent magnet(PM) field part. The PM field part composed magnet modules and iron coke, is the damper marts itself. We Present the motional resistance and reactance of mass/spring system and the system impedance of AMD and HMD according to the frequency.