Sami El-Borgi

Nonlinear Analysis of MEMS Electrostatic Microactuators: Primary and Secondary Resonances of the First Mode

We use a discretization technique that combines the differential quadrature method (DQM) and the finite difference method (FDM) for the space and time, respectively, to study the dynamic behavior of a microbeam-based electrostatic microactuator. The adopted mathematical model based on the Euler— Bernoulli beam theory accounts for the system nonlinearities due to mid-plane stretching and electrostatic force. The nonlinear algebraic system obtained by the DQM—FDM is used to investigate the limit-cycle solutions of the microactuator. The stability of these solutions is ascertained using Floquet theory and/or long-time integration. The method is applied for large excitation amplitudes and large quality factors for primary and secondary resonances of the first mode in case of hardening-type and softening-type behaviors. We show that the combined DQM—FDM technique improves convergence of the dynamic solutions. We identify primary, subharmonic, and superharmonic resonances of the microactuator. We observe the occurrence of dynamic pull-in due to subharmonic and superharmonic resonances as the excitation amplitude is increased. Simultaneous resonances of the first and higher modes are identified for large orbits in both primary and secondary resonances.

Axial Vibration Confinement in Nonhomogenous Rods

A design methodology for the vibration confinement of axial vibrations in nonhomogenous rods is proposed. This is achieved by a proper selection of a set of spatially dependent functions characterizing the rod material and geometric properties. Conditions for selecting such properties are established by constructing positive Lyapunov functions whose derivative with respect to the space variable is negative. It is shown that varying the shape of the rod alone is sufficient to confine the vibratory motion. In such a case, the vibration confinement requires that the eigenfunctions be exponentially decaying functions of space, where the notion of spatial domain stability is introduced as a concept dual to that of the time domain stability. It is also shown that vibration confinement can be produced if the rod density and/or stiffness are varied with respect to the space variable while the cross-section area is kept constant. Several case studies, supporting the developed conditions imposed on the spatially dependent functions for vibration confinement in vibrating rods, are discussed. Because variation in the geometric and material properties might decrease the critical buckling loads, we also discuss the buckling problem.

Time-Delay Effects on Controlled Seismically Excited Linear and Nonlinear Structures

The main purpose of this paper is to examine the influence of time delay associated with a semi-active variable viscous (SAVV) damper on the response of seismically excited linear and nonlinear structures. The maximum time delay is estimated on the basis of stability criteria, which consist of analyses of structural modal properties. Numerical computation of the critical time delay is performed by using dichotomic approach, which is based on multiple solving of the eigenvalue problem. Simulation results indicate that variable dampers can be effective in reducing the seismic response of structures, and that time-delay effects are important factors in control design of seismically excited structures. Furthermore, simulation results show degradation of performance whenever the actual delay exceeds the calculated critical time delay, which shows the accuracy and reliability of the proposed approach.

Static fracture and modal analysis simulation of a gas turbine compressor blade and bladed disk system

This paper presents a methodology for conducting a 3-D static fracture analysis with applications to a gas turbine compressor blade. An open crack model is considered in the study and crack-tip driving parameters are estimated by using 3-D singular crack-tip elements in ANSYS

Wavelet Transform-Based Damage Identification in Bladed Disks and Rotating Blades

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Identification of Breathing Cracked Shaft Models from Measurements

®. The static fracture analysis is verified with a special purpose fracture code (FRANC3D). Once the crack front is perfectly defined and validated, a free vibration study is conducted by analyzing the natural frequencies and modeshapes for both a single blade and bladed disk system. Taking advantage of high performance computing resources, a high fidelity finite element model is considered in the parametric investigation. In the fracture simulation, the influence of the size of a single edged crack as well as the rotational velocity on fracture parameters (stress intensity factors and J-Integral) are evaluated. Results demonstrate that for the applied loading condition, a mixed mode crack propagation is expected. In the modal analysis study, increasing the depth of the crack leads to a decrease in the natural frequencies of both the single blade and bladed disk system, while increasing the rotational velocity increases the natural frequencies. The presence of a crack also leads to mode localization for all mode families, a phenomenon that cannot be captured by a single blade analysis.

Eringen’s nonlocal theories of beams accounting for moderate rotations

We propose a hybrid control strategy, aimed at confining and suppressing simultaneously the vbratory motion in seismically excited structures. It is assumed that these structures are composed of n floors that are sensitive to vibrations, resulting from earthquake excitations. A number (m) of inter-story bracing elements, assumed to be the non-sensitive parts, are added to the structures to confine the vibration. The proposed strategy makes use of (n + p) force actuators that are placed at all floors of the structure and p < m active bracing elements. The design objective is to devise a feedback scheme that leads to transferring the vibrational energy in the floors to the bracing elements. In order to keep away from the buildup of transferred energy into the bracing elements, the feedback scheme considers, along with the confinement, the suppression of vibrations in the floors and bracing elements. A three-floor structure is used to demonstrate the viability of the proposed strategy.

Non-linear analysis of functionally graded microbeams using Eringen's non-local differential model

Blade vibration and blade clearance are effective diagnostic features for the identification of blade damage in rotating machines. Blade tip-timing (BTT) is a noncontact method that is often used to monitor the vibration and clearance of blades in a rotating machinery. Standard signal processing of BTT measurements give one blade response sample per revolution of the machine which is often insufficient for the diagnosis of damage. This paper uses the raw data signals from the sensors directly and employs a wavelet energy-based mistuning index (WEBMI) to predict the presence and locations of damage in rotating blades. The Lipschitz exponent is derived from the wavelet packet coefficients and used to estimate the severity of the damage. In this study, experiments were conducted to obtain BTT measurements on rotating blades at  rpm using three different sensors: an active eddy current sensor, a passive eddy current sensor, and an optical sensor. In addition, hammer excitation experiments were conducted for various added mass (damage) cases to compute the damage severity for a bladed disk. To simulate the damage experimentally in the bladed disk and rotating blades, masses were added to the blades to alter their dynamics and mimic the damage. The results indicate that the WEBMI can detect the presence and location of damage in rotating blades using measurements from common BTT sensors. To check the robustness of the proposed damage severity index, the experimental results were compared with numerical simulation for the bladed disk and showed good agreement.