• Coupled systems mechanics
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• 제2권2호
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• pp.159-174
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• 2013

The present work aims at investigating the nonlinear dynamics, bifurcations, and stability of an axially accelerating beam with an intermediate spring-support. The problem of a parametrically excited system is addressed for the gyroscopic system. A geometric nonlinearity due to mid-plane stretching is considered and Hamilton's principle is employed to derive the nonlinear equation of motion. The equation is then reduced into a set of nonlinear ordinary differential equations with coupled terms via Galerkin's method. For the system in the sub-critical speed regime, the pseudo-arclength continuation technique is employed to plot the frequency-response curves. The results are presented for the system with and without a three-to-one internal resonance between the first two transverse modes. Also, the global dynamics of the system is investigated using direct time integration of the discretized equations. The mean axial speed and the amplitude of speed variations are varied as the bifurcation parameters and the bifurcation diagrams of Poincare maps are constructed.

• 소음진동
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• 제3권3호
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• pp.245-251
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• 1993

The problem of sound radiation from infinite elastic beams under the action on harmonic moving line forces is studies. The reaction due to fluid loading on the vibratory response of the beam is taken into account. The beam is assumed to occupy the plane z=0 and to be axially infinite. The beam material and elastic foundation are assumed to be lossless and Bernoulli-Euler beam theory including a tension force (T), damping coefficient (C) and stiffness of foundation $(\kappa_s)$ will be employed. The non-dimensional sound power is derived through integration of the surface intensity distribution over the entire beam. The expression for sound power is integrated numerically and the results examined as a function of Mach number (M), wavenumber ratio$(\gamma{)}$ and stiffness factor $(\Psi{)}$. Here, our purpose is to explain the response of sound power over a number of non-dimensional parameters describing tension, stiffness, damping and foundation stiffness.

• 한국산학기술학회:학술대회논문집
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• 한국산학기술학회 2011년도 춘계학술논문집 2부
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• pp.529-532
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• 2011

A theoretical model has been studied to describe the sound radiation analysis for structure vibration noise of vehicle tires under the action of random moving line forces. When a tire is analyzed, it had been modeled as curved beams with distributed springs and dash pots that represent the radial, tangential stiffness and damping of tire, respectively. The reaction due to fluid loading on the vibratory response of the curved beam is taken into account. The curved beam is assumed to occupy the plane y=0 and to be axially infinite. The expression for sound power is integrated numerically and the results examined as a function of Mach number, wave-number ratio and stiffness factor. The experimental investigation for structure vibration noise of vehicle tire under the action of random moving line forces has been made. Based on the Spatial Transformation of Sound Field techniques, the sound power and sound radiation are measured. Results strongly suggest that operation condition in the tire material properties and design factors of the tire govern the sound power and sound radiation characteristics.

• 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.

• Advances in nano research
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• 제16권2호
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• pp.141-154
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• 2024

This study aims to develop explicit models to investigate thermo-mechanical interactions in moving nanobeams. These models aim to capture the small-scale effects that arise in continuous mechanical systems. Assumptions are made based on the Euler-Bernoulli beam concept and the fractional Zener beam-matter model. The viscoelastic material law can be formulated using the fractional Caputo derivative. The non-local Eringen model and the two-phase delayed heat transfer theory are also taken into account. By comparing the numerical results to those obtained using conventional heat transfer models, it becomes evident that non-localization, fractional derivatives and dual-phase delays influence the magnitude of thermally induced physical fields. The results validate the significant role of the damping coefficient in the system's stability, which is further dependent on the values of relaxation stiffness and fractional order.

• 한국음향학회:학술대회논문집
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• 한국음향학회 2004년도 추계학술발표대회논문집 제23권 2호
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• pp.221-224
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• 2004

A theoretical model has been studied to describe the sound radiation analysis for structure vibration noise of vehicle tires under the action of random moving line forces. When a tire is analyzed, it had been modeled as curved beams with distributed springs and dash pots that represent the radial , tangential stiffness and damping of tire, respectively. The reaction due to fluid loading on the vibratory response of the curved beam is taken into account. The curved beam is assumed to occupy the plane y=0 and to be axially infinite. The curved beam material and elastic foundation are assumed to be lossless Bernoulli-Euler beam theory including a tension force, damping coefficient and stiffness of foundation will be employed. The expression for sound power is integrated numerically and the results examined as a function of Mach number, wave-number ratio and stiffness factor. The experimental investigation for structure vibration noise of vehicle tire under the action of random moving line forces has been made. Based on the Spatial Transformation of Sound Field techniques, the sound power and sound radiation are measured. Results strongly suggest that operation condition in the tire material properties and design factors of the tire govern the sound power and sound radiation characteristics.