Flexure System Research Articles

Steady-state responses and wave propagations in the periodic plate

Expressions that describe the steady-state behavior of a multi-span rib-stiffened rectangular plate and the flexural wave propagation are derived, and lateral disturbances are taken into account. The vibrational behavior of periodic plate systems can be expressed in terms of waves of both propagating and near-field types. A wave incident upon the line discontinuities gives rise to transmitted and reflected waves of both kinds whose amplitudes may be found from the reflection and transmission coefficients. Here, all of the transmitted and reflected waves of given flexural wave incident upon the periodic plate systems at some specified location are found and superposed, and the approach is extended to the case of incident near-field wave. A method is developed for numerical analysis of quasi-one-dimensional periodic flexural systems, and the relation between the wave-field of incident waves and the wave-field of resulting waves on any span can be expressed by use of it. As an example, the application of the results to the analysis of a multi-span rib-stiffened rectangular plate is then demonstrated. The steady-state responses from a given wave injected at a given span are determined.

Variations in elastic thickness and flexure of the Maracaibo block

We estimate the lateral variations of the elastic thickness of the Maracaibo block with a 3D numerical approach by using centered finite differences. The calculation is based on solving the fourth-order partial differential equation that governs the bending of a thin plate fixed on its boundaries (zero displacement) with variable thickness (or elastic thickness for this particular case). An initial plate-load model is built and is iteratively modified to fit the general basement configuration and gravity data. The final result is an elastic thickness map that covers the Maracaibo block and the surrounding sections of the South American plate. It shows that the elastic thickness ranges from 30 km to 18 km with a mean value of 23.6 km and a mode of 26 km. The largest elastic thickness values are associated with the location of the Santa Marta Mountains and the Barinas Apure Basin, while the smallest ones with the Mérida Andes-Maracaibo Basin flexural system. The current basement configuration within the Maracaibo basin, formed as a result of its geodynamic evolution, has affected the mechanical properties of the Maracaibo block near the current Mérida Andes position. The load of the Perijá Range is compensated by a complex stress tensor , and that of the Santa Marta Mountains does not have an isostatic root as it is held by a relatively strong lithosphere. • Elastic thickness variations of the Maracaibo block are estimated using a 3D numerical approach. • Current elastic thickness is a result of the geodynamic evolution of the region. • Maracaibo block evolution is presented pointing out the events that might have led to the current Te variations.

Application of Digital Image Processing Techniques in the Vessel Flexure System

For a vessel flexure of measure ship under the influence of internal and external environmental factors, which resulting data errors of measuring equipment, the development of the "Vessel Flexure System" can solve the problem. The paper briefly describes the principle and hardware components of Vessel Flexure System, focuses on the application of digital image processing techniques used on linear CCD, put forward the interpretation method of gravity-center, which can determine the location of the center of facula accurately.

Six degrees of freedom vibration transmissibility measurement of flexural opto-mechanical structures with 3-axis acceleration sensors

Abstract At an early stage of a high-resolution flexural opto-mechanical system design, it is essential to analyze its dynamic characteristics for assessing image quality due to environmental vibration, an experimental method to measure six degrees of freedom (6-DoFs) vibration transmissibility of flexural opto-mechanical structures is proposed in this article. A typical flexural opto-mechanical structure consists of an optical component, a mechanical component and several flexural modules. Using the developed method, optical and mechanical components are considered as rigid bodies. Two feature points which are uncoupled in motion are set in the components separately, and they can express 6-DoFs vibration of each component moderately. Several key points are set in each component too, and their vibrational accelerations are measured with 3-axis acceleration sensors firstly. Then, motion relations between the feature points and key points are established, 6-DoFs vibrational acceleration spectrums of the two feature points are analyzed, and 6-DoFs vibration transmissibility between them is calculated. Thirdly, the experiment is carried out for twenty times, and average 6-DoFs vibration transmissibility is calculated. Uncertainties of this method are discussed with numerical analysis and experiments.

Modeling and generating parallel flexure elements

Abstract This work introduces the principles necessary to model and generate parallel flexure elements (i.e., compliant members or flexible joints) that may be used to synthesize next-generation precision flexure systems. These principles are extensions of the Freedom and Constraint Topologies (FACT) synthesis approach, which utilizes geometric shapes to help designers synthesize flexure systems that achieve desired degrees of freedom (DOFs). Prior to this paper, FACT was limited to the design of flexure systems that consisted primarily of simple wire or blade flexure elements only. In this paper, the principles are introduced that enable designers to use the same shapes of FACT to synthesize parallel flexure elements of any geometry, including new and often irregularly-shaped elements (e.g., hyperboloids or hyperbolic paraboloids). The ability to recognize such elements within the shapes of FACT, therefore, enables designers to consider a larger body of solution options that satisfy a broader range of kinematic, elastomechanical, and dynamic design requirements. Example flexure systems that consist of flexure elements, generated using this theory, are provided as case studies.

Designing hybrid flexure systems and elements using Freedom and Constraint Topologies

Abstract. In this paper we introduce the principles necessary to synthesize hybrid flexure systems and elements. Flexure systems consist of rigid bodies that are joined together by flexure elements that elastically deform to guide the system's rigid bodies with desired degrees of freedom (DOFs). The principles introduced here for synthesizing hybrid flexure systems and elements are extensions of the Freedom and Constraint Topologies (FACT) synthesis approach. FACT utilizes a comprehensive library of geometric shapes from which designers can rapidly consider and compare a multiplicity of flexure concepts that achieve any desired set of DOFs. Prior to this paper, designers primarily used these shapes to synthesize parallel and serial flexure systems and elements. With this paper, designers may now use these same shapes to synthesize more general flexures that consist of various combinations of parallel and serial systems and elements (i.e., hybrid configurations). As such, designers can access a larger body of flexure solutions that satisfy demanding design requirements. Instructions for helping designers utilize or avoid the advantages and challenges of over-, under-, and exact-constraint are also provided. Hybrid systems and elements are analysed and designed as case studies.

Synthesizing Parallel Flexures That Mimic the Kinematics of Serial Flexures Using Freedom and Constraint Topologies

The principles of the freedom and constraint topologies (FACT) synthesis approach are adapted and applied to the design of parallel flexure systems that mimic degrees of freedom (DOFs) primarily achievable by serial flexure systems. FACT provides designers with a comprehensive library of geometric shapes. These shapes enable designers to visualize the regions wherein compliant flexure elements may be placed for achieving desired DOFs. By displacing these shapes far from the point of interest of the stage of a flexure system, designers can compare a multiplicity of concepts that utilizes the advantages of both parallel and serial systems. A complete list of which FACT shapes mimic which DOFs when displaced far from the point of interest of the flexure system's stage is provided as well as an intuitive approach for verifying the completeness of this list. The proposed work intends to cater to the design of precision motion stages, optical mounts, microscopy stages, and general purpose flexure bearings. Two case studies are provided to demonstrate the application of the developed procedure.

MEMS Accelerometer Design Optimization Using Genetic Algorithm

MEMS (Microelectromechanical Systems) refers to the technology integrating electrical and mechanical components with feature size of 1~1000 microns. Due to its small size, low cost, low power consumption and high efficiency, MEMS technology has been widely used in many fields.In this paper,the design optimization of MEMS accelerometer is discussed.The main objective of this investigation is to find a optimum design of MEMS,which satisfies a set of given constraints. The accelerometer employs a double folded beam flexure system and the mass being displaced is the proof mass.Due to the complex nature of the problem,a genetic algorithm (GA) is developed for the optimization of MEMS.The GA attempts to minimize the die area and so the four optimal parameter values can be determined. MEMS accelerometers can be used in air-bag deployment systems in automobiles.The experimental results will show the optimal design of MEMS.

The power output and efficiency of a negative capacitance shunt for vibration control of a flexural system

A negative capacitance shunt is a basic, analog, active circuit electrically connected to a piezoelectric transducer to control the vibrations of flexural bodies. The shunt circuit consists of a resistor and a synthetic negative capacitor to introduce a real and imaginary impedance on a vibrating mechanical system. The electrical impedance of the negative capacitance shunt modifies the effective modulus of the piezoelectric transducer to reduce the stiffness and increase the damping, which causes a decrease in amplitude of the vibrating structure to which the elements are bonded. To gain an insight into the electromechanical coupling and power output, the shunt and the electrical properties of the piezoelectric transducer are modeled using circuit modeling software. The power output of the model is validated with experimental measurements of a shunt connected to a piezoelectric transducer pair bonded to a vibrating aluminum cantilever beam. The model is used to select the passive components of the negative capacitance shunt to increase the efficiency and quantify the voltage output limit of the op-amp.

Design of a precision flexural linear stage system with sub-nanometer resolution and 12-mm travel range

Precision ball-bearing-based or roller-bearing-based positioning stage systems are capable of providing a large travel range. However, it is not possible to meet requirements in sub-nanometer positioning resolution, high tilting stiffness, and microradian-level straightness of trajectory repeatability with a simple rolling element guiding system. To meet those requirements and still allow for large travel range, we have designed a novel precision flexural linear stage. It is capable of sub-nanometer positioning resolution and 12-mm travel range for synchrotron radiation instrumentation applications. The design and preliminary test results for a prototype stage system are discussed in this paper.

Constraint Optimization of a Novel Flexure System with Two Rotation Freedom Degree

A two freedom flexure system is presented. All the constraints are selected in Case 2, type 1 and Case 2, type 2 in FACT chart. The locations of the non-redundant constraints are optimizated by change laws of the three order natural frequency with the position of constraint. All the redundant constraints are selected to increase the add symmetry to the flexure system. Results of Simulation of static calibration dominates that the flexure system is decoupled. The synthesis process of the two freedom flexure system proposes important reference for design of the flexure system.

Optimum CFRP Configuration to Efficiently Repair Laterally Damaged, Simply Supported Rectangular Reinforced Concrete Beams

This research investigated flexural behavior of repaired RC beams that experienced simulated lateral damage to replicate vehicle impact/collision. The experimental program included the testing of 34 RC beams, which were laterally damaged and then repaired using carbon-fiber-reinforced polymer (CFRP) fabrics. The damaged beams were repaired using various levels of strengthening (number of CFRP soffit layers) and multiple configurations of anchoring CFRP U-wrapping. Specific attention was paid to understanding the effects of intermediate U-wrapping on strains developed in the longitudinal soffit laminates and the beams’ ultimate capacity. Other details for the flexural repair system, such as end-peeling previsions, were also addressed. The test results indicated that CFRP repairs have the ability to restore and enhance the capacity of damaged RC beams by up to 353%. The results also suggest an optimum range for spacing intermediate U-wrappings to suppress strains felt by longitudinal soffit laminates, thereby mitigating premature debonding failures. Design considerations and recommendations for optimum CFRP configuration, level of strengthening, and application details for repairing laterally damaged RC beams are proposed.

Assessment of effectiveness of CFRP repaired RC beams under different damage levels based on flexural stiffness

This paper presents a study to determine the effectiveness of Carbon Fiber Reinforced Polymer (CFRP) sheets as a flexural repair system for Reinforced Concrete (RC) beams. The effectiveness of these sheets is ascertained by monitoring the flexural stiffness recovery. Experimental work is conducted on scaled beams where four beams are used as the datum. The first beam is without CFRP sheets, the second is a repaired beam after pre-damaged under design load limit, whilst the third is a repaired beam after pre-damaged under steel yield load limit, and the fourth is a repaired beam after pre-damaged under ultimate load. Comparisons are made based on the flexural stiffness recovery, crack patterns, load capacity, and failure modes of the beams. The study validates the ability of the flexural stiffness change in order to monitor the effect of the damage as well as the effectiveness of the repair on stiffness recovery. The results prove the effectiveness of the CFRP sheets as a repair technique which increases the flexural stiffness and the ultimate load capacity whatever the pre-repair damage levels. In addition, this study indicates the ability of re-repairing the beams in the case of CFRP debonding. The failure modes are controlled by the pre-repair damage flexural crack wherein it causes the CFRP debonding.

A building block synthesis approach for precision flexure systems with integrated, strain-based position sensing

Abstract Early stage design of precision flexure systems that utilize strain-based displacement sensing is difficult due to the strong coupling between the mechanical and sensing subsystems. Traditional tools for flexure system and compliant mechanism synthesis are not capable of simultaneously optimizing the mechanical and sensing subsystems. The building block synthesis approach developed in this work is the only tool capable of designing compliant mechanisms with integrated strain based sensing. Building block modeling allows for rapid synthesis and vetting of concepts. This approach also allows the designer to determine concept feasibility, identify performance limits and tradeoffs, and obtain 1st order estimates of flexure geometry. In short, this method enables one to find an optimal design and set first order design parameters. The utility of the building block approach is detailed in a case study detailing the synthesis and modeling of three different one degree-of-freedom translational stages that are all derived from the series and parallel addition of fixed-guided cantilever beam building blocks.

Estimating Natural Periods of Steel Plate Shear Wall Frames

AbstractA steel plate shear wall (SPSW) with thin, unstiffened web plates is one type of seismic lateral force–resisting system that is gaining popularity. SPSWs are used in low to midrise building construction typically with two or more frames in each orthogonal direction to resist seismic loading combined with gravity framing. The SPSWs therefore control the lateral force response of the building and the building’s natural periods of vibration. For design of any seismic load–resisting system, an estimation of the building’s first-mode period is necessary to calculate seismic loads and estimate resulting frame drift. This paper presents a method for estimating the first three natural periods of a SPSW with nonuniform properties along its height, accounting for both shear and flexural deformations of the system. The proposed method approximates the SPSW frame as shear and flexural systems separately to determine corresponding frequencies and then combines these frequencies using Dunkerley’s equation. A co...

Macroscopic quantum tunneling in nanoelectromechanical systems

The experimental observation of quantum phenomena in mechanical degrees of freedom is difficult, as the systems become linear toward low energies and the quantum limit, and thus reside in the correspondence limit. Here we investigate how to access quantum phenomena in flexural nanomechanical systems which are strongly deflected by a voltage. Near a metastable point one can achieve a significant nonlinearity in the electromechanical potential at the scale of zero-point energy. The system can then escape from the metastable state via macroscopic quantum tunneling (MQT). We consider two model systems suspended atop a voltage gate, namely, a graphene sheet and a carbon nanotube. We find that the experimental demonstration of the phenomenon is currently possible but demanding, since the MQT crossover temperatures fall in the milli-Kelvin range. A carbon nanotube is suggested as the most promising system.

Large‐scale flexuring and antithetic extensional faulting along a nascent plate boundary in the SE Afar rift

Terra Nova, 23, 416–420, 2011AbstractNew structural data from the SE Afar margin in Djibouti lead us to discriminate two recent (<1 Ma) extensional fault networks between the Afar accreted crust, and the South Danakil block to the east. Emphasis is placed on the N–S‐oriented Makarassou fault system which dissects the prominent westward‐(riftward‐)facing topographic flexure between the two structural domains. The most striking characteristic of the Makarassou fault belt is a closely spaced network of continentward‐dipping extensional faults, bounding domino blocks of 3–1 Ma tilted lavas of the Stratoid series. The Makarassou fault–flexure system is interpreted as an extensional faulted monocline that developed in response to differential subsidence and crustal downwarping of the Afar magmatically accreted transitional crust. Large‐scale flexuring and associated structures along the eastern flank of the Asal–Manda‐Inakir incipient plate boundary are regarded as indicative of a nascent volcanic rifted margin in SE Afar.

Synthesis of precision serial flexure systems using freedom and constraint topologies (FACT)

Abstract In this paper we introduce the principles necessary to synthesize the complete body of serial flexure system concepts, which satisfy desired design requirements using Freedom and Constraint Topologies (FACT). FACT utilizes a comprehensive library of geometric shapes that represent regions were constraints may be placed for synthesizing flexure systems that possess designer-specified degrees of freedom (DOFs). Prior to the theory of this paper, FACT was limited to the synthesis of parallel flexure systems only. The ability to synthesize serial flexure systems is important because serial flexure systems (i) may possess DOFs not accessible to parallel flexure systems, (ii) exhibit larger ranges of motion, and (iii) enable cancellation of parasitic errors. Geometric shapes that represent motions only accessible to serial flexure systems have been derived and added to the existing body of FACT shapes initially intended for parallel flexure synthesis only. Systematic rules and guidelines have been created that help designers use these shapes to generate every parallel and serial flexure concept that satisfies the desired functional requirements. We demonstrate how to use these shapes to utilize or avoid underconstraint in serial flexure synthesis. A serial flexure system is designed that interfaces the lead screw of a lathe to the carriage that it drives as a case study to demonstrate the theory of this paper.

Corrigendum to “A screw theory basis for quantitative and graphical design tools that define layout of actuators to minimize parasitic errors in parallel flexure systems” [Precis. Eng. 34 (4) (2010) 767–776

Corrigendum to “A screw theory basis for quantitative and graphical design tools that define layout of actuators to minimize parasitic errors in parallel flexure systems” [Precis. Eng. 34 (4) (2010) 767–776

The Influence of Crack Length and Delamination Width on the Mode-III Energy Release Rate of Laminated Composites

In this article, the modified split-cantilever beam (MSCB) is applied to investigate the dependence of the mode-III energy release rate (at crack initiation) on the crack length and the specimen width. The main goal of this study is to apply the same specimen geometry to both double-cantilever beam and end-notched flexure systems. The energy release rate of the specimen was calculated by an improved beam theory scheme, which was used to reduce the experimental data. The obtained results are comparable to those obtained by mode-I and mode-II tests, and they indicate the important role of the MSCB specimen. The results show that the energy release rate decreases significantly with the initial crack length and there is no crack length where the energy release rate becomes independent of it.