Programmable Multistable Mechanisms: Synthesis and Modeling

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Mohamed Zanaty ◽  
Ilan Vardi ◽  
Simon Henein
Keyword(s):  
Compliant Mechanisms ◽  
Reaction Force ◽  
Stable State ◽  
Beam Theory ◽  
Qualitative Behavior ◽  
Stable States ◽  
New Family ◽  
Fixed Constant ◽  
Numerical Finite Element ◽  
Euler Bernoulli Beam

Compliant mechanisms can be classified according to the number of their stable states and are called multistable mechanisms if they have more than one stable state. We introduce a new family of mechanisms for which the number of stable states is modified by programming inputs. We call such mechanisms programmable multistable mechanisms (PMM). A complete qualitative analysis of a PMM, the T-mechanism, is provided including a description of its multistability as a function of the programming inputs. We give an exhaustive set of diagrams illustrating equilibrium states and their stiffness as one programming input varies while the other is fixed. Constant force behavior is also characterized. Our results use polynomial expressions for the reaction force derived from Euler–Bernoulli beam theory. Qualitative behavior follows from the evaluation of the zeros of the polynomial and its discriminant. These analytical results are validated by numerical finite element method simulations.

Theoretical Analysis on Nonlinear Buckling, Post-buckling of Slender Beams and Bi-stable Mechanisms

2021 ◽  
pp. 1-14
Author(s):  
Ke Wu ◽  
Gang Zheng
Keyword(s):  
Compliant Mechanisms ◽  
Beam Theory ◽  
Stable States ◽  
Nonlinear Buckling ◽  
Theoretical Derivation ◽  
Deforma Tion ◽  
Theoretical Investigations ◽  
Slender Beams ◽  
Post Buckling ◽  
Kinematic Models

Abstract Compliant Mechanisms (CMs) are used to transfer motion, force and energy, taking advantages of the elastic deforma- tion of the involved compliant members. A branch of spe- cial type of elastic phenomenon called (post) buckling has been widely considered in CMs: avoiding buckling for better payload-bearing capacity and utilizing post-buckling to pro- duce multi-stable states. This paper digs into the essence of beam's bucking and post-bucking behaviors where we start from the famous Euler–Bernoulli beam theory and then ex- tend the mentioned linear theory into geometrically nonlin- ear one to handle multi-mode buckling problems via intro- ducing the concept of bifurcation theory. Five representative beam buckling cases are studied in this paper, followed by detailed theoretical investigations of their post-buckling be- haviors where the multi-state property has been proved. We finally propose a novel type of bi-stable mechanisms termed as Pre-buckled Bi-stable Mechanisms (PBMs) that integrate the features of both rigid and compliant mechanisms. The theoretical insights of PBMs are presented in detail for future studies. To the best of our knowledge, this paper is the first ever study on the theoretical derivation of the kinematic models of PBMs, which could be an important contribution to this field.

An Analytical Model for Beam Flexure Modules Based on the Timoshenko Beam Theory

2017 ◽  
Author(s):  
M. H. Kahrobaiyan ◽  
M. Zanaty ◽  
S. Henein
Keyword(s):  
Timoshenko Beam ◽  
Axial Load ◽  
Compliant Mechanisms ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Bernoulli Beam ◽  
Model Based ◽  
Bernoulli Beam Theory ◽  
Euler Bernoulli Beam

Short beams are the key building blocks in many compliant mechanisms. Hence, deriving a simple yet accurate model of their elastokinematics is an important issue. Since the Euler-Bernoulli beam theory fails to accurately model these beams, we use the Timoshenko beam theory to derive our new analytical framework in order to model the elastokinematics of short beams under axial loads. We provide exact closed-form solutions for the governing equations of a cantilever beam under axial load modeled by the Timoshenko beam theory. We apply the Taylor series expansions to our exact solutions in order to capture the first and second order effects of axial load on stiffness and axial shortening. We show that our model for beam flexures approaches the model based on the Euler-Bernoulli beam theory when the slenderness ratio of the beams increases. We employ our model to derive the stiffness matrix and axial shortening of a beam with an intermediate rigid part, a common element in the compliant mechanisms with localized compliance. We derive the lateral and axial stiffness of a parallelogram flexure mechanism with localized compliance and compare them to those derived by the Euler-Bernoulli beam theory. Our results show that the Euler-Bernoulli beam theory predicts higher stiffness. In addition, we show that decrease in slenderness ratio of beams leads to more deviation from the model based on the Euler-Bernoulli beam theory.

Tuning Stiffness Nonlinearity: Theory and Applications

2020 ◽  
Author(s):  
Mohamed Zanaty ◽  
Ilan Vardi ◽  
Simon Henein
Keyword(s):  
Compliant Mechanisms ◽  
Real Life ◽  
Beam Theory ◽  
Elastic Behavior ◽  
Bernoulli Beam ◽  
Stiffness Constant ◽  
Real Life Situation ◽  
Tuning Methods ◽  
Nonlinear Elastic ◽  
Euler Bernoulli Beam

Abstract Perfect elasticity is not achievable in real-life situation, so spring stiffness is not perfectly constant. In this paper, we study the effect of modifying non-linear stiffness terms while keeping the nominal stiffness constant. We introduce three methods to design and tune linear and nonlinear elastic behavior in the context of compliant mechanisms and we present mechanical realizations. These designs are modeled using Euler-Bernoulli beam theory. Numerical simulation and experimental measurement show a good match with the theoretical model. We then present applications of our stiffness tuning methods to mechanical meta-materials, mechanical resonators, and mechanical computation.

Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yan-Shin Shih ◽  
Chen-Yuan Chung
Keyword(s):  
Governing Equation ◽  
Moving Boundary ◽  
Beam Theory ◽  
Crack Model ◽  
Breathing Crack ◽  
Connecting Rod ◽  
Bernoulli Beam ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Crank Mechanism

This paper investigates the dynamic response of the cracked and flexible connecting rod in a slider-crank mechanism. Using Euler–Bernoulli beam theory to model the connecting rod without a crack, the governing equation and boundary conditions of the rod's transverse vibration are derived through Hamilton's principle. The moving boundary constraint of the joint between the connecting rod and the slider is considered. After transforming variables and applying the Galerkin method, the governing equation without a crack is reduced to a time-dependent differential equation. After this, the stiffness without a crack is replaced by the stiffness with a crack in the equation. Then, the Runge–Kutta numerical method is applied to solve the transient amplitude of the cracked connecting rod. In addition, the breathing crack model is applied to discuss the behavior of vibration. The influence of cracks with different crack depths on natural frequencies and amplitudes is also discussed. The results of the proposed method agree with the experimental and numerical results available in the literature.

Chaotic vibrations of carbon nanotubes subjected to a traversing force considering nonlocal elasticity theory

2021 ◽  
pp. 239779142110633
Author(s):  
Reza Ebrahimi
Keyword(s):  
Nonlocal Parameter ◽  
Power Spectra ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Effective Control ◽  
Maximum Lyapunov Exponent ◽  
Harmonic Force ◽  
Spectra Analysis ◽  
Chaotic Vibrations ◽  
Euler Bernoulli Beam

The existence of chaos in the lateral vibration of the carbon nanotube (CNT) can contribute to source of instability and inaccuracy within the nano mechanical systems. So, chaotic vibrations of a simply supported CNT which is subjected to a traversing harmonic force are studied in this paper. The model of the system is formulated by using nonlocal Euler–Bernoulli beam theory. The equation of motion is solved using the Rung–Kutta method. The effects of the nonlocal parameter, velocity and amplitude of the traversing harmonic force on the nonlinear dynamic response of the system are analyzed by the bifurcation diagrams, phase plane portrait, power spectra analysis, Poincaré map and the maximum Lyapunov exponent. The results indicate that the nonlocal parameter, velocity and amplitude of the traversing harmonic force have considerable effects on the bifurcation behavior and can be used as effective control parameters for avoiding chaos.

Fatigue Life Prediction of Drill-String Subjected to Random Loadings

2014 ◽  
Author(s):  
Jiahao Zheng ◽  
Hongyuan Qiu ◽  
Jianming Yang ◽  
Stephen Butt
Keyword(s):  
Fatigue Life ◽  
Time History ◽  
Beam Theory ◽  
Drill String ◽  
Finite Element Models ◽  
Bernoulli Beam ◽  
Stress Cycles ◽  
Rainflow Counting ◽  
Euler Bernoulli Beam ◽  
Random Nature

Based on linear damage accumulation law, this paper investigates the fatigue problem of drill-strings in time domain. Rainflow algorithms are developed to count the stress cycles. The stress within the drill-string is calculated with finite element models which is developed using Euler-Bernoulli beam theory. Both deterministic and random excitations to the drill-string system are taken into account. With this model, the stress time history in random nature at any location of the drill-string can be obtained by solving the random dynamic model of the drill-string. Then the random time history is analyzed using rainflow counting method. The fatigue life of the drill-string under both deterministic and random excitations can therefore be predicted.

Experimental and Theoretical Study of a Dual-Beam Piezoelectric Energy Harvester With Misaligned Magnets

2018 ◽  
Author(s):  
Wei-Jiun Su ◽  
Hsuan-Chen Lu
Keyword(s):  
Energy Harvester ◽  
Theoretical Study ◽  
Beam Theory ◽  
Main Beam ◽  
Bernoulli Beam ◽  
Potential Wells ◽  
Piezoelectric Energy ◽  
Dual Beam ◽  
Frequency Sweeps ◽  
Euler Bernoulli Beam

In this study, a dual-beam piezoelectric energy harvester is proposed. This harvester consists of a main beam and an auxiliary beam with a pair of magnets attached to couple their motions. The potential energy of the system is modeled to understand the influence of the potential wells on the dynamics of the harvester. It is noted that the alignment of the magnets significantly influences the potential wells. A theoretical model of the harvester is developed based on the Euler-Bernoulli beam theory. Frequency sweeps are conducted experimentally and numerically to study the dynamics of the harvester. It is shown that the dual-beam harvester can exhibit hardening effect with different configurations of magnet alignments in frequency sweeps. The performance of the harvester can be improved with proper placement of the magnets.

Optimal Design of Bi- and Multi-Stable Compliant Cellular Structures

2018 ◽  
Author(s):  
Quantian Luo ◽  
Liyong Tong
Keyword(s):  
Optimal Design ◽  
Virtual Work ◽  
Reaction Force ◽  
Nonlinear Finite Element ◽  
Cellular Structures ◽  
Stress And Strain ◽  
Principle Of Virtual Work ◽  
Stable States ◽  
Threshold Method ◽  
Element Analysis

This paper presents optimal design for nonlinear compliant cellular structures with bi- and multi-stable states via topology optimization. Based on the principle of virtual work, formulations for displacements and forces are derived and expressed in terms of stress and strain in all load steps in nonlinear finite element analysis. Optimization for compliant structures with bi-stable states is then formulated as: 1) to maximize the displacement under specified force larger than its critical one; and 2) to minimize the reaction force for the prescribed displacement larger than its critical one. Algorithms are developed using the present formulations and the moving iso-surface threshold method. Optimal design for a unit cell with bi-stable states is studied first, and then designs of multi-stable compliant cellular structures are discussed.

scholarly journals Path-dependent institutions drive alternative stable states in conservation

2018 ◽  
Vol 116 (2) ◽  
pp. 689-694 ◽  
Author(s):  
Edward W. Tekwa ◽  
Eli P. Fenichel ◽  
Simon A. Levin ◽  
Malin L. Pinsky
Keyword(s):  
Renewable Resources ◽  
Path Dependence ◽  
Alternative Stable States ◽  
Stable State ◽  
Empirical Support ◽  
Stable States ◽  
Alternative Stable State ◽  
Important Challenge ◽  
Quantitative Analyses ◽  
Path Dependent

Understanding why some renewable resources are overharvested while others are conserved remains an important challenge. Most explanations focus on institutional or ecological differences among resources. Here, we provide theoretical and empirical evidence that conservation and overharvest can be alternative stable states within the same exclusive-resource management system because of path-dependent processes, including slow institutional adaptation. Surprisingly, this theory predicts that the alternative states of strong conservation or overharvest are most likely for resources that were previously thought to be easily conserved under optimal management or even open access. Quantitative analyses of harvest rates from 217 intensely managed fisheries supports the predictions. Fisheries’ harvest rates also showed transient dynamics characteristic of path dependence, as well as convergence to the alternative stable state after unexpected transitions. This statistical evidence for path dependence differs from previous empirical support that was based largely on case studies, experiments, and distributional analyses. Alternative stable states in conservation appear likely outcomes for many cooperatively managed renewable resources, which implies that achieving conservation outcomes hinges on harnessing existing policy tools to navigate transitions.

scholarly journals Influence of Frequency on the Resolution of Magnetostrictive Bio-Inspired Whisker Sensors

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ran Zhao ◽  
Bo-wen Wang ◽  
Quan-guo Lu ◽  
Jian-wu Yan ◽  
Xiao-cui Yuan
Keyword(s):  
Vibration Frequency ◽  
Dynamic Testing ◽  
Theoretical Calculations ◽  
Beam Theory ◽  
Experimental System ◽  
Flow Sensors ◽  
Maximum Resolution ◽  
Sensing Model ◽  
Euler Bernoulli Beam ◽  
Good Agreement

Magnetostrictive biomimetic whiskers have been used as tactile and flow sensors. Compared to other types of whiskers, such whiskers have the advantage of being able to perform static and dynamic measurements. For dynamic measurement, the whisker’s resolution changes with varying vibration frequency; however, the mechanism for this influence has not been studied yet. Thus, the aim of this study is to investigate the resolution–frequency correlation. First, the structure and operation principle of the whisker were analyzed. Then, the Euler–Bernoulli beam theory was employed to establish the sensing model of the magnetostrictive whisker. Finally, the mapping relationship between sensor resolution and frequency was obtained. The eigenfrequency analysis was implemented by FEM to obtain the frequency response of the whisker. A vibration experimental system was built for dynamic testing. The experimental results were in good agreement with the theoretical calculations. Furthermore, it was noted that the resolution was positively correlated with frequency, and the maximum resolution was attained at the natural frequency (two peak values appeared at the first-order and second-order eigenfrequencies). Our research reveals the manner in which a whisker sensor’s resolution is affected by the vibration frequency. The theoretical model can be used to predict the resolution of magnetostrictive whisker sensors.

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