• Steel and Composite Structures
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• v.24 no.2
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• pp.141-149
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• 2017

In this study, vibration analysis of fluid conveying microbeams under non-ideal boundary conditions (BCs) is performed. The objective of the present paper is to describe the effects of non-ideal BCs on linear vibrations of fluid conveying microbeams. Non-ideal BCs are modeled as a linear combination of ideal clamped and ideal simply supported boundary conditions by using the weighting factor (k). Non-ideal clamped and non-ideal simply supported beams are both considered to show the effects of BCs. Equations of motion of the beam under the effect of moving fluid are obtained by using Hamilton principle. Method of multiple scales which is one of the perturbation techniques is applied to the governing linear equation of motion. Approximate solutions of the linear equation are obtained and the effects of system parameters and non-ideal BCs on natural frequencies are presented. Results indicate that, natural frequencies of fluid conveying microbeam changed significantly by varying the weighting factor k. This change is more remarkable for clamped microbeams rather than simply supported ones.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.10a
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• pp.160-165
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• 1997

Structural boundary condition is very important as a part of a structural system because it determines the dynamic characteristics of the structure. It is often to experience that experimental measurements of structural dynamic characteristics are somewhat different from the analytical predictions in which idealized boundary conditions are usually assumed. However, real structural boundary conditions are not so ideal; not perfectly clamped, for instance. Thus this paper introduces a new method to determine the non-ideal structural boundary conditions in the frequency domain. In this method, structural boundary conditions are modeled by both extensional (vertical) and torsional elastic springs. The effective springs are then determined from experimental FRFs (frequency response functions) by using the spectral element method (SEM). For a cantilevered beam experiments are conducted to determine the real boundary conditions in terms of effective springs. Dynamic characteristics (analytically predicted) based on identified boundary conditions are found to be much closer to experimental measurements when compared with those based on ideal boundary conditions.

• Smart Structures and Systems
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• v.18 no.6
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• pp.1087-1109
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• 2016

In this manuscript, the small scale and thermal effects on vibration behavior of preloaded nanobeams with non-ideal boundary conditions are investigated. The boundary conditions are assumed to allow small deflections and moments and the concept of non-ideal boundary conditions is applied to the nonlocal beam problem. Governing equations are derived through Hamilton's principle and then are solved applying Lindstedt-Poincare technique to derive fundamental natural frequencies. The good agreement between the results of this research and those available in literature validated the presented approach. The influence of various parameters including nonlocal parameter, thermal effect, perturbation parameter, aspect ratio and pre-stress load on free vibration behavior of the nanobeams are discussed in details.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.95-107
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• 1998

In this paper we prove the Hopf-Rinow theorem for CAT(0) spaces and show that the ideal boundaries of complete CAT(0) manifolds of dimension 2 or 3 with some additional conditions are homeomorphic to the circle or 2-sphere by the characterization of the local shadows around the branch points.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.597-605
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• 2015

In this study, linear vibrations of an axially moving beam under non-ideal support conditions have been investigated. The main difference of this study from the other studies; the non-ideal clamped support allow minimal rotations and non-ideal simple support carry moment in minimal orders. Axially moving Euler-Bernoulli beam has simple and clamped support conditions that are discussed as combination of ideal and non-ideal boundary with weighting factor (k). Equations of the motion and boundary conditions have been obtained using Hamilton's Principle. Method of Multiple Scales, a perturbation technique, has been employed for solving the linear equations of motion. Linear equations of motion are solved and effects of different parameters on natural frequencies are investigated.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.351-361
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• 1995

Let M be a complete open Riemannian manifold. When the sectional curvature $K_M$ of M is nonpositive, Gromov has defined, in his lectures [3], the ideal boundary of M, and used it to study the geometric structure of M. In a Hadamard manifold, a simply connected manifold with nonpositive sectional curvature, a point at infinity can be defined as an equivalence class of rays. He proved many interesting theorems using this definition of ideal boundary and the so-called Tit's metric on it. He also suggested a counterpart to this for nonnegative curvature case. This idea has been taken up by Kasue to study the structure of complete open manifolds with asympttically nonnegative curvature [14]. Motivated by these works, we will define an idela boundary of a general noncompact manifold M, and study its structure.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.12
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• pp.1759-1771
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• 2017

In this paper, an improved continuous integral variable structure systems(ICIVSS) with the prescribed control performance is designed for simple regulation controls of uncertain general linear systems. An integral sliding surface with an integral state having a special initial condition is adopted for removing the reaching phase and predetermining the ideal sliding trajectory from a given initial state to the origin in the state space. The ideal sliding dynamics of the integral sliding surface is analytically obtained and the solution of the ideal sliding dynamics can predetermine the ideal sliding trajectory(integral sliding surface) from the given initial state to the origin. Provided that the value of the integral sliding surface is bounded by certain value by means of the continuous input, the norm of the state error to the ideal sliding trajectory is analyzed and obtained in Theorem 1. A corresponding discontinuous control input with the exponential stability is proposed to generate the perfect sliding mode on the every point of the pre-selected sliding surface. For practical applications, the discontinuity of the VSS control input is approximated to be continuous based on the proposed modified fixed boundary layer method. The bounded stability by the continuous input is investigated in Theorem 3. With combining the results of Theorem 1 and Theorem 3, as the prescribed control performance, the pre specification on the error to the ideal sliding trajectory is possible by means of the boundary layer continuous input with the integral sliding surface. The suggested algorithm with the continuous input can provide the effective method to increase the control accuracy within the boundary layer by means of the increase of the $G_1$ gain. Through an illustrative design example and simulation study, the usefulness of the main results is verified.

• Advances in nano research
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• v.8 no.2
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• pp.169-182
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• 2020

This study presents the hygro-thermo-electromagnetic mechanical vibration attributes of elastically restrained piezoelectric nanobeam considering effects of beam surface for various elastic non-ideal boundary conditions. The nonlocal Eringen theory besides the surface effects containing surface stress, surface elasticity and surface density are employed to incorporate size-dependent effects in the whole of the model and the corresponding governing equations are derived using Hamilton principle. The natural frequencies are derived with the help of differential transformation method (DTM) as a semi-analytical-numerical method. Some validations are presented between differential transform method results and peer-reviewed literature to show the accuracy and the convergence of this method. Finally, the effects of spring constants, changing nonlocal parameter, imposed electric potential, temperature rise, magnetic potential and moisture concentration are explored. These results can be beneficial to design nanostructures in diverse environments.

• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.309-321
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• 2004

For a complete open Riemannian manifold, the ideal boundary consists of points at infinity. The so-called Busemann-functions play the role of distance functions for points at infinity. We study the similarity and difference between Busemann-functions and ordinary distance functions.

• Journal of Power Electronics
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• v.17 no.5
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• pp.1268-1277
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• 2017

Three-phase pulse width modulation (PWM) rectifiers are usually designed under the assumption of ideal ac power supply and input inductance. However, non-ideal circuit parameters may lead to a voltage collapse of PWM rectifiers. This paper investigates the mechanism of voltage collapse in three-phase PWM rectifiers. An analytical stability boundary expression is derived by analyzing the equilibrium point of the averaging state space model, which can not only accurately locate the voltage collapse boundary in the circuit parameter domain, but also reveal the essential characteristic of the voltage collapse. Results are obtained and compared with those of the trial-error method and the Jacobian method. Based on the analysis results, the system parameters can be divided into two categories. One of these categories affects the critical point, and other affects only the instability process. Furthermore, an effective control strategy is proposed to prevent a vulnerable system from being driven into the instability region. The analysis results are verified by the experiments.