An Efficient Reduced-Order Model to Investigate the Behavior of an Imperfect Microbeam Under Axial Load and Electric Excitation

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Laura Ruzziconi ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Axial Load ◽  
Single Mode ◽  
Reduced Order Model ◽  
Nonlinear Phenomena ◽  
Order Model ◽  
Dynamic Simulations ◽  
Initial Shape ◽  
Reduced Order ◽  
Electric Excitation ◽  
Nonlinear Static

In this study an efficient reduced-order model for a MEMS device is developed and investigations of the nonlinear static and the dynamic behavior are performed. The device is constituted of an imperfect microbeam under an axial load and an electric excitation. The imperfections, typically due to microfabrication processes, are simulated assuming a shallow arched initial shape. The axial load is deliberately added with an elevated value. The structure has a bistable static configuration of double potential well with possibility of escape. We derive a single-mode reduced-order model via the Ritz technique and the Padé approximation. This model, while simple, is able to combine both a sufficient accuracy, which enables to detect the main qualitative features of the device response up to elevated values of electrodynamic excitation, and a remarkable computational efficiency, which is essential for systematic global nonlinear dynamic simulations. We illustrate the nonlinear phenomena arising in the device, such as the coexistence of various competing in-well and cross-well attractors, which leads to a considerable versatility of behavior. We discuss their physical meaning and their practical relevance for the engineering design of the microstructure, since this is an uncommon and very attractive aspect in applications.

Nonlinear Dynamics of an Imperfect Microbeam Under an Axial Load and Electric Excitation

2011 ◽  
Author(s):  
Laura Ruzziconi ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Microelectromechanical Systems ◽  
Complex Dynamics ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Theoretical Point ◽  
Initial Shape ◽  
Electric Excitation

This study is motivated by the growing attention, both from a practical and a theoretical point of view, toward the nonlinear behavior of microelectromechanical systems (MEMS). We analyze the nonlinear dynamics of an imperfect microbeam under an axial force and electric excitation. The imperfection of the microbeam, typically due to microfabrication processes, is simulated assuming the microbeam to be of a shallow arched initial shape. The device has a bistable static behavior. The aim is that of illustrating the nonlinear phenomena, which arise due to the coupling of mechanical and electrical nonlinearities, and discussing their usefulness for the engineering design of the microstructure. We derive a single-mode-reduced-order model by combining the classical Galerkin technique and the Pade´ approximation. Despite its apparent simplicity, this model is able to capture the main features of the complex dynamics of the device. Extensive numerical simulations are performed using frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior charts. We investigate the overall scenario, up to the inevitable escape, obtaining the theoretical boundaries of appearance and disappearance of the main attractors. The main features of the nonlinear dynamics are discussed, stressing their existence and their practical relevance. We focus on the coexistence of robust attractors, which leads to a considerable versatility of behavior. This is a very attractive feature in MEMS applications. The ranges of coexistence are analyzed in detail, remarkably at high values of the dynamic excitation, where the penetration of the escape (dynamic pull-in) inside the double well may prevent the safe jump between the attractors.

Nonlinear Dynamics of a NEMS Carbon Nanotube Resonator

2012 ◽  
Author(s):  
Laura Ruzziconi ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Response ◽  
Ritz Method ◽  
Single Mode ◽  
Reduced Order Model ◽  
Phase Portraits ◽  
Order Model ◽  
Reduced Order ◽  
Combined Use ◽  
Dynamic Voltage ◽  
Carbon Nanotube Resonator

In this study we consider a slacked CNT and analyze the nonlinear response under electrostatic and electrodynamic actuation. We introduce a reduced-order model, which takes into account the single-mode dynamics and is derived via the Ritz method and the Padé approximation. The overall scenario of the device behavior is investigated when both the frequency and the electrodynamic voltage are varying. Extensive numerical simulations are performed by the combined use of frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior chart. Our aim is that of illustrating the richness of the nonlinear events that may undergo in the device due to the coupling of mechanical and electrical nonlinearities. We observe that the CNT exhibits coexisting competing attractors, which lead to a versatile behavior. We examine the multistability in detail. The response is explored not only at low electrodynamic voltages, where the safe jump between attractors is ensured, but also at large electrodynamic excitation, where the inevitable escape (dynamic pull-in) becomes impending. We detect the theoretical boundaries of appearance and disappearance of the main attractors, which provide a complete description of the response.

scholarly journals Dynamics of an Imperfect Microbeam Considering its Exact Shape

2014 ◽  
Author(s):  
Ahmad M. Bataineh ◽  
Mohammad I. Younis
Keyword(s):  
Experimental Data ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Reduced Order Model ◽  
Effective Length ◽  
Mode Shapes ◽  
Nonlinear Phenomena ◽  
Nonlinear Ordinary Differential Equations ◽  
Order Model ◽  
Reduced Order

We study the static and dynamic behavior of electrically actuated micromachined arches. First, we conduct experiments on micromachined polysilicon beams by driving them electrically and varying their amplitude and frequency of voltage loads. The results reveal several interesting nonlinear phenomena of jumps, hysteresis, and softening behaviors. Next, we conduct analytical and theoretical investigation to understand the experiments. First, we solve the Eigen value problem analytically. We study the effect of the initial rise on the natural frequency and mode shapes, and use a Galerkin-based procedure to derive a reduced order model, which is then used to solve both the static and dynamic responses. We use two symmetric modes in the reduced order model to have accurate and converged results. We use long time integration to solve the nonlinear ordinary differential equations, and then modify our model using effective length to match experimental results. To further improve the matching with the experimental data, we curve-fit the exact profile of the microbeam to match the experimentally measured profile and use it in the reduced-order model to generate frequency-response curves. Finally, we use another numerical technique, the shooting technique, to solve the nonlinear ordinary differential equations. By using shooting and the curve fitted function, we found that we get good agreement with the experimental data.

Reduced Order Model for the Geometric Nonlinear Response of Complex Structures

2012 ◽  
Author(s):  
Ricardo Perez ◽  
X. Q. Wang ◽  
Andrew Matney ◽  
Marc P. Mignolet
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Model Parameters ◽  
Complex Structures ◽  
Order Model ◽  
Plate Structures ◽  
Reduced Order ◽  
Nonlinear Static ◽  
Selection Of

This paper focuses on the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting “large” deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology successfully validated in recent years on simpler beam and plate structures by: (i) developing a novel identification strategy of the reduced order model parameters that enables the consideration of the large number of modes (> 50 say) that would be needed for complex structures, and (ii) extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. The above novel developments are successfully validated on the nonlinear static response of a 9-bay panel structure modeled with 96,000 degrees of freedom within Nastran.

scholarly journals An Object-Oriented R744 Two-Phase Ejector Reduced-Order Model for Dynamic Simulations

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1282
Author(s):  
Michal Haida ◽  
Rafal Fingas ◽  
Wojciech Szwajnoch ◽  
Jacek Smolka ◽  
Michal Palacz ◽  
...  
Keyword(s):  
Dynamic Simulation ◽  
Object Oriented ◽  
Operating Conditions ◽  
Reduced Order Model ◽  
Refrigeration System ◽  
Order Model ◽  
Two Phase ◽  
Dynamic Simulations ◽  
Climate Zones ◽  
Reduced Order

The object-oriented two-phase ejector hybrid reduced-order model (ROM) was developed for dynamic simulation of the R744 refrigeration system. OpenModelica software was used to evaluate the system’s performance. Moreover, the hybrid ROM results were compared to the results given by the non-dimensional and one-dimensional mathematical approaches of the R744 two-phase ejector. Accuracy of all three ejector models was defined through a validation procedure for the experimental results. Finally, the dynamic simulation of the hybrid ROM ejector model integrated with the R744 refrigeration system was presented based on the summer campaign at three different climate zones: Mediterranean, South American and South Asian. The hybrid ROM obtained the best prediction of ejector mass flow rates as compared with other ejector models under subcritical and transcritical operating conditions. The dynamic simulations of the R744 ejector-based system indicated the ejector efficiency variations and the best efficiency at the investigated climate zones. The coefficient of performance (COP) varied from 2.5 to 4.0 according to different ambient conditions. The pressure ratio of 1.15 allowed a more stabilised system during the test campaign with an ejector efficiency from 20% to over 30%.

AN IMPERFECT MICROBEAM UNDER AN AXIAL LOAD AND ELECTRIC EXCITATION: NONLINEAR PHENOMENA AND DYNAMICAL INTEGRITY

2013 ◽  
Vol 23 (02) ◽  
pp. 1350026 ◽  
Author(s):  
LAURA RUZZICONI ◽  
STEFANO LENCI ◽  
MOHAMMAD I. YOUNIS
Keyword(s):  
Axial Load ◽  
Single Mode ◽  
Quantitative Information ◽  
Structural Safety ◽  
Nonlinear Phenomena ◽  
Practical Case ◽  
Electric Excitation ◽  
Dynamic Voltage ◽  
Final Response ◽  
Dynamical Integrity

This work deals with the nonlinear dynamics of a microelectromechanical system constituted by an imperfect microbeam under an axial load and an electric excitation. The device is characterized by a bistable static configuration. We analyze the single-mode dynamics and describe the overall scenario of the response, up to the inevitable escape, when both the frequency and the electrodynamic voltage are considered as driving parameters. We observe the presence of several competing attractors leading to a considerable versatility of behavior, which may have many feasible applications. Extensive numerical simulations are performed. The frequency-dynamic voltage behavior chart is obtained, which detects the theoretical boundaries of appearance and disappearance of the main attractors. Taking into account the erosion of the double well, we investigate the final response when each attractor vanishes. All these results represent the limit when disturbances are absent, which never occurs in practice. To extend them to the practical case where disturbances exist, we develop a dynamical integrity analysis. This is performed via curves of constant percentage of local integrity measure, which give quantitative information about the changes in the structural safety. For each attractor, we examine both the practical disappearance, by analyzing the robustness of its basin along the range of existence, and the practical final response, by detecting where safe jump to another attractor may be ensured and where instead dynamic pull-in may arise. These curves may be used to establish safety factors in order to operate the device according to the desired outcome, depending on the expected disturbances.

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