On Localization in Coupled, Spinning, Circular Plates

1994 ◽  
Vol 116 (4) ◽  
pp. 555-561 ◽  
Author(s):  
C. O. Orgun ◽  
B. H. Tongue
Keyword(s):  
Analytical Model ◽  
Rotation Speed ◽  
Response Mode ◽  
Circular Plates ◽  
Mode Localization ◽  
Central Spindle ◽  
Vibrational Response ◽  
Modal Response ◽  
Weakly Coupled ◽  
All Speeds

The vibrational response of multiple rotating circular plates, stacked together on a central spindle and coupled through stationary springs, is investigated. An analytical model is derived and a Rayleigh-Ritz approach employed in order to obtain the system’s modal response. Mode localization is shown to occur at all speeds of rotation for weakly coupled subcomponents and the degree to which the system exhibits localized behavior is shown to increase with rotation speed.

scholarly journals Nonlinear Analytical Model of Two Weakly Coupled MEMS Cantilevers for Mass Sensing Using Electrostatic Actuation

Proceedings ◽  
2018 ◽  
Vol 2 (13) ◽  
pp. 1084
Author(s):  
Toky Rabenimanana ◽  
Vincent Walter ◽  
Najib Kacem ◽  
Patrice Le Moal ◽  
Joseph Lardiès
Keyword(s):  
Analytical Model ◽  
Beam Theory ◽  
Continuous System ◽  
Mode Localization ◽  
Dc Voltage ◽  
Weakly Coupled ◽  
Flexible Supports ◽  
Nonlinear Analytical Model ◽  
Mems Mass Sensor ◽  
Mems Cantilevers

This paper presents a nonlinear analytical model of MEMS mass sensor, which is composed of two cantilevers of 98 µm and 100 µm length, 20 µm width and 1.3 µm thick. They are connected by a coupling beam and only the shortest cantilever is actuated by a combined AC-DC voltage. The DC voltage is used to equilibrate the system and the phenomenon of mode localization is investigated when a mass perturbation is applied. The sensor is modeled as a continuous system with beam theory and non-ideal boundary conditions are considered by using flexible supports. With a low AC voltage of 10 mV, a DC voltage of 5.85 V can counterbalance the length difference. This DC voltage decreases at 5.60 V when we increase the AC voltage, due to the effect of electrostatic nonlinearities. For a relative added mass of 0.1%, the amplitude change in the two cantilevers is more important when the coupling is weaker.

scholarly journals A Low-g MEMS Accelerometer with High Sensitivity, Low Nonlinearity and Large Dynamic Range Based on Mode-Localization of 3-DoF Weakly Coupled Resonators

Micromachines ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 310
Author(s):  
Muhammad Mubasher Saleem ◽  
Shayaan Saghir ◽  
Syed Ali Raza Bukhari ◽  
Amir Hamza ◽  
Rana Iqtidar Shakoor ◽  
...  
Keyword(s):  
Microelectromechanical Systems ◽  
Dynamic Range ◽  
Proof Mass ◽  
Amplitude Ratio ◽  
Silicon On Insulator ◽  
Coupled Resonators ◽  
Mode Localization ◽  
Mems Accelerometer ◽  
Weakly Coupled ◽  
Input Acceleration

This paper presents a new design of microelectromechanical systems (MEMS) based low-g accelerometer utilizing mode-localization effect in the three degree-of-freedom (3-DoF) weakly coupled MEMS resonators. Two sets of the 3-DoF mechanically coupled resonators are used on either side of the single proof mass and difference in the amplitude ratio of two resonator sets is considered as an output metric for the input acceleration measurement. The proof mass is electrostatically coupled to the perturbation resonators and for the sensitivity and input dynamic range tuning of MEMS accelerometer, electrostatic electrodes are used with each resonator in two sets of 3-DoF coupled resonators. The MEMS accelerometer is designed considering the foundry process constraints of silicon-on-insulator multi-user MEMS processes (SOIMUMPs). The performance of the MEMS accelerometer is analyzed through finite-element-method (FEM) based simulations. The sensitivity of the MEMS accelerometer in terms of amplitude ratio difference is obtained as 10.61/g for an input acceleration range of ±2 g with thermomechanical noise based resolution of 0.22 and nonlinearity less than 0.5%.

Effect of Multimaterial Layering on the Response of a Generic Hull Structure

1997 ◽  
Author(s):  
Aaron D. Gupta ◽  
Christopher Meyer
Keyword(s):  
Dynamic Response ◽  
Support System ◽  
Comparative Evaluation ◽  
Single Layer ◽  
Circular Opening ◽  
Vibrational Response ◽  
Multilayered Composite ◽  
Modal Response ◽  
Hull Structure ◽  
Composite Armor

Abstract The dynamic response of a basic, generic, multilayered, composite vehicle hull with a large, circular opening for the turret assembly has been compared with that of an equivalent single-layer, basic metallic hull with identical geometry to assess the influence of a multilayered, composite armor panel structure on the modal response. Both models, without the engine block, mountings, transmission, and base support system consisting of tracks, wheels, sprockets, torsion bars, etc., were generated using PATRAN 3 to facilitate computational modal analysis and comparative evaluation of the influence of multilayered construction on the free vibrational response.

Mode Localization in Coupled Circular Plates

1994 ◽  
Vol 116 (3) ◽  
pp. 286-294 ◽  
Author(s):  
C. O. Orgun ◽  
B. H. Tongue
Keyword(s):  
Periodic Structures ◽  
Qualitative Change ◽  
Disk Drive ◽  
Circular Plates ◽  
Mode Localization ◽  
Infinite Dimensional ◽  
Write Heads ◽  
The Individual ◽  
Support Motion ◽  
Computer Disk

When analyzing structures that are comprised of many similar pieces (periodic structures), it is common practice to assume perfect periodicity. Such an assumption will lead to the existence of eigenmodes that are global in character, i.e., the structural deflections will occur throughout the system. However, research in structural mechanics has shown that, when only weak coupling is present between the individual pieces of the system, small amounts of disorder can produce a qualitative change in the character of the eigenmodes. A typical eigenmode of such a system will support motion only over a limited extend of the structure. Often only one or two of the smaller pieces that make up the structure show any motion, the rest remain quiescent. This phenomenon is known as “mode localization”, since the modes become localized at particular locations on the overall structure. This paper will examine the behavior of several circular plates that are coupled together through springs, a system that models a multiple disk computer disk drive. These drives typically consist of several disks mounted on a single spindle, coupled by read/write heads, which act as weak springs, thus leading one to suspect the possibility of localization. Since such an effect would impact accurate read/write operations at small fly heights, the problem deserves attention. Although computer disk drives contain space fixed read/write heads, this paper will consider springs that are fixed to the plates in order to understand the effect of localization on a set of infinite dimensional structures (the circular plates). Later work will extend the model to the case of space fixed springs and the wave behavior and destabilizing effects that such a configuration will induce.

Theoretical Study of Mode Localization Phenomenon in Bottom-Hole Assemblies in Oil-Well Drilling

1999 ◽  
Vol 121 (3) ◽  
pp. 183-188
Author(s):  
A. S. Yigit ◽  
M. D. Al-Ansary ◽  
M. Khalid
Keyword(s):  
Theoretical Study ◽  
Oil Well ◽  
Well Drilling ◽  
Mode Localization ◽  
Localization Phenomenon ◽  
Bottom Hole ◽  
Weakly Coupled ◽  
Bending Stresses ◽  
First Time ◽  
Strong Mode

The mode localization phenomena in bottom-hole assemblies (BHA) used in oil-well drilling is investigated. A fully gaged stabilizer model is shown to produce weak coupling between segments of drillcollars separated by stabilizers. It is observed that in a weakly coupled BHA, small disorder in span length can cause strong mode localization. For the first time, it is demonstrated that gravity induces a stiffness disorder, which in turn causes strong mode localization in an inclined wellbore, even though no other disorder is present. The effect of localized modes for failure is presented by examining the maximum bending stresses with and without mode localization. The results show that design and operation of drillstrings should consider the possibility of mode localization for an accurate prediction of dynamic behavior.

A Multiple-Scales Analysis of Nonlinear, Localized Modes in a Cyclic Periodic System

1993 ◽  
Vol 60 (2) ◽  
pp. 388-397 ◽  
Author(s):  
A. Vakakis ◽  
T. Nayfeh ◽  
M. King
Keyword(s):  
Vibration Isolation ◽  
Multiple Scales ◽  
Algebraic Equations ◽  
Localized Modes ◽  
Mode Localization ◽  
Nonlinear Mode ◽  
Weakly Coupled ◽  
Passive Vibration Isolation ◽  
Coupling Stiffness ◽  
Multiple Scales Analysis

In this work the nonlinear localized modes of an n-degree-of-freedom (DOF) nonlinear cyclic system are examined by the averaging method of multiple scales. The set of nonlinear algebraic equations describing the localized modes is derived and is subsequently solved for systems with various numbers of DOF. It is shown that nonlinear localized modes exist only for small values of the ratio (k/μ), where k is the linear coupling stiffness and μ is the coefficient of the grounding stiffness nonlinearity. As (k/μ) increases the branches of localized modes become nonlocalized and either bifurcate from “extended” antisymmetric modes in inverse, “multiple” Hamiltonian pitchfork bifurcations (for systems with even-DOF), or reach certain limiting values for large values of(k/μ) (for systems with odd-DOF). Motion confinement due to nonlinear mode localization is demonstrated by examining the responses of weakly coupled, perfectly periodic cyclic systems caused by external impulses. Finally, the implications of nonlinear mode localization on the active or passive vibration isolation of such structures are discussed.

scholarly journals Large-scale parallelization of nanomechanical mass spectrometry with weakly-coupled resonators

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Stefano Stassi ◽  
Giulia De Laurentis ◽  
Debadi Chakraborty ◽  
Katarzyna Bejtka ◽  
Angelica Chiodoni ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Large Scale ◽  
Coupled Resonators ◽  
Nanomechanical Resonator ◽  
Technological Breakthrough ◽  
Physical Size ◽  
Vibrational Response ◽  
Physical Mechanisms ◽  
Real Time Analysis ◽  
Weakly Coupled

Abstract Nanomechanical mass spectrometry is a recent technological breakthrough that enables the real-time analysis of single molecules. In contraposition to its extreme mass sensitivity is a limited capture cross-section that can hinder measurements in a practical setting. Here we show that weak-coupling between devices in resonator arrays can be used in nanomechanical mass spectrometry to parallelize the measurement. This coupling gives rise to asymmetric amplitude peaks in the vibrational response of a single nanomechanical resonator of the array, which coincide with the natural frequencies of all other resonators in the same array. A rigorous theoretical model is derived that explains the physical mechanisms and describes the practical features of this parallelization. We demonstrate the significance of this parallelization through inertial imaging of analytes adsorbed to all resonators of an array, with the possibility of simultaneously detecting resonators placed at distances a hundred times larger than their own physical size.

Analytic Study of Linear and Nonlinear Mode Localization

1993 ◽  
Vol 60 (2) ◽  
pp. 555-557 ◽  
Author(s):  
A. F. Vakakis
Keyword(s):  
Nonlinear Systems ◽  
Analytical Method ◽  
Normal Modes ◽  
Nonlinear Stiffness ◽  
Mode Localization ◽  
Weakly Coupled ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems ◽  
Exact Analytical Method ◽  
Vibrating Systems

The localization of the normal modes of weakly coupled vibrating systems is examined with a new exact, analytical method. Both linear and nonlinear systems are considered and the mode localization is examined by means of “balancing diagrams.” This study complements previous studies of the author and co-workers on investigating mode localization in systems with nonlinear stiffness elements.

Analytical model in a weakly coupled sandwich for memory purposes

1996 ◽  
Vol 79 (8) ◽  
pp. 6649
Author(s):  
Zhigang Wang ◽  
Yoshihisa Nakamura
Keyword(s):  
Analytical Model ◽  
Weakly Coupled
Sign in / Sign up

Export Citation Format

Share Document