Ismail Kucuk

Variational principles for multiwalled carbon nanotubes undergoing vibrations based on nonlocal timoshenko beam theory

Variational principles are derived for multiwalled carbon nanotubes undergoing linear vibrations using the semi-inverse method with the governing equations based on nonlocal Timoshenko beam theory which takes small scale effects and shear deformation into account. Physical models based on the nonlocal theory approximate the nanoscale phenomenon more accurately than the local theories by taking small scale phenomenon into account. Variational formulation is used to derive the natural and geometric boundary conditions which give a set of coupled boundary conditions in the case of free boundaries which become uncoupled in the case of the local theory. Hamiltons principle applicable to this case is also given.

An efficient computational method for the optimal control problem for the Burgers equation

Pointwise control of the viscous Burgers equation in one spatial dimension is studied with the objective of minimizing the distance between the final state function and target profile along with the energy of the control. An efficient computational method is proposed for solving such problems, which is based on special orthonormal functions that satisfy the associated boundary conditions. Employing these orthonormal functions as a basis of a modal expansion method, the solution space is limited to the smallest lower subspace that is sufficient to describe the original problem. Consequently, the Burgers equation is reduced to a set of a minimal number of ordinary nonlinear differential equations. Thus, by the modal expansion method, the optimal control of a distributed parameter system described by the Burgers equation is converted to the optimal control of lumped parameter dynamical systems in finite dimension. The time-variant control is approximated by a finite term of the Fourier series whose unknown coefficients and frequencies giving an optimal solution are sought, thereby converting the optimal control problem into a mathematical programming problem. The solution space obtained is based on control parameterization by using the Runge-Kutta method. The efficiency of the proposed method is examined using a numerical example for various target functions.

Design and optimization of an instrument for measuring bughole rating of concrete surfaces

Abstract Bugholes are surface imperfections that appear as small pits and craters on concrete surface after the casting process. Bugholes are cosmetic surface imperfections and do not affect the structural integrity of the concrete structure. However, existences of these imperfections increase cost since bugholes require additional surface preparations before painting or finishing the concrete surface. Additionally, these surface imperfections cause secondary problems by decreasing the cover on RC making incretion of salts into the reinforcement bars inside RC. In this paper, authors discuss development of a new device to measure “bughole” rating of concrete surface. The innovative technique used in design enables us to manufacture a compact instrument, which is physically small, lightweight and practical. The paper explains the design principles of the device and the procedure used for optimization of design parameters for the best performance. Last section of the paper gives simulation results to compare the performance of the device to current state of the art methods used for bughole rating in industry.

Parametric sensitivity: A case study comparison

This article presents a comparative analysis of three derivative-based parametric sensitivity approaches in multi-response regression estimation: marginal sensitivity, profile-based approach developed by [Sulieman, H., McLellan, P.J., Bacon, D.W., 2004, A Profile-based approach to parametric sensitivity in multiresponse regression models, Computational Statistics & Data Analysis, 45, 721-740] and the commonly used approach of the Fourier Amplitude Sensitivity Test (FAST). We apply the classical formulation of FAST in which Fourier sine coefficients are utilized as sensitivity measures. Contrary to marginal sensitivity, profile-based and FAST approaches provide sensitivity measures that account for model nonlinearity and are pertinent to linear and nonlinear regression models. However, the primary difference between FAST and profile-based sensitivity is that traditional FAST fails to account for parameter dependencies in the model system while these dependencies are considered in the analysis procedure of profile-based sensitivity through the re-estimation of the remaining model parameters conditional on the values of the parameter of interest. An example is discussed to illustrate the comparisons by applying the three sensitivity methods to a model described by set of non-linear differential equations. Some computational aspects are also explored.

Optimal control of a beam with Kelvin-Voigt damping subject to forced vibrations using a piezoelectric patch actuator

A maximum principle is derived for the optimal control of a beam with Kelvin–Voigt damping subject to an external excitation with the control exercised by means of piezoelectric patch actuators. The objective functional is defined as a weighted quadratic functional of the displacement and velocity which is to be minimized at a given terminal time. A penalty term is also part of the objective functional defined as the control voltage used in the control process. The maximum principle makes use of a Hamiltonian defined in terms of an adjoint variable and the control function. The optimal control problem is expressed as a coupled system of partial differential equations in terms of state, adjoint and control variables subject to boundary, initial and terminal conditions. The solution is obtained by expanding the state and adjoint variables in terms of eigenfunctions and determining the optimal control using the maximum principle. Numerical examples are given to demonstrate the applicability and the efficiency of the proposed method.

Optimal control of a distributed parameter system with applications to beam vibrations using piezoelectric actuators

Abstract This paper addresses the issue of the active vibration control of the transverse modes in a flexible elastic systems. The control is implemented by discrete sets of piezoelectric actuators that apply the optimal forces. The performance index is a time-dependent quadratic functional of state variables and their time derivatives, and control forces which are determined by minimizing the objective functional subject to a penalty term on the control functions. A combination of Galerkin and variational approaches are employed to determine the control forces in the time domain explicitly in terms of coupled amplitudes and velocities. The effectiveness of the proposed method is demonstrated by applying it to a physical problem controlled by piezoelectric patch actuators.

Optimal piezoelectric control of a plate subject to time-dependent boundary moments and forcing function for vibration damping

Active vibration control problem for a rectangular plate subject to moment boundary conditions and forcing function is solved by means of a maximum principle. The control is exercised by a patch actuator and the solution is formulated using an adjoint variable leading to a coupled boundary-initial-terminal value problem. The application of the maximum principle yields the optimal control expression as well as the explicit solution for a simply supported plate. The objective functional to be minimized is defined as a quadratic functional of displacement and velocity and also includes a penalty in terms of control voltage applied to the piezoelectric patch actuator. The penalty term limits the amount of control energy spent during the control process. Numerical results are presented to assess the effect of the optimal control algorithm.

Active piezoelectric vibration control for a Timoshenko beam

Abstract Optimal piezoelectric vibration control problem for a Timoshenko beam is considered. The performance index function to be minimized by using the minimum level of the control voltage consists of a weighted quadratic function of displacement and velocity of the beam and also includes a quadratic functional of the control voltage function as a penalty term. The optimal control function is derived by means of a maximum principle which transforms the control problem to an initial-boundary-terminal value problem. In order to show the effectiveness of the control actuation, numerical results are given by MATLAB in table and graphical forms.

Active Open-Loop Control of Plates with Multiple Piezoelectric Patches via the Maximum Principle.

The active vibration of plates integrated with distributed piezoelectric actuators is studied using control theory. The optimization problem consists of finding the control voltage applied to distributed piezoelectric patch actuators, which suppresses the transient displacements and velocities of plates with the least control effort. An explicit optimal control law is derived by utilizing the maximum principle theory for the structural dynamic systems in two space dimensions. The implementation of the theory is presented in an example, and the effectiveness of the proposed control is investigated by a numerical simulation.

A robust technique for solving optimal control of coupled Burgers' equations

A methodology is described for solving optimal pointwise control of a coupled system of Burgers’ equations. It is aimed to determine the optimal pointwise control that minimizes a given performance measure. The performance measure is specified as a quadratic functional of the distance between a final state function and a predefined target function along with the energy due to the control effort. The modal expansion method is used to reduce the optimal control of distributed parameter systems into the control of the invariant lumped parameter systems. A system of non-linear algebraic equations are derived as necessary conditions of optimality and solved by Runge–Kutta method to obtain the optimal Fourier coefficients and frequencies. The feasibility of the proposed methodology is demonstrated by numerical simulations.