• International Journal of Precision Engineering and Manufacturing
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• v.3 no.4
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• pp.54-63
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• 2002

In recent years, mechanical systems such as high speed vehicles and railway trains moving on elastic beam structures have become a very important issue to consider. In this paper, a general approach, which can predict the dynamic behavior of a constrained mechanical system moving on a flexible beam structure, is proposed. Various supporting conditions for the foundation support are considered for the elastic beam structure. The elastic structure is assumed to be a non-uniform and linear Bernoulli-Euler beam with a proportional damping effect. Combined differential-algebraic equation of motion is derived using the multi-body dynamics theory and the finite element method. The proposed equations of motion can be solved numerically using the generalized coordinate partitioning method and predictor-corrector algorithm, which is an implicit multi-step integration method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.1054-1059
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• 2002

A linearly tapered beam immersed partially in other material is considered and is modelled as a linearly tapered Bernoulli-Euler beam fixed at the bottom with a concentrated mass at the top. Its governing equations is derived and its free vibration analysis is performed for various boundary conditions. And the rotatory inertia of the eccentric lumped tip mass is considered. The problem of determining the natural frequencies leads to an eighth order determinant. The solutions of the frequency equations are obtained numerically. The non-dimensional frequency parameters are given in tabular form and the influence of non-dimensional parameters on natural frequency is discussed for various conditions.

• Structural Engineering and Mechanics
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• v.45 no.1
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• pp.69-93
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• 2013

The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton's Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.

• Structural Engineering and Mechanics
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• v.47 no.3
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• pp.307-329
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• 2013

The bending problem of Euler-Bernoulli discontinuous beams is dealt with, in which the discontinuities are due to the loads and eventually to essential constrains applied along the beam axis. In particular, the loads are modelled as random delta-correlated processes acting along the beam axis, while the ulterior eventual discontinuities are produced by the presence of external rollers applied along the beam axis. This kind of structural model can be considered in the static study of bridge beams. In the present work the exact expression of the response quantities are given in terms of means and variances, thanks to the use of the stochastic analysis rules and to the use of the generalized functions. The knowledge of the means and the variances of the internal forces implies the possibility of applying the reliability ${\beta}$-method for verifying the beam.

• Structural Engineering and Mechanics
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• v.63 no.1
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• pp.11-21
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• 2017

In this paper, the efficiency and the accuracy of classical (CE) and high order (HE) beam element are improved by introducing two novel techniques. The first proposed element (FPE) provides an alternative for (HE) by taking the mode shapes of the clamped-clamped (C-C) beam into account. The second proposed element (SPE) which could be utilized instead of (CE) and (HE) considers not only the mode shapes of the (C-C) beam but also some virtual nodes. It is numerically proven that the eigenvalue problem and the frequency response function for Euler-Bernoulli beam are obtained more accurate and efficient in contrast to the traditional ones.

• Structural Engineering and Mechanics
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• v.61 no.6
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• pp.765-773
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• 2017

The quadratic B-spline finite element method yields mass and stiffness matrices which are half the size of matrices obtained by the conventional finite element method. We solve the free vibration problem of a rotating Rayleigh beam using the quadratic B-spline finite element method. Rayleigh beam theory includes the rotary inertia effects in addition to the Euler-Bernoulli theory assumptions and presents a good mathematical model for rotating beams. Galerkin's approach is used to obtain the weak form which yields a system of symmetric matrices. Results obtained for the natural frequencies at different rotating speeds show an accurate match with the published results. A comparison with Euler-Bernoulli beam is done to decipher the variations in higher modes of the Rayleigh beam due to the slenderness ratio. The results are obtained for different values of non-uniform parameter ($\bar{n}$).

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.11
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• pp.1006-1011
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• 2004

Carbon nanotubes have outstanding properties which make them useful for a number of high-technology applications. Especially, single-walled carbon nanotube (SWNT), working under physical conditions (in aqueous solution) and converting electrical energy into mechanical energy directly, can be a good substitute for artificial muscle. The carbon nanotube structure simulated in this paper is an isotropic cantilever type with an adhesive tape which is sandwiched between two SWNTs. For predicting the geometrical and physical parameters such as deflection, slope, bending moment and induced force with various applied voltages, the analytical model for a 3 layer bimorph nanotube actuator is developed by applying Euler-Bernoulli beam theory. The governing equation and boundary conditions are derived from energy Principles. Also, the brief history of carbon nonotube is overviewed and its properties are compared with other functional materials. Moreover, an electro-mechanical coupling coefficient of the carbon nanotube actuator is discussed to identify the electro-mechanical energy efficiency.

• East Asian mathematical journal
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• v.36 no.1
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• pp.13-24
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• 2020

The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations. We also obtain integral representations, implicit and explicit formulas and relations for these polynomials and numbers. Furthermore, we consider some relationships for Apostol type (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.343-363
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• 2010

The present paper is concerned with vibrations of an elastic bridge loaded by a moving elastic beam of a finite length, which is an extension of the authors' previous study where the second beam was modeled as a semi-infinite beam. The second beam, which represents a train, moves with a constant speed along the bridge and is assumed to be connected to the bridge by the limiting case of a rigid interface such that the deflections of the bridge and the train are forced to be equal. The elastic stiffness and the mass of the train are taken into account. The differential equations are developed according to the Bernoulli-Euler theory and formulated in a non-dimensional form. A solution strategy is developed for the flexural vibrations, bending moments and shear forces in the bridge by means of symbolic computation. When the train travels across the bridge, concentrated forces and moments are found to take place at the front and back side of the train.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.04a
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• pp.573-578
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• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfies the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfies the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beam.