Macro and Nano Serially-Compounded Cantilevers for Resonance-Shift Mass Detection

2007 ◽  
Author(s):  
Nicolae Lobontiu ◽  
Iulian Lupea ◽  
Rob Ilic
Keyword(s):  
Analytical Model ◽  
Natural Frequencies ◽  
Displacement Sensor ◽  
Frequency Change ◽  
Mass Detection ◽  
Compliant Structure ◽  
Nano Scale ◽  
Resonance Shift ◽  
Element Simulation ◽  
Macro Scale

Detecting extraneous matter that deposits on a compliant receiver platform can be performed by means of the resonance shift method, whereby the original and altered natural frequencies of the host structure are compared to evaluate the amount and/or position of the attached matter. By scaling structural dimensions down to the nanometer range, it becomes possible to discern quantities in the molecular realm. One simple and convenient structural detector is the cantilever, whose out-of-the-plane resonant vibrations can be excited/monitored with relative ease. The proposed paper studies a few aspects of the mass attachment detection through monitoring of the natural frequency change of cantilevers, by focusing on the two ends of the dimensional spectrum: the macro- and nano-scale domains. The paper develops an analytical model that enables predicting the mass of attached matter in case its location is point-like and pre-specified. At nano-scale, locating mass attachment is realized through adequate surface functionalizing, while at macro-scale a displacement sensor can be placed conveniently on the compliant structure. The model accommodates cantilever configurations formed of several single-profile segments that are serially connected. Of all possible combinations, the two-segment, circularly-notched design is explicitly studied. Finite element simulation is utilized to check the analytical model validity. The bending natural frequencies of several macro-scale and nano-scale circularly-notched cantilever specimens have been investigated experimentally. Based on the agreement between analytical, numerical and experimental data, the analytical model was further utilized to study the relationships between geometric parameters, deposited mass, mass attachment position and the change in the bending resonant frequency.

Tuning the Static and Modal Response of Microcantilevers Through Lumped-Parameter Model-Based Design

Aerospace ◽  
2003 ◽  
Author(s):  
Ephrahim Garcia ◽  
Nicolae Lobontiu ◽  
Yoonsu Nam
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Rectangular Cross Section ◽  
Lumped Parameter Model ◽  
Mass Detection ◽  
Force Microscopy ◽  
Lumped Parameter ◽  
Element Simulation ◽  
Three Degree Of Freedom ◽  
Circular Notch

The paper introduces the circular-notch microcantilever design that can be utilized in mass detection and atomic force microscopy (AFM) microsystems. The microcantilever is modeled as a three degree-of-freedom member which is sensitive to bending and torsion. A lumped-parameter model is formulated that gives directly the stiffness closed-form equations and the inertia fractions about the degrees of freedom. It is thus possible to qualify and tune the static and modal responses of this specific microcantilever design in order to match or, on the contrary, to avoid, stiffness and frequency ranges that are of interest by means of only geometry alterations. The microcantilever’s sensitivity to bending and torsion can also be modified by simple manipulation of the defining geometric parameters. The analytical model predictions are confirmed through limit calculations and finite element simulation. The stiffness factors of the circular-notch microcantilever design are compared to the ones of a similar constant rectangular cross-section configuration by means of the analytical model developed herein.

Identifying Product Scaling Principles: A Tool for Bioinspired Design and Beyond

2011 ◽  
Author(s):  
Angel G. Perez ◽  
Julie S. Linsey
Keyword(s):  
Scaling Laws ◽  
Initial Step ◽  
Nano Scale ◽  
Bioinspired Design ◽  
Macro Scale ◽  
Design By Analogy ◽  
Global Principles ◽  
Physical Principles

There are countless products that perform the same function but are engineered to suit a different scale. Designers are often faced with the problem of taking a solution at one scale and mapping it to another. This frequently happens with design-by-analogy and bioinspired design. Despite various scaling laws for specific systems, there are no global principles for scaling systems, for example from a biological nano-scale to macro-scale. This is likely one of the reasons bioinspired design is difficult. Very often scaling laws assume the same physical principles are being used, but this study of products indicates that a variety of changes occur as scale changes, including changing the physical principles to meet a particular function. Empirical product research was used to determine a set of principles by observing and understanding numerous products to unearth new generalizations. The function a product performs is examined in various scales to view subtle and blatant differences. Principles are then determined. This study provides an initial step in creating new innovative designs based on existing solutions in nature or other products that occur at very different scales. Much further work is needed by studying additional products and bioinspired examples.

scholarly journals Assessment of Substrate and TBC Damage Effects on Resonance Frequencies for Blade Health Monitoring

2022 ◽  
Vol 12 (1) ◽  
pp. 1-19
Author(s):  
Jason van Dyke ◽  
Michel Nganbe
Keyword(s):  
Natural Frequencies ◽  
Hot Spot ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Early Assessment ◽  
Element Simulation ◽  
Resonance Frequencies ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Local Plastic Deformation

The reliability of critical aircraft components continues to shift towards onboard monitoring to optimize maintenance scheduling, economy efficiency and safety. Therefore, the present study investigates changes in dynamic behavior of turbine blades for the detection of defects, with focus on substrate cracks and TBC spallation as they relate to vibration modes 1 to 6. Two‐dimensional and three-dimensional finite element simulation is used. The results indicate that TBC spallation reduces natural frequencies due to the ensuing hot spot and overall increase in temperature, leading to drops in blade stiffness and strength. Cracks cause even larger frequency shifts due to local plastic deformation at the crack that changes the energy dissipation behavior. Mode 1 vibration shows the largest shifts in natural frequencies that best correlate to the size of defects and their position. As such, it may be most appropriate for the early assessment of the severity and location of defects.

Experimental Identification Approach of Dynamic Parameters of Precise Horizontal Machining Centre Based on Component-System

2011 ◽  
Vol 467-469 ◽  
pp. 1686-1690
Author(s):  
Zhi Feng Liu ◽  
Zhong Hua Chu ◽  
Qiang Cheng ◽  
Guang Bo Liu ◽  
Dong Sheng Xuan
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Modal Testing ◽  
Element Calculation ◽  
Element Simulation ◽  
Modes Of Vibration ◽  
Identification Approach ◽  
Comparison Of The Results ◽  
Machine Structure

This paper integrates experiment modal analysis and the analytical modal analysis to study on the vibration phenomena occurring occasionally at the different components of a precise horizontal machining centre. The paper is focused on extracting the mode shape of the major components of the machine in order to ensure resonance phenomena as a cause of vibration. At first the main natural frequencies with the corresponding modes of vibration of the machine structure are obtained by the experiment modal analysis. Then the dynamic behavior of the machine components is simulated using a finite element simulation model. The comparison of the results based on finite element calculation with their experimental counterparts shows the reasonableness. The model is evaluated and corrected with experimental results by modal testing of the machine components.

Glued-in-rod timber joints: analytical model and finite element simulation

2018 ◽  
Vol 51 (3) ◽  
Author(s):  
A. Hassanieh ◽  
H. R. Valipour ◽  
M. A. Bradford ◽  
R. Jockwer
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Analytical Model ◽  
Element Simulation ◽  
Timber Joints

Updating of Non-Conservative Systems Using Inverse Methods

1997 ◽  
Author(s):  
Ladislav Starek ◽  
Milos Musil ◽  
Daniel J. Inman
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Model Updating ◽  
Analytical Models ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Data

Abstract Several incompatibilities exist between analytical models and experimentally obtained data for many systems. In particular finite element analysis (FEA) modeling often produces analytical modal data that does not agree with measured modal data from experimental modal analysis (EMA). These two methods account for the majority of activity in vibration modeling used in industry. The existence of these discrepancies has spanned the discipline of model updating as summarized in the review articles by Inman (1990), Imregun (1991), and Friswell (1995). In this situation the analytical model is characterized by a large number of degrees of freedom (and hence modes), ad hoc damping mechanisms and real eigenvectors (mode shapes). The FEM model produces a mass, damping and stiffness matrix which is numerically solved for modal data consisting of natural frequencies, mode shapes and damping ratios. Common practice is to compare this analytically generated modal data with natural frequencies, mode shapes and damping ratios obtained from EMA. The EMA data is characterized by a small number of modes, incomplete and complex mode shapes and non proportional damping. It is very common in practice for this experimentally obtained modal data to be in minor disagreement with the analytically derived modal data. The point of view taken is that the analytical model is in error and must be refined or corrected based on experimented data. The approach proposed here is to use the results of inverse eigenvalue problems to develop methods for model updating for damped systems. The inverse problem has been addressed by Lancaster and Maroulas (1987), Starek and Inman (1992,1993,1994,1997) and is summarized for undamped systems in the text by Gladwell (1986). There are many sophisticated model updating methods available. The purpose of this paper is to introduce using inverse eigenvalues calculated as a possible approach to solving the model updating problem. The approach is new and as such many of the practical and important issues of noise, incomplete data, etc. are not yet resolved. Hence, the method introduced here is only useful for low order lumped parameter models of the type used for machines rather than structures. In particular, it will be assumed that the entries and geometry of the lumped components is also known.

Realization of Mechanical Properties Prediction from Nano- to Macro- Scale Structure: An Achievement of C-S-H Hydrated Phases

2019 ◽  
Vol 956 ◽  
pp. 332-341 ◽  
Author(s):  
Jia Fu
Keyword(s):  
Mechanical Properties ◽  
High Density ◽  
Theoretical Research ◽  
Step Method ◽  
Material Technology ◽  
Micro Scale ◽  
Nano Scale ◽  
Macro Scale ◽  
Mechanical Properties Prediction ◽  
Technology Modeling

The performance prediction of C-S-H gel is critical to the theoretical research of cement-based materials. In the light of recent computational material technology, modeling from nano-scale to micro-scale to predict mechanical properties of structure has become research hotspots. This paper aims to find the inter-linkages between the monolithic "glouble" C-S-H at nano-scale and the low/high density C-S-H at the micro-scale by step to step method, and to find a reliable experimental verification method. Above all, the basic structure of tobermorite and the "glouble" C-S-H model at nano-scale are discussed. At this scale, a "glouble" C-S-H structure of about 5.5 nm3 was established based on the 11Å tobermorite crystal, and the elastic modulus ​​of the isotropic "glouble" is obtained by simulation. Besides, by considering the effect of porosity on the low/high density of the gel morphology, the C-S-H phase at micro-scale can be reversely characterized by the "glouble". By setting different porosities and using Self-Consistent and Mori-Tanaka schemes, elastic moduli of the low density and high density C-S-H ​​from that of "glouble" are predicted, which are used to compare with the experimental values of the outer and inner C-S-H. Moreover, the nanoindentation simulation is carried out, where the simulated P-h curve is in good agreement with the accurate experimental curve in nanoindentation experiment by the regional indentation technique(RET), thus the rationality of the "glouble" structure modeled is verified and the feasibility of Jennings model is proved. Finally, the studies from the obtained ideal "glouble" model to the C-S-H phase performance has realized the mechanical properties prediction of the C-S-H structure from nano-scale to micro-scale, which has great theoretical significance for the C-S-H structural strengthening research.

Free Vibration of Bistable Clamped–Clamped Beams: Modeling and Experiment

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Xiaolei Song ◽  
Haijun Liu
Keyword(s):  
Analytical Model ◽  
Natural Frequencies ◽  
Classical Problem ◽  
Mode Shapes ◽  
Wide Range ◽  
Fundamental Understanding ◽  
Clamped Beams ◽  
Transverse Deflection ◽  
Symmetric And Antisymmetric Modes ◽  
Good Agreement

Abstract Bistable clamped–clamped beams have been used in a wide range of applications such as switches, resonators, energy harvesting, and vibration reduction. Most studies on this classic buckling problem focus on obtaining either the static configuration and the required critical axial load or the natural frequencies and mode shapes of postbuckling vibrations analytically. In this article, we present our study including analytical modeling and experimental method on bistable clamped–clamped beams, aiming to understand the detailed snap-through process and the ensuing vibration. In the analytical model, by decomposing the transverse deflection into static buckling configuration and linear vibration, we obtain the natural frequencies and mode shapes for the buckled beam and investigate the effects of static deflection on the symmetric and antisymmetric modes. An experimental design using noncontact methods is implemented to directly measure the response of the whole beam in the snap-through process and the sound generated by the vibrating beam. The measurements are characterized in both time and frequency domain and found to be in good agreement with the analytical model. The study presented in this article enhances the fundamental understanding of the classical problem of bistable clamped–clamped beams.

Tolerance Induced Performance Variation of a High-Resolution Compliant Micro Stage

2007 ◽  
Author(s):  
Jhy-Cherng Tsai ◽  
Mandy Hsiao ◽  
Jau-Liang Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Resolution ◽  
Natural Frequency ◽  
Sensitivity Analyses ◽  
Compliant Structure ◽  
Nano Scale ◽  
Leaf Springs ◽  
Performance Variation ◽  
Element Method

Micro stage employs compliant structure is crucial for precision machinery as it can achieve nano-scale resolution fine displacement by deformation. This paper investigates the variations of stiffness and natural frequency due to dimensional tolerances of such a compliant micro stage that is suspended by four leaf springs and rotates with respect to hinges. Performances of the stage are evaluated by finite element method for various dimensions to investigate the effects of dimensions. A series of sensitivity analyses are also performed to investigate how tolerances affect the performance of the stage. It shows that the stiffness and natural frequency of the stage are strongly affected by the dimensions of leaf springs and the hinges. That is, tolerances of these dimensions are crucial and must be well designed and strictly controlled. It further shows that performance variation due to tolerances are nonlinear but can be properly designed with this approach.

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