• Structural Engineering and Mechanics
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• 제15권6호
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• pp.705-716
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• 2003

Gradient elastic flexural beams are dynamically analysed by analytic means. The governing equation of flexural beam motion is obtained by combining the Bernoulli-Euler beam theory and the simple gradient elasticity theory due to Aifantis. All possible boundary conditions (classical and non-classical or gradient type) are obtained with the aid of a variational statement. A wave propagation analysis reveals the existence of wave dispersion in gradient elastic beams. Free vibrations of gradient elastic beams are analysed and natural frequencies and modal shapes are obtained. Forced vibrations of these beams are also analysed with the aid of the Laplace transform with respect to time and their response to loads with any time variation is obtained. Numerical examples are presented for both free and forced vibrations of a simply supported and a cantilever beam, respectively, in order to assess the gradient effect on the natural frequencies, modal shapes and beam response.

• Structural Engineering and Mechanics
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• 제48권4호
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• pp.519-545
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• 2013

An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and rotation are comprised into single equation with deflection and analytical solutions of natural vibrations for different boundary conditions are given. Double frequency phenomenon for simply supported beam is investigated. The Timoshenko beam theory is modified by decomposition of total deflection into pure bending deflection and shear deflection, and total rotation into bending rotation and axial shear angle. The governing equations are condensed into two independent equations of motion, one for flexural and another for axial shear vibrations. Flexural vibrations of a simply supported, clamped and free beam are analysed by both theories and the same natural frequencies are obtained. That fact is proved in an analytical way. Axial shear vibrations are analogous to stretching vibrations on an axial elastic support, resulting in an additional response spectrum, as a novelty. Relationship between parameters in beam response functions of all type of vibrations is analysed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.1333-1337
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• 2000

The flexural vibration of laminated composite beams with active and passive constrained-layer damping has been investigated to design structure with maximum possible damping capacity. The equations of motion are derived for flexural vibrations of symmetrical, multi-layer laminated beams. The damping ratio and modal damping of the first bending mode are calculated by means of iterative complex eigensolution method. This paper addresses a design strategy of laminated composite under flexural vibrations with active control.

• Structural Engineering and Mechanics
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• 제44권4호
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• pp.521-538
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• 2012

In this study, the transverse vibrations of an axially moving flexible beams resting on multiple supports are investigated. The time-dependent velocity is assumed to vary harmonically about a constant mean velocity. Simple-simple, fixed-fixed, simple-simple-simple and fixed-simple-fixed boundary conditions are considered. The equation of motion becomes independent from geometry and material properties and boundary conditions, since equation is expressed in terms of dimensionless quantities. Then the equation is obtained by assuming small flexural rigidity. For this case, the fourth order spatial derivative multiplies a small parameter; the mathematical model converts to a boundary layer type of problem. Perturbation techniques (The Method of Multiple Scales and The Method of Matched Asymptotic Expansions) are applied to the equation of motion to obtain approximate analytical solutions. Outer expansion solution is obtained by using MMS (The Method of Multiple Scales) and it is observed that this solution does not satisfy the boundary conditions for moment and incline. In order to eliminate this problem, inner solutions are obtained by employing a second expansion near the both ends of the flexible beam. Then the outer and the inner expansion solutions are combined to obtain composite solution which approximately satisfying all the boundary conditions. Effects of axial speed and flexural rigidity on first and second natural frequency of system are investigated. And obtained results are compared with older studies.

• 한국세라믹학회지
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• 제40권11호
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• pp.1062-1066
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• 2003

Design of a piezoelectric actuator for the ultrasonic motor must ensure that contact point has elliptic trajectory of movement. The new idea of an elliptic trajectory formation of the piezoelectric actuator is investigated in the paper. Shaking beam for the piezoelectric linear ultrasonic motor was introduced to realize this new idea. The principle is based on the excitation of longitudinal and flexural vibrations of the actuator by using two sources of longitudinal mechanical vibrations shifted by $\pi$/2. Mode-frequency and harmonic response analyses of the actuator based on FEM have been carried out. The moving trajectory of the contact point has been defined. Finally, The experimental research of shaking beam has been confirmed an opportunity of the elliptic trajectory reception with the help of one stable mode of the vibrations.

• International Journal of Precision Engineering and Manufacturing
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• 제4권1호
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• pp.37-42
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• 2003

Active control of flexural vibrations of smart laminated composite beams has been carried out using piezoceramic sensor/actuator and viscoelastic material. The beams with passive constrained layer damping have been analyzed by formulating the equations of motion through the use of extended Hamilton's principle. The dynamic characteristics such as damping ratio and modal damping of the beam are calculated for various fiber orientations by means of iterative complex eigensolution method. This paper addresses a design strategy of laminated composite under flexural vibrations to design structure with maximum possible damping capacity.

• 한국소음진동공학회논문집
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• 제12권12호
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• pp.964-969
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• 2002

The flexural vibration of laminated composite beams with passive constrained layer damping has been investigated to design structure with maximum possible damping capacity. The equations of motion are derived for flexural vibrations of symmetrical, multi-layer laminated beams. The damping ratio and modal damping of the first bending mode are calculated by means of Iterative complex eigensolution method. This paper addresses a design strategy of laminated composite under flexural vibrations.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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• pp.764-767
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• 2005

This paper deals with the flexural-torsional free vibrations of circular strip foundations with a variable breadth. The breadth of strip foundation varies with the linear functional fashion, which is symmetric about the mid-arc. Differential equations governing free vibrations of such foundations are derived, in which Winkler foundation is considered as the model of elastic soils. Effects of the rotatory and torsional inertias and shear deformation are included in the governing equations. Differential equations are numerically solved to calculate the natural frequencies. In the numerical examples, the free-free end constraint is considered. Effects of the rotatory and torsional inertias and shear parameter on the natural frequencies are reported. Parametric studies between frequency parameters and various system parameters are investigated.

• 소음진동
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• 제11권3호
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• pp.416-421
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• 2001

The flexural vibration of laminated composite beams with an electro-rheological(ER) fluid has been investigated to design a structure with maximum possible damping capacity. The equations of motion are derived for flexural vibrations of symmetrical, mu1ti-layer laminated beams. The damping radio and modal damping of the first bending mode are calculated by means of iterative complex eigensolution method. Finite element method is used for the analysis of dynamic characteristics of the laminated composite beams with an ER fluid. For the validation of modeling methodology using viscoelastic theory the predicted dynamic properties are compared to the measured ones by author's previous work. They are in good agreement. This paper addresses a design strategy of laminated composite under flexural vibrations with an ER fluid.

• 한국소음진동공학회논문집
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• 제11권7호
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• pp.261-266
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• 2001

The flexural vibration of laminated composite beams with active and passive constrained layer damping has been investigated to design a structure with maximum possible damping capacity. The equations of motion are derived fro flexural vibrations of symmetrical,. multi-layer laminated beams. The damping ratio and model damping of the first bending mode are calculated by means of iterative complex eigensolution method. The direct negative velocity feedback control is used for the active constrained layer damping. It is shown that the flexible laminated beam is more effective in the vibration control for both active and passive constrained layer damping. and this paper addresses a design strategy of laminated composite under flexural vibrations with constrained layer damping.