• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.695-700
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• 2000

The dynamic stability of spinning beam with free boundary conditions for both edges subjected to a tip follower force $P_0+P_1cos{\Omega}t$ is analyzed. It is studied that the beam has a concentrated mass. and then the effects of the axial locations of the mass are studied. The beam is modelled with the Timoshenko type shear deformations. The Hamilton's principle is used to derive the equations of motion, and the critical spinning speed of a beam subjected to a follower force with various non-dimensional parameters is investigated. The finite elements are used with $C^0$ continuity to analyze the spinning beam model, and the method of multiple scales is tried to investigate the dynamic instability regions. The governing equations of motion involve periodic coefficients, which are not in the form of standard Mathieu-Hill equations. The result shows that the concentrated mass increases the dynamic stability of the spinning free-free beam subjected to a thrust.

• Journal of Mechanical Science and Technology
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• v.14 no.2
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• pp.159-167
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• 2000

A computational method for the dynamic analysis of a constrained mechanical system is presented in this paper. The partial velocity matrix, which is the null space of the Jacobian of the constraint equations, is used as the key ingredient for the derivation of reduced equations of motion. The acceleration constraint equations are solved simultaneously with the equations of motion. Thus, the total number of equations to be integrated is equivalent to that of the pseudo generalized coordinates, which denote all the variables employed to describe the configuration of the system of concern. Two well-known conventional methods are briefly introduced and compared with the present method. Three numerical examples are solved to demonstrate the solution accuracy, the computational efficiency, and the numerical stability of the present method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.743-750
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• 2000

This paper presents an equivalent linearization method and application to the equations of motion of a 6 degree-of-freedom PRRS HexaSlide type parallel manipulators which are characterized as the architecture with constant link lengths that are attached to moving sliders on the ground and to a mobile platform. Since dynamic equations of parallel manipulators are complicated and highly nonlinear, control bandwidth, adjustable control gain as well as vibration characteristics cannot be easily found. The proposed equivalent linearization method can be applied over specified workspace as well as on a path of mobile platform. Through an equivalent linearization method, one can easily get a simple linear dynamic model. This linearized dynamic model may be utilized in a simplified computed torque control strategy.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.1
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• pp.101-111
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• 2001

Recursive formulas have been effective in solving the equations of motion for large scale constratined mechanical sys-tems. However, derivation of the formulas has been limited to individual terms in the equations of motion, such as veloci-ty, acceleration. and generalized forces. The recursive formulas are generalized in this paper. The velocity transformation method is employed to transform the equations of motion from Cartesian to the joint spaces. Computational structure of the equations of motion in the joint space is carefully examined to classify all necessary computational operations into sev-eral categories. The generalized recursive formula for each category is then developed and applied whenever such a cate-gory of computation is encountered. Since the velocity transformation method yields the equations of motion in a compact form and computational efficiency is achieved by generalized recursive formulas, the proposed method is not only easy to implement but is also efficient. A library of generalized recursive formulas is developed to implement a dynamic analysis algorithm using backward difference.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.8
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• pp.791-799
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• 2012

In this paper free vibration analysis of symmetric and cross-ply elastic laminated shells based on FSDT was performed through discretization of equations of motion and boundary condition. Structural model of laminated composite cylindrical shells subjected to a combination of magnetic and thermal fields is developed via Hamilton's variational principle. These coupled equations of motion are based on the electromagnetic equations(Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. Variations of dynamic characteristics of composite shells with applied magnetic field, temperature gradient, and stacking sequence are investigated and pertinent conclusions are derived.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.10a
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• pp.653-660
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• 2012

In this paper free vibration analysis of symmetric and cross-ply elastic laminated shells based on FSDT with two different boundary conditions(C-C, S-S) was performed through discretization of equations of motion and boundary condition. Model of laminated composite cylindrical shells subjected to a combination of magnetic and thermal fields is developed via Hamilton's variational principle. These coupled equations of motion are based on the electromagnetic equations (Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. Variations of dynamic characteristics of composite shells with applied magnetic field, temperature gradient, and stacking sequence for each boundary conditions are investigated and pertinent conclusions are derived.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.451-456
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• 2006

This paper is concerned with the dynamic modeling and controller design for a cylindrical shell equipped with MFC actuators. The dynamic model was derived by using Rayleigh-Ritz method based on Donnel-Mushtari shell theory. The actuator and sensors for the MFC actuator equations were derived based on pin-force model. The boundary conditions at both ends were assumed to be shear diaphragm. After calculating the natural vibration characteristics, the positive position feedback controller was designed to cope with the first two modes. To this end, the equations of motion were reduced to modal equations of motion by considering the modes of interest. The theoretical results show that vibrations can be successfully suppressed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.75-80
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• 2007

This paper is concerned with the dynamic modeling and controller design for a cylindrical shell equipped with MFC actuators. The dynamic model was derived by using Rayleigh-Ritz method based on Donnel-Mushtari shell theory. The actuator and sensors for the MFC actuator equations were derived based on pinforce model. The boundary conditions at both ends were assumed to be shear diaphragm. After calculating the natural vibration characteristics, the positive position feedback controller was designed to cope with the first two modes. To this end, the equations of motion were reduced to modal equations of motion by considering the modes of interest. The theoretical results show that vibrations can be successfully suppressed.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.366-371
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• 2001

Dynamic stability of an oscillating cantilever plate is investigated in this paper. The equations of motion include harmonically oscillating parameters which originate from the motion-induced stiffness variation. Using the multiple scale perturbation method is employed to obtain a stability diagram. The tability diagram shows that relatively large unstable regions exist when the frequency of oscillation is near twice the frequencies of the 1st torsion natural mode and the 1st chordwide bending mode.

• Structural Engineering and Mechanics
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• v.54 no.6
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• pp.1153-1174
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• 2015

Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.