• Journal of Ocean Engineering and Technology
• /
• v.24 no.1
• /
• pp.34-38
• /
• 2010

An analytical solution procedure for the dynamic response of beams with variable properties is developed by using an asymptotic solution and the Green's function. This asymptotic closed form solution is derived for the transverse vibration of beams under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is still found to be very accurate even in the case of large variation, such as step change in cross-section, mass, and tension. Therefore, this derived asymptotic closed form solution and the Green's function can be easily applied to find dynamic responses for various kind of beam vibration problems.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.8
• /
• pp.1883-1897
• /
• 1993

Interactive computer-aided analysis of mechanical systems has recently been undergoing an evolution due to highly efficient computer graphics. The industrial implementation of state-of-the-art analytical developments in mechanisms has been facilitated by computer-aided design packages because these rigid-body mechanism analysis programs dramatically reduce the time required for linkage design. This paper proposes a component modular approach to computeraided kinematic motion analysis for general planar multiloop mechanisms. Most multiloop mechanisms can be decomposed into serveral components. The kinematic properties (position, velocity, and acceleration) of every node can then be determined from the kinematic analysis of the corresponding component modules by a closed-form solution procedure. In this paper, 8 types of modules are defined and formulations for kinematic analysis of the component modules are derived. Then a computer-aided kinematic analysis program is developed using the proposed approach and the solution procedure of an example shows the effectiveness and accuracy on the approach.

• Journal of KSNVE
• /
• v.9 no.5
• /
• pp.966-974
• /
• 1999

This paper introduces modeling and its modal analysis procedure for exact and closed form solution of in-plane vibrations of general Timoshenko frame structures using exact dynamic element method(EDEM). The derivation procedure of the exact system dynamic matrices for Timoshenko beam frames is described. A new modal analysis procedure is also proposed since the conventional modal analysis schemes are not adequate for the proposed, exact system dynamic matrix. The proposed method provides exact modal parameters as well as all kinds of closed form solutions for general frame structures. Two numerical examples are presented for validating and illustrating the proposed method. The numerical study proves that the proposed method is useful for dynamic analysis of frame structures.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.24 no.4
• /
• pp.457-462
• /
• 2011

In this study, a simplified design procedure for friction dampers of a multi-story structure in order to reduce seismic response is proposed. To get insight for control effect of the structure with friction dampers is difficult, because of a nonlinear characteristic by a friction damper. Since a control force of a friction damper is influenced by coupling velocity between floors, adjoining modes are coupled. Thus structural response are derived by assuming steady-state response in resonance. As it is impossible that an exact solution is obtained for seismic load, first, a closed form solution can be achieved under harmonic vibration. Second, to convert a three-story building into a single-degree-of-freedom(SDOF) structure, modal analysis is performed. Third, an equivalent damping ratio is derived with utilizing closed form solution. And response reducing factor is proposed by it. Finally, friction force of a damper is designed for using response reducing factor, and then designed dampers are verified for seven seismic data. The nonlinear analysis results confirm the validity of the proposed procedure.

• Computers and Concrete
• /
• v.2 no.1
• /
• pp.55-77
• /
• 2005

The closed form solution of the equilibrium equations in the ultimate design of reinforced concrete sections under biaxial bending is presented. The stresses in the materials are described by the Model Code 1990 equations. Computation of the integral equations is performed generally in terms of all variables. The deformed shape of the section in the ultimate conditions is defined by Heaviside functions. The procedure is convenient for the use of mathematical manipulation programs and the results are easily included into nonlinear analysis codes. The equations developed for rectangular sections can be applied for other sections, such as T, L, I for instance, by decomposition into rectangles. Numerical examples of the developed model for rectangular sections and composed sections are included.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.6
• /
• pp.1421-1429
• /
• 1994

An algorithm is developed for solving the inverse kinematic problem of a 6-degree-of-freedom robot with a wrist offset for which the closed form inverse solutions are not obtainable, but knowledge of one joint variable allows closed form solutions of the remaining joint variables. The algorithm does not require Forward Kinematics nor Jacobian but uses the implicit kinematic relationships between joint variables and the given hand position. An iterative back substitution method is used to solve the inversion and the optimal conditions of the convergence are incoporated. An example is given to illustrate the concepts, the solution procedure and its convergency.

• Structural Engineering and Mechanics
• /
• v.44 no.5
• /
• pp.681-704
• /
• 2012

The dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analysed. The non-dimensional form of the motion equation of a beam crossed by a moving harmonic load is solved through a perturbation technique based on a two-scale temporal expansion, which permits a straightforward interpretation of the analytical solution. The dynamic response is expressed through a harmonic function slowly modulated in time, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude. In case of ideal Euler-Bernoulli beams with elastic rotational springs at the support points, starting from analytical expressions for eigenfunctions, closed form solutions for the time-history of the dynamic response and for its maximum value are provided. Two dynamic factors are discussed: the Dynamic Amplification Factor, function of the non-dimensional speed parameter and of the structural damping ratio, and the Transition Deamplification Factor, function of the sole ratio between the two non-dimensional parameters. The influence of the involved parameters on the dynamic amplification is discussed within a general framework. The proposed procedure appears effective also in assessing the maximum response of real bridges characterized by numerically-estimated mode shapes, without requiring burdensome step-by-step dynamic analyses.

• Earthquakes and Structures
• /
• v.26 no.2
• /
• pp.163-174
• /
• 2024

Dynamic equilibrium equations for finite element analysis were derived for the free field one-dimensional shear wave propagation through the horizontally layered soil deposits with the elastic half-space. We expressed Rayleigh's viscous damping consisting of mass and stiffness proportional terms. We considered two cases where damping matrices are defined in the total and relative displacement fields. Two forms of equilibrium equations are presented; one in terms of total motions and the other in terms of relative motions. To evaluate the performance of new equilibrium equations, we conducted two sets of site response analyses and directly compared them with the exact closed-form frequency domain solution. Results show that the base shear force as earthquake load represents the simpler form of equilibrium equation to be used for the finite element method. Conventional finite element procedure using base acceleration as earthquake load predicts exact solution reasonably well even in soil deposits with unrealistically high damping.

• Proceedings of the KSME Conference
• /
• 2000.11a
• /
• pp.541-547
• /
• 2000

This paper presents the closed-form forward kinematics of the 6-6 Stewart platform of planar base and moving platform. Based on algebraic elimination method and with one extra linear sensor, it first derives an 8th-degree univariate equation and then finds tentative solution sets out of which the actual solution is to be selected. In order to provide more exact solution despite the error between measured sensor value and the theoretical one, a correction method is also used. The overall procedure requires so little computation time that it can be efficiently used for realtime applications. In addition, unlike the iterative schemes e.g. Newton-Raphson, the algorithm does not require initial estimates of solution and is free of the problems that it does not converge to actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and accuracy of the developed algorithm.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.4
• /
• pp.981-989
• /
• 1995

A new weight function approach to determine SIF(stress intensity factor) using single-layer potential has been presented. The crack surface displacement field was represented by one boundary integral term whose kernel was modified from Kelvin's fundamental solution. The proposed method enables the calculation of SIF using only one SIF solution without any modification for the crack geometries symmetric in two-dimensional plane such as a center crack in a plate with or without an internal hole, double edge cracks, circumferential crack or radial cracks in a pipe. The application procedure to those crack problems is very simple and straightforward with only one SIF solution. The necessary information in the analysis is two reference SIFs. The analysis results using present closed-form solution were in good agreement with those of the literature.