Restoring Force Surface Analysis of Nonlinear Vibration Data From Micro-Cantilever Beams

The responses of micro-cantilever beams, with lengths ranging from 100-1500 microns, have been found to exhibit nonlinear dynamic characteristics at very low vibration amplitudes and in near vacuum. This work seeks to find a functional form for the nonlinear forces acting on the beams in order to aide in identifying their cause. In this paper, the restoring force surface method is used to non-parametrically identify the nonlinear forces acting on a 200 micron long beam. The beam response to sinusoidal excitation contains as many as 19 significant harmonics within the measurement bandwidth. The nonlinear forces on the beam are found to be oscillatory and to depend on the beam velocity. A piecewise linear curve is fit to the response in order to more easily compare the restoring forces obtained at various amplitudes. The analysis illustrates the utility of the restoring force surface method on a system with complex and highly nonlinear forces.

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Development of an Efficient Response Surface Method for Highly Nonlinear Systems from Sparse Sampling Data Using Bayesian Compressive Sensing

ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems Part A Civil Engineering ◽

10.1061/ajrua6.0001155 ◽

2021 ◽

Vol 7 (4) ◽

pp. 04021050

Author(s):

Peiping Li ◽

Yu Wang

Keyword(s):

Nonlinear Systems ◽

Compressive Sensing ◽

Response Surface ◽

Response Surface Method ◽

Sparse Sampling ◽

Surface Method ◽

Highly Nonlinear

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Response surface method strategies coupled with NLFEA for structural reliability analysis of prestressed bridges

10.2749/ghent.2021.1813 ◽

2021 ◽

Author(s):

Silvia J. Sarmiento Nova ◽

Jaime Gonzalez-Libreros ◽

Gabriel Sas ◽

Rafael A. Sanabria Díaz ◽

Maria C. A. Texeira da Silva ◽

...

Keyword(s):

Reliability Analysis ◽

Response Surface ◽

Response Surface Method ◽

Structural Reliability ◽

Limit State ◽

Material Behavior ◽

Nonlinear Material ◽

State Function ◽

Surface Method ◽

Highly Nonlinear

<p>The Response Surface Method (RSM) has become an essential tool to solve structural reliability problems due to its accuracy, efficacy, and facility for coupling with Nonlinear Finite Element Analysis (NLFEA). In this paper, some strategies to improve the RSM efficacy without compromising its accuracy are tested. Initially, each strategy is implemented to assess the safety level of a highly nonlinear explicit limit state function. The strategy with the best results is then identified and used to carry out a reliability analysis of a prestressed concrete bridge, considering the nonlinear material behavior through NLFEA simulation. The calculated value of 𝛽 is compared with the target value established in Eurocode for ULS. The results showed how RSM can be a practical methodology and how the improvements presented can reduce the computational cost of a traditional RSM giving a good alternative to simulation methods such as Monte Carlo.</p>

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An Analytical and Numerical Study of Magnetic Spring Suspension with Energy Recovery Capabilities

Energies ◽

10.3390/en11113126 ◽

2018 ◽

Vol 11 (11) ◽

pp. 3126 ◽

Cited By ~ 5

Author(s):

Yu Jia ◽

Shasha Li ◽

Yu Shi

Keyword(s):

Energy Recovery ◽

Numerical Study ◽

Numerical Models ◽

Limited Range ◽

Paradigm Shifts ◽

Restoring Force ◽

Highly Nonlinear ◽

Spring Mechanism ◽

Paved Road ◽

Rider Comfort

As the automotive paradigm shifts towards electric, limited range remains a key challenge. Increasing the battery size adds weight, which yields diminishing returns in range per kilowatt-hour. Therefore, energy recovery systems, such as regenerative braking and photovoltaic cells, are desirable to recharge the onboard batteries in between hub charge cycles. While some reports of regenerative suspension do exist, they all harvest energy in a parasitic manner, and the predicted power output is extremely low, since the majority of the energy is still dissipated to the environment by the suspension. This paper proposes a fundamental suspension redesign using a magnetically-levitated spring mechanism and aims to increase the recoverable energy significantly by directly coupling an electromagnetic transducer as the main damper. Furthermore, the highly nonlinear magnetic restoring force can also potentially enhance rider comfort. Analytical and numerical models have been constructed. Road roughness data from an Australian road were used to numerically simulate a representative environment response. Simulation suggests that 10’s of kW to >100 kW can theoretically be generated by a medium-sized car travelling on a typical paved road (about 2–3 orders of magnitude higher than literature reports on parasitic regenerative suspension schemes), while still maintaining well below the discomfort threshold for passengers (<0.315 m/s 2 on average).

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Generalized closed-form models for pull-in analysis of micro cantilever beams subjected to partial electrostatic load

Sensors and Actuators A Physical ◽

10.1016/j.sna.2012.07.020 ◽

2012 ◽

Vol 185 ◽

pp. 109-116 ◽

Cited By ~ 16

Author(s):

Cuong Do ◽

Maryna Lishchynska ◽

Kieran Delaney ◽

Martin Hill

Keyword(s):

Closed Form ◽

Cantilever Beams ◽

Micro Cantilever

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Analysis of Piecewise Linear Systems With Displacement and Time Regions by Vector Fields

Volume 7A: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8037 ◽

1999 ◽

Author(s):

Mikio Nakai ◽

Shinji Murata ◽

Seiji Hagio

Keyword(s):

Linear Systems ◽

Vector Fields ◽

Matrix Representation ◽

Piecewise Linear ◽

Generalized Solution ◽

State Variables ◽

Piecewise Linear Systems ◽

Restoring Forces ◽

Pass Through ◽

Solution Methodology

Abstract A generalized solution methodology based on piecewise linear vector fields is proposed for piecewise linear systems with singular regions or asymmetric restoring forces which vary spatially and temporally. In matrix representation for these systems, state variables in each region can be explicitly expressed as a function of the time the orbit spends between two boundaries or the time the orbit takes to pass through the boundary. The time can be determined by the Brent method, and periodic solutions can then be obtained. Analytical solutions are validated on a system with 3-regions of displacement and 2-regions of time, a circumferential vibration of gear meshing system, by using the newly developed numerical method.

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Model Predictive Control of a Highly Nonlinear Process Based on Piecewise Linear Wiener Models

2006 1ST IEEE International Conference on E-Learning in Industrial Electronics ◽

10.1109/icelie.2006.347195 ◽

2006 ◽

Cited By ~ 5

Author(s):

Ghobad Shafiee ◽

MohammadMehdi Arefi ◽

MohammadReza Jahed-Motlagh ◽

AliAkbar Jalali

Keyword(s):

Model Predictive Control ◽

Predictive Control ◽

Piecewise Linear ◽

Nonlinear Process ◽

Highly Nonlinear ◽

Wiener Models

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Miniaturized Broadband Vibration Energy Harvester With Piecewise-Linear Asymmetric Restoring Force

ASME 2019 Conference on Smart Materials, Adaptive Structures and Intelligent Systems ◽

10.1115/smasis2019-5616 ◽

2019 ◽

Author(s):

Arata Masuda ◽

Feng Zhao

Keyword(s):

Energy Harvester ◽

Piecewise Linear ◽

Experimental Studies ◽

Resonance Peak ◽

Vibration Energy ◽

Restoring Force ◽

Vibration Energy Harvester ◽

Resonance Band ◽

Compact Size ◽

The Asymmetry

Abstract This paper presents a design study of a miniaturized broadband nonlinear vibration energy harvester (VEH) with piecewise-linear restoring force based on a mechanically-sprung resonator with stoppers. It is commonly recognized that a VEH based on a nonlinearly-sprung resonator can show broadband frequency characteristics while keeping its maximum power performance due to its bent resonance peak. The resonator to be investigated in this study consists of a magnet composite as a mass moving through an induction coil, two planar springs, and mechanical stoppers. The magnet composite is comprised of two repelling cylindrical magnets and a steel disk between them, all encapsulated in a thin stainless-steel cylinder. The planar springs with spiral-like shape are respectively connected to the both ends of the magnet composite so that they provide soft linear stiffness in a compact size. The mechanical stoppers installed to constrain the deformation of the spring give the resonator piecewise-linear hardening characteristics which effectively broaden the resonance band. In this study, the prototype VEH developed in the previous study is presented, and the gaps between the springs and stoppers are adjusted so that the resultant piecewise-linear restoring force shows symmetric or asymmetric property with respect to the equilibrium point. Experimental studies and analyses are carried out to examine the performance of the presented VEH in terms of the frequency response. The comparison of three different configurations of the stopper illustrates how the asymmetry in the bilinear restoring force affects the shape of the resonance peak. It is also suggested that the asymmetry may help the VEH operate in broader band by exploiting its ability of tailoring the resonance characteristics, which still needs further investigation.

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MODELING OF MONOCRYSTALLINE MAGNESIUM MICROBEAM BENDING

Acta Polytechnica CTU Proceedings ◽

10.14311/app.2018.15.0069 ◽

2018 ◽

Vol 15 ◽

pp. 69-73

Author(s):

Jiří Němeček ◽

Jan Maňák ◽

Jiří Němeček

Keyword(s):

Focused Ion Beam ◽

Ion Beam ◽

Three Dimensional ◽

Deformation Energy ◽

Displacement Curve ◽

Fe Model ◽

Cantilever Beams ◽

Elastoplastic Behavior ◽

Load Displacement ◽

Micro Cantilever

This paper presents a numerical simulation of a micro-scale experiment on a magnesium alloy. Micro cantilever beams were fabricated using Focused Ion Beam technology in a single crystal of Mg. The cantilever beams have dimensions in the order of a few micrometers and a pentagonal cross section. Nanoindenter was used for cantilever beam bending and load-displacement curve was received. Cantilevers with two different crystallographic orientations were chosen for the experiment. Three dimensional numerical FE model with elastoplastic behavior respecting crystal anisotropy was used to fit experimental load displacement curves. Strengths and deformation energy were evaluated from the models for each cantilever.

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Multiple Sliding Surface Control: Theory and Application

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1321268 ◽

2000 ◽

Vol 122 (4) ◽

pp. 586-593 ◽

Cited By ~ 58

Author(s):

J. K. Hedrick ◽

P. P. Yip

Keyword(s):

Controller Design ◽

Sliding Mode ◽

Control Input ◽

Sliding Surface ◽

Nonlinear Controller ◽

Automotive Control ◽

Surface Control ◽

Surface Method ◽

Highly Nonlinear ◽

Automated Highway

This paper discusses the development of a nonlinear controller design methodology and its application to an automotive control problem. The method is called the “Multiple Sliding Surface” method and is closely related to sliding mode control, input/output linearization and integrator backstepping. The method was developed for a class of systems, typical of automotive control systems, where the uncertainties are “mismatched” and where many of the equations contain sparse, experimentally obtained maps. The error bounds on these maps are often unknown and their sparseness makes them difficult to differentiate. The developed method does not require any derivatives and has guaranteed semi-global stability. This paper summarizes the development of the method and applies it to the design of a highly nonlinear system. The example is a combined brake/throttle controller for precision vehicle following. This controller was implemented on the California PATH vehicles in DEMO’97, an automated highway technology demonstration that occurred in San Diego, California in August of 1997. [S0022-0434(00)03004-5]

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