• Structural Engineering and Mechanics
• /
• v.55 no.3
• /
• pp.655-674
• /
• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

• Journal of Institute of Control, Robotics and Systems
• /
• v.7 no.3
• /
• pp.198-208
• /
• 2001

In this paper, vibration suppression of an elastic beam fixed on a moving cart and carrying a fixed or moving mass is considered. A modified pulse sequence method with RIC(Robust Internal-loop Compensator) is proposed to suppress the single model residual vibration and to get accurate positioning of the beam-mass-cart system. The performance of the proposed input preshaping method is compared with that of the previous ones through simulations and experiments. Using the proposed method, it is able to suppress the initial vibration of the beam-mass-cart system carrying a concentrated mass. Accurate PTP(point-to-point) positioning of the moving mass without residual vibration is also obtained experimentally by modifying the proposed pulse sequence method. Finally, the proposed input preshaping method is applied successfully to the system to follow square trajectories of the moving mass without residual vibration.

• Proceedings of the Korean Society For Composite Materials Conference
• /
• 1999.11a
• /
• pp.5-14
• /
• 1999

Free vibration characteristics of a cantilevered laminated composite beam with multiple non-propagating transverse open cracks are investigated. In the present analysis a special ply-angle distribution referred to as asymmetric stiffness configuration inducing the elastic coupling between chord-wise bending and extension is considered. The multiple open cracks are modelled as equivalent rotational springs whose spring constants are calculated based on the fracture mechanics of composite material structures. Governing equations of a composite beam with open cracks are derived via Hamilton's Principle and Timoshenko beam theory encompassing transverse shear and rotary inertia effect is adopted. The effects of various parameters such as the ply angle, fiber volume fraction, crack numbers, crack positions and crack depthes on the free vibration characteristics of the beam with multiple cracks are highlighted. The numerical results show that the existence of the multiple cracks in an anisotropic composite beam affects the free vibration characteristics in a more complex fashion compared with the beam with a single crack.

• Structural Engineering and Mechanics
• /
• v.19 no.5
• /
• pp.477-501
• /
• 2005

In this study, a new smart beam finite element is proposed for the finite element modeling of beam-type smart structures that are equipped with bonded plate-type piezoelectric sensors and actuators. Constitutive equations for the direct piezoelectric effect and converse piezoelectric effect of piezoelectric materials are considered in the formulation. By using a variational principle, the equations of motion for the smart beam finite element are derived. The proposed 2-node beam finite element is an isoparametric element based on Timoshenko beam theory. The proposed smart beam finite element is applied to the free vibration control adopting a constant gain feedback scheme. The electrical force vector, which is obtained in deriving an equation of motion, is the control force equivalent to that in existing literature. Validity of the proposed element is shown through comparing the analytical results of the verification examples with those of other previous researchers. With the use of smart beam finite elements, simulation of free vibration control is demonstrated by sensing the voltage of the piezoelectric sensors and by applying the voltages to the piezoelectric actuators.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2010.05a
• /
• pp.499-499
• /
• 2010

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11a
• /
• pp.403-403
• /
• 2002

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the spectral element model is formulated for the axially moving Timoshenko beam under a uniform axial tension. (omitted)

• Structural Engineering and Mechanics
• /
• v.77 no.5
• /
• pp.587-599
• /
• 2021

Based on Euler-Bernoulli beam theory and continuous element method, the free vibration of bi-dimensional functionally graded beams is investigated. It is assumed that the material properties vary exponentially along the beam thickness and length. The characteristic frequency equations of beams with different boundary conditions are obtained by transfer matrix method. The validity of the proposed method is assessed through comparison with available results. Parametric studies are carried out to analyze the influences of the gradient indexes and the beam slenderness ratio on the natural frequencies of bi-dimensional functionally graded beams.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1997.04a
• /
• pp.199-204
• /
• 1997

This paper proposes a new 'finite element for the vibration analysis of thin-walled beams of rectangular closed sections. To predict the dynamic behavior of the thin-walled beam accurately, warping and distortion deformations should be considered for the analysis. The motivation of the present development is that conventional beam elements cannot describe correctly deformations such as warping and lozenging which are not negligible in some situations. Several numerical examples are studied to confirm the validity of the present element.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2005.05a
• /
• pp.707-710
• /
• 2005

In this paper, we studied about the dynamic behavior of a cracked rotating cantilever beam. The influences of a rotating angular velocity, the crack depth and the crack position on the dynamic behavior of a cracked cantilever beam have been studied by the numerical method. The cracked cantilever beam is modeled by the Euler-Bernoulli beam theory. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The lateral tip displacement and the axial tip deflection of a rotating cantilever beam is more sensitive to the rotating angular velocity than the depth and position of crack. Totally, as the crack depth is increased, the natural frequency of a rotating cantilever beam is decreased in the first and second mode of vibration.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2007.05a
• /
• pp.215-218
• /
• 2007

In this paper a dynamic behavior(natural frequency) of a cracked cantilever beam subjected to follower force is presented. In addition, an analysis of the flutter and buckling instability of a cracked cantilever beam subjected to a follower compressive load is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter insstability based on the variation of the first two resonant frequencies of the beam. Besides, the effect of the crack's intensity and location on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.