• Smart Structures and Systems
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• v.12 no.5
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• pp.501-521
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• 2013

This paper is concerned with static and dynamic shape control of a laminated Bernoulli-Euler beam hosting a uniformly distributed array of resistively interconnected piezoelectric patches. We present an analytical one-dimensional model for a laminated piezoelectric beam with material discontinuities within the framework of Bernoulli-Euler and extent the model by a network of resistors which are connected to several piezoelectric patch actuators. The voltage of only one piezoelectric patch is prescribed: we answer the question how to design the interconnected resistive electric network in order to annihilate lateral vibrations of a cantilever. As a practical example, a cantilever with eight patch actuators under the influence of a tip-force is studied. It is found that the deflection at eight arbitrary points along the beam axis may be controlled independently, if the local action of the piezoelectric patches is equal in magnitude, but opposite in sign, to the external load. This is achieved by the proper design of the resistive network and a suitable choice of the input voltage signal. The validity of our method is exact in the static case for a Bernoulli-Euler beam, but it also gives satisfactory results at higher frequencies and for transient excitations. As long as a certain non-dimensional parameter, involving the number of the piezoelectric patches, the sum of the resistances in the electric network and the excitation frequency, is small, the proposed shape control method is approximately fulfilled for dynamic load excitations. We evaluate the feasibility of the proposed shape control method with a more refined model, by comparing the results of our one-dimensional calculations based on the extended Bernoulli-Euler equations to three-dimensional electromechanically coupled finite element results in ANSYS 12.0. The results with the simple Bernoulli-Euler model agree well with the three-dimensional finite element results.

• The Journal of the Korea institute of electronic communication sciences
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• v.4 no.3
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• pp.236-242
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• 2009

When two-link flexible arm is rotated about an joint axis, transverse vibration may occur. In this paper, vibration dynamics of flexible robot arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Using the fact that matrix $\dot{D}$-2C is skew symmetric, new controllers which have a simplified structure with less computational burden is proposed. Lyapunov stability theory is applied to achieve a stable deterministic nonlinear controller for the regulation of joint angle.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.195-200
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• 2002

We consider the Bernoulli two-armed bandit problem. It is well known that the my optic strategy is optimal when the prior distribution is concentrated at two points in the unit square. We investigate several cases in the unit square whether the my optic strategy is optimal or not. In general, the my optic strategy is not optimal when the prior distribution is not concentrated at two points in the unit square.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.11-17
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• 2001

We consider the M/G/1 with Bernoulli feedback, where the served customers wait in the feedback queue for rework with probability p. It is important to decide the moment of dispatching in feedback systems because of the dispatching cost for rework. Up to date, researches have analyzed for the instantaneous-dispatching model or the case that dispatching epoch is determined by the state of feedback queue. In this paper we deal with a dispatching model whose dispatching epoch depends on main queue. We adopt supplementary variable method for our model and a numerical example is given for clarity.

• Steel and Composite Structures
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• v.15 no.4
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• pp.439-449
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• 2013

In this study simply supported nonlinear Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads is investigated. A new kind of analytical technique for a non-linear problem called He's Energy Balance Method (EBM) is used to obtain the analytical solution for non-linear vibration behavior of the problem. Analytical expressions for geometrically non-linear vibration of Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads are provided. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. The variation of different parameter to the nonlinear frequency is considered completely in this study. The nonlinear vibration equation is analyzed numerically using Runge-Kutta $4^{th}$ technique. Comparison of Energy Balance Method (EBM) with Runge-Kutta $4^{th}$ leads to highly accurate solutions.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.417-445
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• 2020

The purpose of this article is to continue the study of q, 𝜔-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al., with emphasis on q, 𝜔-Apostol Bernoulli and Euler polynomials, Ward-𝜔 numbers and multiple q, 𝜔power sums. Like before, the q, 𝜔-module for the alphabet of q, 𝜔-real numbers plays a crucial role, as well as the q, 𝜔-rational numbers and the Ward-𝜔 numbers. There are many more formulas of this type, and the deep symmetric structure of these formulas is described in detail.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.11a
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• pp.229-233
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• 2003

This paper describes a practical formulation of Non-Bernoulli-Compatibility Truss Model. Not only equilibrium conditions but also some approximations are employed to solve for the unknowns included in the proposed model. By assuming that the ratio of $V_a$ to V remains to be constant along the shear span, the relationship between $\alpha$ and z is mathematically established as an arch shape function. $V_m$ is also approximated to be an empirical value that is equal to the least membrane shear strength. The coefficient a is made utilizing a nonlinear finite element analysis. The adequacy of the model is examined by test results available in literatures, and the predicted values are shown to be in excellent agreement with the experimental results.

• Journal of Advanced Marine Engineering and Technology
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• v.32 no.6
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• pp.877-885
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• 2008

Steam injection heater is the most widely used method for fresh water generator throughout industry. This method is often chosen because of its simplicity. The steam bubbles condense and give up their heat to the surrounding liquid. Experimental study on steam injection heater has been performed in order to find the effect of major parameter. And conservation equation and Bernoulli obstruction theory are used for numerical simulation model of vapor flow-rate. Qualitative comparisons between simulations and measurements show a good agreement and the simulation models are thereby verified.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.623-630
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• 1995

The impulse response functions (force-strain relations) for Euler-Bernoulli and Timoshenko beams are considered. The response of a beam to a transverse impact force is numerically obtained with the convolution approach using the impulse response function obtained by Laplace transform. Using this relation, the impact force history is determined in the time domain and results are compared with those from Hertz's contact law. The parameters of timpact force model are identified using the recovered force and compared with the Hertz's contact model. In order to verify the proposed algorithm, measurements were done using an impact hammer and a steel ball drop test and these results are also compared with the simulated values.

• Journal of KSNVE
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• v.8 no.3
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• pp.524-532
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• 1998

The purpose of this paper is to investigate the free vibrations of horizontally curved beams resting on Winkler-type foundations. Based on the classical Bernoulli-Euler beam theory, the governing differential equations for circular curved beams are derived and solved numerically. Hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered in numerical examples. The free vibration frequencies calculated using the present analysis have been compared with the finite element's results computed by the software ADINA. Numerical results are presented to show the effects on the natural frequencies of curved beams of the horizontal rise to span length ratio, the foundation parameter, and the width ratio of contact area between the beam and foundation.