Bistable Buckled Beam: Modelling and Piezoelectric Actuation

2008 ◽  
Vol 54 ◽  
pp. 281-286 ◽  
Author(s):  
C. Maurini ◽  
Joel Pouget ◽  
Stefano Vidoli
Keyword(s):  
Piezoelectric Actuation ◽  
Nonlinear Properties ◽  
Buckled Beams ◽  
System A ◽  
Buckled Beam ◽  
Piezoelectric Beam ◽  
Transversal Motion ◽  
Bistable Structures ◽  
Two Parameter ◽  
Two Equilibria

Bistable structures, such as buckled beams, are characterized by a two-well potential. Their nonlinear properties are currently exploited in actuators to produce relatively high displacements and forces with low actuation energies. We investigate the use of distributed multiparameter actuation to control the buckling and postbuckling behaviour of a three-layer piezoelectric beam pinned at either end. A two-parameter bending actuation controls the transversal motion, whilst an axial actuation modulates the tangent bending stiffness. The postbuckling behaviour is studied by reducing to a 2 dof system a nonlinear extensible elastica model. When the bending actuation is spatially symmetric, the postbuckling phenomena are characterized by a snapthrough instability. The use of a two-parameter actuation opens new transition scenarios, where it is possible to get quasi-static transitions between the two equilibria of the buckled beam, without any instability phenomenon.

Investigation on Free Vibration of Buckled Beams

2012 ◽  
Vol 433-440 ◽  
pp. 41-44 ◽  
Author(s):  
Ming Hsu Tsai ◽  
Wen Yi Lin ◽  
Kuo Mo Hsiao ◽  
Fu Mio Fujii
Keyword(s):  
Free Vibration ◽  
Virtual Work ◽  
Beam Theory ◽  
Taylor Series Expansion ◽  
Element Formulation ◽  
Governing Equations ◽  
Nonlinear Beam ◽  
Buckled Beams ◽  
Buckled Beam ◽  
D’Alembert Principle

The objective of this study is to investigate the deformed configuration and free vibration around the deformed configuration of clamped buckled beams by co-rotational finite element formulation. The principle of virtual work, d'Alembert principle and the consistent second order linearization of the nonlinear beam theory are used to derive the element equations in current element coordinates. The governing equations for linear vibration are obtained by the first order Taylor series expansion of the equation of motion at the static equilibrium position of the buckled beam. Numerical examples are studied to investigate the natural frequencies of clamped buckled beams with different slenderness ratios under different axial compression.

Modeling and Experimental Validation of Actuating a Bistable Buckled Beam Via Moment Input

2015 ◽  
Vol 82 (5) ◽  
Author(s):  
Jonathon Cleary ◽  
Hai-Jun Su
Keyword(s):  
Theoretical Model ◽  
Experimental Test ◽  
Experimental Validation ◽  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Computational Tool ◽  
Specific Mechanism ◽  
Test Setup ◽  
Buckled Beams ◽  
Buckled Beam

Bistable mechanisms have two stable equilibrium positions separated by a higher energy unstable equilibrium position. They are well suited for microswitches, microrelays, and many other macro- and micro-applications. This paper discusses a bistable buckled beam actuated by a moment input. A theoretical model is developed for predicting the necessary input moment. A novel experimental test setup was created for experimental verification of the model. The results show that the theoretical model is able to predict the maximum necessary input moment within 2.53%. This theoretical model provides a guideline to design bistable compliant mechanisms and actuators. It is also a computational tool to size the dimensions of buckled beams for actuating a specific mechanism.

The Polarizability of Molecular Hydrogen H2

1936 ◽  
Vol 32 (2) ◽  
pp. 260-264 ◽  
Author(s):  
C. E. Easthope
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Molecular Hydrogen ◽  
Applied Field ◽  
Minimum Energy ◽  
Wave Functions ◽  
The Other ◽  
System A ◽  
The One ◽  
Two Parameter

1. The problem of calculating the polarizability of molecular hydrogen has recently been considered by a number of investigators. Steensholt and Hirschfelder use the variational method developed by Hylleras and Hassé. For ψ0, the wave function of the unperturbed molecule when no external field is present, they take either the Rosent or the Wang wave function, while the wave functions of the perturbed molecule were considered in both the one-parameter form, ψ0 [1+A(q1 + q2)] and the two-parameter form, ψ0 [1+A(q1 + q2) + B(r1q1 + r2q2)], where A and B are parameters to be varied so as to give the system a minimum energy, q1 and q2 are the coordinates of the electrons 1 and 2 in the direction of the applied field as measured from the centre of the molecule, and r1 and r2 are their respective distances from the same point. Mrowka, on the other hand, employs a method based on the usual perturbation theory. Their numerical results are given in the following table.

CONDITIONS FOR APPEARANCE AND DISAPPEARANCE OF LIMIT CYCLES IN THE SHIMIZU–MORIOKA SYSTEM

2011 ◽  
Vol 21 (09) ◽  
pp. 2489-2503
Author(s):  
LINGLING LIU ◽  
BO GAO
Keyword(s):  
Numerical Simulations ◽  
Limit Cycles ◽  
Center Manifold ◽  
Normal Forms ◽  
Hopf Bifurcations ◽  
Algebraic Varieties ◽  
System A ◽  
Parameter Dependent ◽  
Generalized Lorenz Canonical Form ◽  
Two Equilibria

This paper deals with the Shimizu–Morioka system, a special generalized Lorenz canonical form. Using techniques of elimination in the computation of algebraic varieties we obtain parameter-dependent normal forms on a center manifold. Our computation shows that the maximal number of limit cycles produced from Hopf bifurcations is four and only even number of limit cycles can be bifurcated near the two equilibria because of [Formula: see text]-symmetry. Our parameter-dependent normal forms enable us to give parameter conditions for the cases of none, two and four limit cycles separately. Furthermore, considering exterior perturbations, we give conditions under which one or three limit cycles can be produced from Hopf bifurcations. Moreover, we also give conditions for fold bifurcations, under which limit cycles coincide or disappear. Finally, our results are illustrated by numerical simulations.

Analytical and Experimental Investigation of Buckled Beams as Negative Stiffness Elements for Passive Vibration and Shock Isolation Systems

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Benjamin A. Fulcher ◽  
David W. Shahan ◽  
Michael R. Haberman ◽  
Carolyn Conner Seepersad ◽  
Preston S. Wilson
Keyword(s):  
Resonance Frequency ◽  
Vibration Isolation ◽  
Negative Stiffness ◽  
Peak Acceleration ◽  
Single Beam ◽  
Buckled Beams ◽  
Buckled Beam ◽  
Double Beam ◽  
Shock Isolation ◽  
Isolation Systems

The behavior of a buckled beam mechanism, which exhibits both bistability and negative stiffness, is investigated for the purposes of passive shock and vibration isolation. The vibration and shock isolation systems investigated in this research include linear, positive stiffness springs in parallel with the transverse motion of buckled beams, resulting in quasizero stiffness behavior. For vibration isolation systems, quasizero stiffness lowers the resonance frequency of the system, thereby reducing its transmissibility at frequencies greater than resonance. For shock isolation systems, quasizero stiffness provides constant-force shock isolation at tailored force levels, thereby enabling increased capacity for absorbing shock energy relative to a comparable positive stiffness system. Single- and double-beam configurations that exhibit first-mode buckling are utilized for vibration isolation, and a single beam that exhibits first- and third-mode buckling is used for shock isolation. For all cases, the static and dynamic behavior of each configuration is modeled analytically. The models are then used to design prototype vibration and shock isolation systems that are fabricated using selective laser sintering (SLS). The dynamic behavior of the systems in response to base excitations is determined experimentally, and the results are compared to model-based predictions. The vibration isolation prototypes display isolation levels that are tunable by varying the axial compression of the beams. Double-beam systems are shown to provide greater reductions in resonance frequency than single-beam systems for comparable levels of axial compression. However, low-frequency isolation capabilities are sensitive to the high levels of precision required to obtain low levels of system stiffness. The shock isolation prototype provides isolation at prespecified threshold levels of force or acceleration. In the prototype system, an input shock with a peak acceleration of approximately 7 g is reduced to a peak acceleration of the isolated mass of approximately 1 g. High levels of negative acceleration are observed in models and prototype systems when the buckled beam snaps back to its original position; however, models indicate that large negative accelerations can be mitigated using one-way dampers.

Design and Optimization of Piezoelectric-Actuated Torsion Mirror With Lever Mechanisms

Volume 3 ◽  
2004 ◽  
Author(s):  
Cho-Chun Wu ◽  
Meng-Ju Lin ◽  
Jin H. Huang
Keyword(s):  
Piezoelectric Material ◽  
Applied Voltage ◽  
Large Angle ◽  
Piezoelectric Actuation ◽  
Design And Optimization ◽  
High Frequency Response ◽  
Moment Arms ◽  
Piezoelectric Beam ◽  
Lever Mechanism ◽  
Structure Layer

Considering with high frequency response and self-detection function, a torsion mirror is designed by using piezoelectric material. For large rotating angle requirement, the torsion mirror contains a mechanism with four levers. The torsion mirror is rotating due to actuated by reflection of a piezoelectric beam deposing on the structure layer. The structure layer connects to the lever mechanism. The lever mechanism has four levers. Three levers enlarge the rotating angles by the different ratio of apply and resist moment arms lengths. The fourth lever has the same apply and resist moment arms lengths to adjust the rotating direction the same as deflection of piezoelectric-actuated beam. For self-detecting rotating angle, another additional beam with piezoelectric material depositing is attached to the mirror plate. Finite element method is used to analyze. To investigate the effect of piezoelectric actuated beam on rotating angle, the results show when the actuated beam has length and width of 300 and 24 μm, the thickness structure and piezoelectric actuation layers are both 1 μm, and the applied voltage is 10 volts, the maximum rotating angles could be 50.4 degree. In this rotating angle, the sensing voltage is 170 volts by the piezoelectric material beam attached to mirror plate. Therefore, the torsion mirror can rotate to large angle and have high resolution of angle sensing. To investigate the effect of ratio of apply and resist moment arms lengths on rotating angle. A maximum value is obtained. To optimize the ratio of apply and resist moment arms lengths, the structure of the torsion mirror with piezoelectric actuated beam being 100 and 8 μm long and wide is investigated. The thickness of structure and piezoelectric actuation layers are both 1 μm. And the applied voltage is 10 volts. It shows that the rotating angle increases nonlinearly as the ratio of apply and resist moment arms lengths increasing. And when the rotating angle reaches the maximum values, the rotating angle decreases fast as the ratio of apply and resist moment arms lengths increasing to 1. The maximum rotating angle is 22.71 degrees and the corresponding ratio of apply and resist moment arms lengths is 46/54. Theoretical analysis is derived and has similar tendency.

scholarly journals On Stress-Strength Interval-System Reliability with Applications in Heart Conditions

2019 ◽  
Vol 5 (1) ◽  
pp. 1-12
Author(s):  
Hoang Pham
Keyword(s):  
Human Heart ◽  
Random Variable ◽  
Minimum Variance ◽  
Interval System ◽  
System A ◽  
Independent Events ◽  
Reliability Estimates ◽  
Chance Events ◽  
Exponential Random Variables ◽  
Two Parameter

The random variable X represents the stress placed on the system by the operating environment and random variable Y represents the strength of the system. A system is able to perform its intended function if its strength is greater than the stress imposed upon it. Reliability of the system is defined as the probability that the system is strong enough to overcome the stress. That is, R = P(Y >X). In other words, reliability is the probability that the strengths of the unit are greater than the stresses. The stress-strength model has found interests in many applications include mechanical engineering and human heart monitoring conditions. The interval-system is defined as a system with a series of chance events that occur in a given interval of time. A k-out-of-n interval-system is a system with a series of n events in a given interval of time which successes (or functions) if and only if at least k of the events succeed (function). In short, the k-out-of-n interval-system is an interval-system which successes if and only if at least k of n events succeeds. The stress-strength reliability inference of the interval-system with a series of n independent events that occurs in a given interval of time is considered. The reliability of the interval-system is the probability that at least k out of n events in a given interval of time succeed. This paper derives uniform minimum variance unbiased and maximum likelihood reliability estimates of k-out-of-n interval-system based on stress-strength inference events where X (stress) and Y (strength) are independent two-parameter exponential random variables. An application in human heart conditions to illustrate the results is discussed.

Sign in / Sign up

Export Citation Format

Share Document