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.

Reduced Order Model of MEMS Sensors Near Natural Frequency

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Jose C. Solis Silva
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Mass Detection ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator sensor for mass detection is investigated. The excitation is near the natural frequency. A first order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for uniform microresonators with mass deposition and without are reported.

Reduced Order Model for MEMS Cantilever Resonators Under Soft AC Voltage Near Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator is investigated. The AC voltage is of frequency near resonator’s natural frequency. A first order fringe correction of the electrostatic force and viscous damping are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for the uniform microresonator are compared with those obtained via the Method of Multiple Scales (MMS).

On a New Nonlinear Reduced-Order Model for Capturing Internal Resonances in Intentionally Mistuned Cyclic Structures

2020 ◽  
Author(s):  
Samuel Quaegebeur ◽  
Benjamin Chouvion ◽  
Fabrice Thouverez ◽  
Loïc Berthe
Keyword(s):  
Nonlinear Response ◽  
Forced Response ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Internal Resonances ◽  
Present Material ◽  
Reduced Order ◽  
Modal Synthesis ◽  
Excitation Force

Abstract Cyclic structures such as turbomachinery present material and geometrical variations between sectors. These discrepancies are called mistuning and break the cyclic symmetry of the structure. Computing the forced response of mistuned cyclic structures is thus a numerical challenge. The Component Nonlinear Complex Mode Synthesis (CNCMS) is one of the few nonlinear reduced-order model formulations that allow to compute the nonlinear response of tuned and mistuned structures. It has been validated successfully for friction problems. However, in the presence of geometric nonlinearities, internal resonances may arise and they cannot be captured correctly with the CNCMS method. The purpose of this work is therefore to present a new methodology for developing a nonlinear reduced-order model that can successfully capture internal resonances for tuned and mistuned structures. This method, called Component Mode Synthesis with Nonlinear Re-evaluation (CMSNR), is based on a variation of the CNCMS approach. The final modal synthesis uses a multi-harmonic procedure and a re-evaluation of the nonlinear forces on each sector independently. The performance and limitations of the proposed approach are assessed using a simplified example of a blisk subject to polynomial nonlinearities. Different internal resonances are exhibited and studied depending on the type of excitation force and on the level of mistuning.

On a New Nonlinear Reduced-Order Model for Capturing Internal Resonances in Intentionally Mistuned Cyclic Structures

2020 ◽  
Author(s):  
Samuel Quaegebeur ◽  
Benjamin Chouvion ◽  
Fabrice Thouverez ◽  
Loïc Berthe
Keyword(s):  
Nonlinear Response ◽  
Forced Response ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Internal Resonances ◽  
Present Material ◽  
Reduced Order ◽  
Modal Synthesis ◽  
Excitation Force

Abstract Cyclic structures such as turbomachinery present material and geometrical variations between sectors. These discrepancies are called mistuning and break the cyclic symmetry of the structure. Computing the forced response of mistuned cyclic structures is thus a numerical challenge. The Component Nonlinear Complex Mode Synthesis (CNCMS) is one of the few nonlinear reduced-order model formulations that allow to compute the nonlinear response of tuned and mistuned structures. It has been validated successfully for friction problems. However, in the presence of geometric nonlinearities, internal resonances may arise and they cannot be captured correctly with the CNCMS method. The purpose of this work is therefore to present a new methodology for developing a nonlinear reduced-order model that can successfully capture internal resonances for tuned and mistuned structures. This method, called Component Mode Synthesis with Nonlinear Re-evaluation (CMSNR), is based on a variation of the CNCMS approach. The final modal synthesis uses a multi-harmonic procedure and a re-evaluation of the nonlinear forces on each sector independently. The performance and limitations of the proposed approach are assessed using a simplified example of a blisk subject to polynomial nonlinearities. Different internal resonances are exhibited and studied depending on the type of excitation force and on the level of mistuning.

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 Dynamic Response of an Electrically Actuated Imperfect Microbeam Resonator

2013 ◽  
Author(s):  
Laura Ruzziconi ◽  
Ahmad M. Bataineh ◽  
Mohammad I. Younis ◽  
Weili Cui ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Theoretical Analysis ◽  
Ritz Method ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Reduced Order Models ◽  
Nonlinear Dynamic Response ◽  
Reduced Order ◽  
Combined Use ◽  
Experimental Complex

We present a study of the dynamic behavior of a MEMS device constituted of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. The nonlinear behavior is highlighted, which includes ranges of multistability, where the non-resonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is capable also to capture the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach.

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