Cantilever Model Research Articles

Finite Element Analysis of Interface Dependence on Nanomechanical Sensing

Nanomechanical sensors and their arrays have been attracting significant attention for detecting, discriminating and identifying target analytes. The sensing responses can be partially explained by the physical properties of the receptor layers coated on the sensing elements. Analytical solutions of nanomechanical sensing are available for a simple cantilever model including the physical parameters of both a cantilever and a receptor layer. These analytical solutions generally rely on the simple structures, such that the sensing element and the receptor layer are fully attached at their boundary. However, an actual interface in a real system is not always fully attached because of inhomogeneous coatings with low affinity to the sensor surface or partial detachments caused by the exposure to some analytes, especially with high concentration. Here, we study the effects of such macroscopic interfacial structures, including partial attachments/detachments, for static nanomechanical sensing, focusing on a Membrane-type Surface stress Sensor (MSS), through finite element analysis (FEA). We simulate various macroscopic interfacial structures by changing the sizes, numbers and positions of the attachments as well as the elastic properties of receptor layers (e.g., Young’s modulus and Poisson’s ratio) and evaluate the effects on the sensitivity. It is found that specific interfacial structures lead to efficient sensing responses, providing a guideline for designing the coating films as well as optimizing the interfacial structures for higher sensitivity including surface modification of the substrate.

Distributed Optical Fiber-Based Approach for Soil-Structure Interaction.

Scour is a hydraulic risk threatening the stability of bridges in fluvial and coastal areas. Therefore, developing permanent and real-time monitoring techniques is crucial. Recent advances in strain measurements using fiber optic sensors allow new opportunities for scour monitoring. In this study, the innovative optical frequency domain reflectometry (OFDR) was used to evaluate the effect of scour by performing distributed strain measurements along a rod under static lateral loads. An analytical analysis based on the Winkler model of the soil was carefully established and used to evaluate the accuracy of the fiber optic sensors and helped interpret the measurements results. Dynamic tests were also performed and results from static and dynamic tests were compared using an equivalent cantilever model.

Prediction of mesoscale deformation in milling micro thin wall based on cantilever boundary

The micro channel cold plate is very suitable for the application environment of high heat consumption liquid cooling such as PCB plate and multi-layer components. However, at mesoscale, the titanium alloy micro channel cold plate is micro thin-walled structure of cantilever boundary with weak stiffness, which leads to significant deformation and resultant poor machining accuracy during micro milling. To effectively control and reduce micro thin-walled deformation, a 3D FE cantilever model is established to predict dynamic milling deformation of micro thin wall. The constitutive model of titanium alloy (Ti-6Al-4 V) that includes the strain gradient to consider size effect in micro milling, the edge geometry of milling cutter, the thin-walled microstructure, and micro milling parameters is involved in milling modeling of thin wall. Moreover, a series of micro milling experiments for micro thin wall of titanium alloy at different machining parameters were carried out to investigate the law and mechanism of thin wall deformation in milling micro thin wall subjected to dynamic alternating forces. By comparing numerical and experimental deformation of micro thin wall in micro milling, the accuracy and validity of the prediction model based on cantilever boundary are verified, which provides theoretical support and model basis for the deformation control in milling micro channel cold plate at mesoscale.

Large deflections of inextensible cantilevers: modeling, theory, and simulation

A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam’sinextensibility– local arc length preservation – rather than traditional extensible effects attributed to fully restricted boundary conditions. Enforcing inextensibility leads to:nonlinear stiffnessterms, which appear as quasilinear and semilinear effects, as well asnonlinear inertiaeffects, appearing as nonlocal terms that make the beam implicit in the acceleration. In this paper we discuss the derivation of the equations of motionviaHamilton’s principle with a Lagrange multiplier to enforce theeffective inextensibility constraint. We then provide the functional framework for weak and strong solutions before presenting novel results on the existence and uniqueness of strong solutions. A distinguishing feature is that the two types of nonlinear terms present independent challenges: the quasilinear nature of the stiffness forces higher topologies for solutions, while the nonlocal inertia requires the consideration of Kelvin-Voigt type damping to close estimates. Finally, a modal approach is used to produce mathematically-oriented numerical simulations that provide insight into the features and limitations of the inextensible model.

Calculation of the stiffness of reinforced concrete structures under the action of torsion and bending

The development of methods for calculating the stiffness of reinforced concrete structures with cracks at the limit states is an urgent task. The proposed method implies that the spatial cracks develop on special bilinear surfaces. It involves dividing a rectangular section into a series of squares, which are subsequently replaced by the circles inscribed in them. This approach requires the introduction of the concept of “equivalence” between the torsional stiffness characteristics of a rectangular section and the circumscribed circle. The equation for determining the tangential torsional stresses (taking into account the deplanation) at any point of the cross section is written in a cylindrical and Cartesian coordinate system. Two variants of modelling a real crack are proposed: in the form of stepwise located three-dimensional finite elements that are detached in common nodes, or using an imaginary crack along which pairs of finite elements are picked out. So, we use a special double cantilever model for the calculation. Having a picture of the applied force and deformation loads (crack opening) in the console nodes, it is possible to determine the values of the work in the state: “before detach” and “after detach” of the double-element model.

Effect of Crown Shape of Rolls on the Distribution of Stress and Elastic Deformation for Rolling Processes

The present work analyzes the influence of crown shape on the distribution of stresses and deformation for rolling processes. This study consists of a Finite Element Analysis considering combinations of crown shape for Back Up Roll and Work Roll, rolling forces, properties of materials and dimensions of rolls and strip. An analysis of the rolls based on a double cantilever model with the fulcrum of the beams in a centerline mill was carried out. The results show that maximum stress concentrations for all combinations of crown shape analyzed appear on both sides 787.4 mm from the mill centerline, exactly on the sides of the strip. In this area, the maximum stress for the best combination of crown shape is larger than in the centerline mill, increasing from 34.2 MPa to 163.0 MPa. This is proportional according to Hooke’s law for which strain of rolls increases from 3.4067 × 10−4 to 4.8368 × 10−4. The worst combinations of crown shapes were obtained when the shapes of the barrel are the same for the BUR and WR; for example: Combination 1 (BUR Positive–WR Positive), Combination 5 (BUR Flat–WR Flat), and Combination 9 (BUR Negative–WR Negative).

Enhanced energy harvesting of cantilevered flexoelectric micro-beam by proof mass

Proof mass can adjust the natural frequency of a cantilevered energy harvester to fit the vibration source frequency and, hence, improve energy efficiency. In this paper, a cantilevered energy harvesting model including a proof mass is presented based on the flexoelectric theory. The electromechanical coupling responses at steady state are obtained for harmonic excitations and then reduced to single-mode expressions for modal excitations. The flexoelectric coupling coefficient, which represents conversion of energy, is investigated. The numerical results reveal that the flexoelectric coupling coefficient can be improved by adjusting the proof mass to make the vibration frequency of the microbeam adapt to that of the ambient vibration source. The adjusting strategies have also been formulated. In addition, the flexoelectric coupling coefficient increases with the decrease in the thickness of the microbeam. As expected, the flexoelectric coupling coefficient can further be enhanced when the beam thickness reaches nanometer scale. For the beam thickness h = 0.3 μm, the current output decreases and the voltage output increases with the increase in the electrical load resistance. When the electrical load resistance is around 100 MΩ, the power output arrives at its maximum. The resonance frequency shifts from 34 693 Hz to 35 350 Hz with the increase in the load resistance from short- to open-circuit conditions, and the flexoelectric coupling coefficient for this thickness lever is kr ≈ 0.19.

An approach dealing with inertia nonlinearity of a cantilever model subject to lateral basal Gaussian white noise excitation

Abstract An uniform inextensible slender cantilever model with longitudinal inertia nonlinearity under lateral basal Gaussian white noise excitation was studied. The effect of inertia nonlinearity was especially taken into account, which is the main novelty of this study. A modified stochastic averaging method for strong nonlinearity was applied to transform the system into an Ito differential equation about the transient equivalent amplitude. After that, a prediction-correction method was presented to improve the predicting accuracy. The stationary probability density function (PDF) of transient equivalent amplitude, as well as the joint PDF of the displacement and velocity was studied. The reliability function and the probability density of first passage failure time were also investigated by the theoretical analysis and the Monte Carlo simulation. The Monte Carlo results vindicated these approaches.

Corrosion damage to cantilever MR walls – Representation in tests and calculations

AbstractAfter the failure of a cantilever retaining wall with counterfort on the Brenner Autobahn, intensive investigation of existing structures showed considerable corrosion damage to cantilever walls with and without counterforts, at the location of construction and day joints. This is difficult to detect and assess due to the placing of the main reinforcement at the back of the construction. The present paper presents a monitoring concept, which enables detection of corrosion damage and also provides a gain of information about the behaviour of the structure. The basis for this concept is the installation of inclination and strain gauges on the front of a retaining wall. In order to explain the functioning of the concept, a rudimentary cantilever model of the effect of corrosion damage is first described. Then the results and findings from a test series with artificial corrosion representation to reinforced concrete structures to validate the presented monitoring concept is described.

Digital control design for an IPMC actuator using adaptive optimal proportional integral plus method: Simulation and experimental study

In this paper, the application of a novel digital control method, called adaptive optimal proportional-integral-plus (AOPIP), to beam-like ionic polymer-metal composite (IPMC) actuators is investigated. First, as a gray-box system, the dynamical model of the IMPC cantilevers is obtained and then AOPIP method is derived and applied to several IPMCs with different physical properties to evaluate the efficacy of the control method. Basically, AOPIP is a proportional-integral-plus (PIP) controller with two additional terms; an optimal gain tuner mechanism with means of linear quadratic regulator (LQR) method and an adaptation term based on recursive least square (RLS) method with Kalman filter (KF), RLS-KF. Therefore, the main advantages of this controller are a) independence of parameters of the system; and b) an optimal performance. To perform a comparative study, in addition to AOPIP, a digital PID controller is designed and applied to the system in simulation. Besides, the comparison of opened-loop techniques to closed-loop ones is investigated as well. Furthermore, an experimental test for comparing AOPIP and digital PID is performed to show the performance of the IPMC in real-time, and under real conditions such as existence of external noise and disturbances. Using several proper numerical indicators, both simulation and experimental results demonstrate the efficacy of the AOPIP and its superiority to the opened-loop techniques and digital PID controller in terms of control effort, desired tracking precision of the IPMCs actuators and its optimality.

Effect of the fabric dimension on limits of the drape coefficient

The effects of fabric dimension on drape deformation are analyzed using a model of a circular segment cantilever for infinite shear stiffness (upper limit) and the deflection of strip cantilevers in radial directions for zero shear stiffness (lower limit). The drape shapes are determined by nondimensional parameters K and K′ in addition to the parameters m and m′, which are given by the ratio of the fabric radius and segment cantilever length, respectively. K and K′ are given by the segment cantilever length for the upper limit and by the differences between the radii of the fabric and support disk for the lower limit, with weights, and bending rigidity. The drape coefficient (DC) limits of fabrics are theoretically obtained using the model in three cases according to the relationship of m and m′. Even for different fabrics, the drape shapes are similar for the same m and K, or m′ and K′, in each case. The effects of dimension on fabric drape are therefore clarified theoretically. The obtained limits are experimentally verified for eight woven fabrics and one sheet. It is found that the DCs of samples are between the two theoretical curves of limits, although there are variations even for the same K or K′. The variations might be due to depressions between adjacent nodes or the presence of double-curvature deformation due to lower shear stiffness. The effects of dimensions in the drape test considering bending rigidity for infinite and zero shear stiffness are thus clarified theoretically and experimentally.

Three-dimensional finite element analysis of cantilever fixed bridge supported by implants with mandibular central incisor

Objective: To investigate effect of the contact surface between the bridge and the adjacent teeth on the stress distribution of the implant and bone tissue and the displacement of the prosthesis in the cantilever fixed implant bridge restoring missing mandibular central incisors. Methods: Two-dimensional images of the mandible and dentition in healthy adults were obtained using CT data. A three-dimensional finite element model of cantilever fixed bridge supported by implants with mandibular central incisor was established by computer reconstruction technique.The contact surface between the bridge and the adjacent natural tooth was designed as "oval" and "trapezoid". The "trapezoid" has a slightly smaller median diameter on the labial side and a slightly larger medial diameter on the lingual side. Loading of 120 N was applied on the tangential margin of the middle line of the long axis of the bridge 41. The direction was set at 0°, which was parallel to the long axis of the tooth and downward. The buccal to lingual and downward angles were 30°, 45° and 60°, respectively, perpendicular to the long axis of the tooth and 90° to the lingual side.The stress distribution of the implant and surrounding bone tissue and the displacement of the prosthesis were compared between the two models. Results: Under axial and buccolingual loading, the maximum equivalent stress peak in the implant and surrounding bone tissue in the cantilever with trapezoidal contact surface design and the maximum displacement of the prosthesis were lower. Moreover, the distribution of stress was more balanced and the concentration range of stress was smaller. With the loading angle increasing, this trend was more obvious. When loading angle increased to 90°, the maximum equivalent stress and the maximum displacement of the elliptic contact surface model implant and surrounding bone tissue were 196 and 101 MPa and 0.196 mm, respectively, while the trapezoidal contact surface model were 157 and 72 MPa and 0.164 mm, respectively. Conclusions: The trapezoidal contact surface of the bridge and the adjacent teeth in the cantilever fixed bridge supported by implants with mandibular central incisor is beneficial to reduce the impact of the leverage on the implant and surrounding bone tissue.

Effect of Scour on the Natural Frequency Responses of Bridge Piers: Development of a Scour Depth Sensor

Local scour is the removal of soil around bridge foundations under the erosive action of flowing water. This hydraulic risk has raised awareness of the need for developing continuous monitoring techniques to estimate scour depth around bridge piers and abutments. One of the emerging techniques is based on monitoring the vibration frequency of either bridge piers or a driven sensor in the riverbed. The sensor proposed in this study falls into the second category. Some unresolved issues are investigated: the effect of the geometry and material of the sensor, the effect of the embedded length and the effect of soil type. To this end, extensive laboratory tests are performed using rods of different materials, with various geometries and lengths. These tests are conducted in both dry sand and a soft clayey soil. Since the sensor will be placed in the riverbed, it is crucial to evaluate the effect of immersed conditions on its response. A numerical 3D finite-element model was developed and compared against experimental data. This model was then used to compute the ‘wet’ frequencies of the sensor. Finally, based on both the experimental and numerical results, an equivalent cantilever model is proposed to correlate the variation of the frequency of the sensor to the scour depth.

Investigación del colapso de un muro de mampostería de ladrillo no reforzada bajo fuerzas de vientos moderadas

Several methodologies used for the collapse assessment of an unreinforced brick masonry wall subject to out-of-plane bending due to moderate wind loads in Medellin, Colombia are presented. Models include a rigid cantilever model of masonry elements, deformable cantilever and frame models of intermediate concrete columns and beams with and without masonry contribution to the wind resistance, and a finite element model with all concrete frame elements, masonry units and panel openings modeled explicitly. Wind demands are estimated using spatial interpolation of actual wind velocity measurements near the site. Results are presented in terms of peak deflections at the wall top, as well as peak force and stress demand-to-capacity ratios on concrete frames and masonry elements, respectively. Wind pressure distribution, P-Delta effects, interaction and relative contribution to the out-of-plane bending resistance of concrete framing and masonry elements with either one- or two-way action are shown to be the main parameters affecting results, in addition to model selection. Despite significant differences between models, recommended parameters and assumptions lead in all cases to the correct determination of the wall's imminent collapse under the estimated wind demands.

Normal Faults on Ceres: Insights Into the Mechanical Properties and Thermal History of Nar Sulcus

AbstractWe characterized two sets of extensional faults that comprise the Nar Sulcus region of Ceres by applying a cantilever model for fault related flexure and derived flexural rigidity values for Nar Sulcus between 2.0 · 1015 and 1.8 · 1016 N·m. This range of flexural rigidity makes Nar Sulcus mechanically akin to extensional structures on Ganymede, Europa, and Enceladus. We combine these observations with an inferred strength profile for the upper mechanical layer of Ceres and estimate its thickness to be 2.9–9.5 km. Surface heat fluxes at Nar Sulcus during its formation were likely ≥10 mW/m2 for estimated strain rates of 10−17–10−14 s−1, which is at least one order of magnitude larger than the current estimated global average. For geologically plausible heat fluxes between 10 and 100 mW/m2, we estimate an upper bound of ~30 vol.% mechanically silicate‐like phases in the near surface at Nar Sulcus, neglecting the effects of porosity.

Flow-Induced Stream-Wise Vibration of Circular Cylinders

Results from a series of studies on the stream-wise vibration of a circular cylinder verifying Japan Society of Mechanical Engineers Standard S012-1998, Guideline for Evaluation of Flow-induced Vibration of a Cylindrical Structure in a Pipe, are summarized and discussed in this paper. Experiments were carried out in a water tunnel and in a wind tunnel using a two-dimensional cylinder model elastically supported at both ends of the cylinder and a cantilevered cylinder model with a finite span length that was elastically supported at one end. These cylinder models were allowed to vibrate with one degree of freedom in the stream-wise direction. In addition, we adopted a cantilevered cylinder model that vibrated with two degrees of freedom in both the stream-wise and cross-flow directions under the same vibration conditions as an actual thermocouple well. The value of the Scruton number (structural damping parameter) was changed over a wide range, so as to evaluate the value of the critical Scruton number that suppressed vibration of the cylinder. For the two-dimensional cylinder, two different types of stream-wise excitations appeared in the reduced velocity range of approximately half of the resonance-reduced velocity. For the stream-wise vibration in the first excitation region, due to a symmetric vortex flow, the response amplitudes were sensitive to the Scruton number, while the shedding frequency of alternating vortex flow was locked-in to half of the Strouhal number of vibrating frequency of a cylinder in the second excitation region. In addition, the effects of the aspect ratio of a cantilevered cylinder on the flow-induced vibration characteristics were clarified and compared with the results of a two-dimensional cylinder. When a cantilevered circular cylinder with a finite length vibrates with one degree of freedom in the stream-wise di-rection, it is found that acylinder with a small aspect ratio has a single excitation region, whereas a cylinder with a large aspect ratio has two excitation regions. Furthermore, the vibration mechanism of a symmetric vortex flow was investigated by installing a splitter plate in the wake to prevent shedding of alternating vortices. The vibration amplitude of acylinder with a splitter plate increased surprisingly more than the amplitude of a cylinder without a splitter plate. For a cantilevered cylinder vibrating with two degrees of freedom, the Lissajous figure of vibration of the first excitation region shows the trajectories of elongated elliptical shapes, and in the second excitation region, the Lissajous trajectories draw a figure “8”. The results and information from these experimental studies proved that Standard S012-1998 provides sufficient design methods for suppressing hazardous vibrations of cylinders in liquid flows.

Engineering analysis of strong ground rocking and its effect on tall structures

Two, the most intensive 6-dof ground motion records were selected from a database of a program of acquiring seismic aftershocks at Kefalonia Greek Island as reported by Perron et al. in 2018 [1]. The maximum Modified Mercalli (MM) intensity VII and peak ground velocity 18.4 cm/s reached during these seismic events made it possible to investigate substantial structural response under combined translational and rotational excitations. Respective horizontal-rocking effects are studied first on a simplified cantilever model of a slender tower. Next, the seismic responses of two 10 and 30 story tall buildings and a 160 m, reinforced concrete industrial chimney under the joint rocking and horizontal excitations are investigated in detail. A complicated pattern of translational-rocking seismic effects on slender structures was observed. It was noted that sometimes the presence of seismic rotations about horizontal axis increases the overall response (up to 30%), sometimes it decreases the combined seismic response. The net effect depends primarily on two, the most important structural parameters: fundamental natural period and effective height of the analysed structure. The rocking response spectrum proposed in Eurocode 8 part 6 for slender structures was compared with seismic time history response analyses of the r/c chimney, yielding its substantial conservatism compared with the time history response computations using the chosen records of 6-dof strong ground motion. It is also concluded that the application of the familiar SRSS rule to combine the horizontal and rocking effects may underestimate the overall seismic response. This may be important for future calibrations of the seismic codes including rocking ground motion effects.

Reduced Order Modeling with Local Enrichment for the Nonlinear Geometric Response of a Cracked Panel

High-speed flight vehicles operating in extreme environments are likely to undergo significant nonlinear dynamic deformation. The accurate response and life predictions of such structures require methods that enable direct time integration over long portions of flight trajectories, and also require the ability to resolve local stress concentrations. The approach proposed here takes root in displacement-based reduced order modeling to allow for direct time integration. The reduced order models (ROMs) are built using first a ROM constructed over the uncracked structure, whose global basis is augmented with localized enrichment basis functions that are constructed to capture the localized impact of a crack on the displacement field of the structure. The enrichment bases are built using a 3D generalized finite element model defined only in the region of the crack itself. Detailed stress information can also be extracted from the 3D fracture model. The proposed approach is demonstrated on a cracked flat cantilevered blade model, and the benefits of coupling the global basis functions and the localized enrichment bases are demonstrated.

Response of a cantilever model with a surface crack under basal white noise excitation

A cantilever with an open surface crack excited by the pedestal movement with the form of the Gaussian white noise was modeled in this paper. The open crack was simplified as an elastic hinge and the modal functions of the cracked cantilever were obtained. The dynamical equation governing the transverse motion was gained with the Kane’s method after sufficient consideration of the geometrical nonlinearity and the axial inertia. Both quasi-conservative stochastic averaging method and the improved energy envelop stochastic averaging method which is effective on strong nonlinearity were applied to analyze the responses of the cantilever model theoretically. The stationary probability density function (PDF) of the amplitude, as well as the joint stationary PDF of the displacement and velocity, was investigated. For the purpose of exploring the reliability of the cantilever, the reliability function was established to avoid the potential fatigue or damage. Numerical simulations were carried out to vindicate the theoretical analysis. The advantage of the improved energy envelop stochastic averaging method was explicated by the digital results of both the stationary PDF of the amplitude and the joint PDF of displacement and velocity. Furthermore, the accuracy of the prediction on the reliability given by the theoretical analysis was also vindicated by the numerical simulation (Monte Carlo method) of the reliability.

Time-series-based nonlinear system identification of strongly nonlinear attachments

This work introduces a new nonlinear system identification procedure for identifying the dynamics of an otherwise linear mechanical system augmented by strongly nonlinear local attachments directly from measured transient response data. The method employs the proper orthogonal decomposition to extract energy-dependent proper orthogonal modes from the measured time series. Then, using known linear properties, the characteristic frequencies of the system are estimated by applying the Rayleigh quotient, and an estimated frequency-energy plot (FEP) is created by plotting the characteristic frequencies as functions of the mechanical energy in the system. The estimated FEP directly reveals the presence of strongly nonlinear modal interactions, in the form of non-smooth perturbations (spikes) that result from transient resonance captures between different harmonic components of the measured data. The nonlinearity is identified by plotting the estimated characteristic frequencies as functions of a defined characteristic displacement and fitting a frequency equation based on the model of the nonlinearity. The method is demonstrated computationally and experimentally using the response of a cantilevered model airplane wing with a strongly nonlinear attachment connected to its tip.