Tip Of Beam Research Articles

Analyzing the Vibration Response of Adhesively Bonded Composite Cantilevers.

In this study, we investigated the vibration of adhesively bonded composite cantilevers consisting of two beech wood lamella and a bondline of flexible polyurethane. The beams had a constant total height, while the thickness of the adhesive layer varied. We analyzed both the driven and free vibration of a single cantilever beam and a cantilever with an additional mass attached to its end. The eigenfrequencies were determined using Fourier analysis of a sweep load response, the response to an impact load excited using an impact hammer, and the response observed via the manual displacement of the beam's tip. The system's damping was estimated according to the recorded logarithmic decrement. Theoretical estimates of the fundamental natural frequency were obtained using the γ-method and employing a linear elastic theory of composite beams. A numerical modal analysis was carried out using the finite element method. Upon comparing the results of our experiments with the numerical estimates and theoretical predictions, a fair agreement was found.

An electromagnetic microactuator with tunable dynamic characteristics using a thick-film FePt permanent magnet

We designed an electromagnetic microactuator with tunable dynamic characteristics using a thick-film FePt permanent magnet. FePt is a promising microactuator material because of its low Young’s modulus, high tensile strength, high ultimate strain as a structural material, and high remanence as a permanent magnet. By employing the laser-assisted heating magnetization method, we successfully reprogrammed the magnetization pattern of the FePt thick film, which led to the tuning of the dynamic characteristics of the 3.85 mm (l) × 0.82 mm (w) × 0.023 mm (t) FePt-based cantilever under the same alternating external magnetic field. When only the tip of the cantilever beam is magnetized, or when the tip and center of the same beam are magnetized in opposite phases, the peak gain of the frequency response characteristics of the former can be tuned to be 19 dB higher than that of the latter in the first-order mode and 19 dB lower than that of the latter in the second-order mode.

Dynamic Analysis of Rigid–Flexible Structures with Piezoelectric Actuation and Control

In this paper, the dynamic equation of a rigid body coupled with two flexible beams was established, considering the rotational motion of the rigid body and the elastic deflection of the flexible beams. The coupling effect between the rigid body rotation and flexible beam vibration was studied in detail. The dynamic response of the flexible beam with piezoelectric effect was established based on Hamilton’s principle. Under the premise of ignoring the nonlinear vibration coupling term of flexible beams, only the first two modes of transverse displacement and one directional rotation motion were studied in case studies. It was found that the coupling term caused by rigid body rotation can slightly alter the natural frequency and amplitude of flexible beams, mainly reflected in the first-order mode. With increasing the external excitation on the rigid body, the induced transverse displacement at the tip of the flexible beam increased significantly. Meanwhile, when the flexible beam was under external excitation, the vibration could also induce rigid body rotation. With the inverse piezoelectric effect, one may actively actuate the flexible beam vibration and rigid body rotation or control the undesired motion of the system. The control effect can be adjusted by varying the applied voltage excitation on the piezoelectric patches as well as patch positions. The conclusions drawn from this study can be applied to active precise control of space facilities such as satellites. Based on the dynamic modeling of rigid–flexible multi-body systems, this paper completed the study of the coupling effects of rigid body rotation and flexible body vibration, and proposed an application idea for completing small-angle maneuvers of rigid–flexible multi-body systems through piezoelectric control.

Control of edgewise vibration of a pre-twisted rotating beam with shunted piezoelectric tuned mass damper

The edgewise vibration control of a pre-twisted beam, rotating in the vertical plane, is considered in this study. A piezoelectric tuned mass damper (PTMD) comprising a spring–mass–damper system and a piezoelectric transducer with its associated shunt circuit is considered the control device. A finite element formulation of the pre-twisted rotating beam with the attached PTMD is developed while considering the effect of centrifugal stiffening due to rotation and the effect of gravity force. The natural frequencies of the beam (without PTMD) obtained using the present formulation are corroborated by comparing them with the results derived from Ansys. A single PTMD attached at the tip end of the beam can effectively suppress the response of the beam subjected to a distributed load in the edgewise direction. The best values of resistance and inductance of the shunt circuit are obtained through a parametric study on the peak and root mean square value of the beam tip response. A qualitative difference in the uncontrolled as well as in the controlled responses can be noticed while considering the effect of the gravity load component in the edgewise direction. Further, it has been observed that the conventional Tuned Mass Damper (TMD) provides better control than the PTMD system for ideally tuned conditions, however, the control performance of TMD degrades rapidly as compared to the PTMD in the presence of detuning. This demonstrates the effectiveness of PTMD in a practical implementation where achieving the perfectly tuned condition is seldom realized. The control performance of PTMD marginally degrades when the beam is subjected to multi-directional excitation. Hence, the proposed control system has the potential for application in rotating beam-type structures, such as wind turbine blades.

Enhanced magnetically coupled rotational piezoelectric energy harvesting based on tailored centrifugal distance

To tackle the issue of limited operating bandwidth encountered by energy harvesters in high-speed rotating contexts, this paper proposes a method for achieving rotational energy harvesting over a relatively high bandwidth through stabilizing high-energy orbit oscillations based on theoretically tailored centrifugal distance. The interaction between the cantilever beam tip permanent magnet and the fixed end magnet introduces nonlinear factors into the rotating piezoelectric energy harvesting system. By exploiting the non-linear matching relationship between the jump-down frequency under bistable condition and the rotational frequency of the external environment, the centrifugal distance theoretically derived is divided into five distinct conditions. Notably, when the centrifugal distance is in condition of 6.5 cm, optimal alignment and overlap are observed between the jump-down curve and the rotational frequency curve within the rotational frequency range of 40–80 rad s−1. Tailoring of different centrifugal distances across the five conditions is then explored and validated through simulations, including velocity profiles and energy harvesting capabilities. Finally, a rotating experimental platform was constructed and the experimental results validate that, at the theoretically tailored centrifugal distance of 6.5 cm, the rotating energy harvester achieves a peak power output of 127.4 μW within the effective bandwidth of 40–80 rad s−1. This study underscores the significance of tailoring centrifugal distance to stabilize high-energy orbit oscillations, thereby enhancing the energy harvesting potential of the device across a relatively wide range of external rotational frequencies.

Active Vibration Damping Using Rotor Torque Control in Electric Aircraft

Vibration damping in aerospace structures can decrease the likelihood of failures and instabilities and improve passenger comfort. This paper introduces the novel idea of damping vibration using the electric proprotors on aircraft without compromising flight control. The equations of motion of a cantilevered beam with a propeller at the tip driven by an electric motor are obtained using Hamilton’s principle, solved analytically in the frequency domain, and approximately in the time domain. Feeding back the beam tip angular rate to the motor torque is shown to asymptotically stabilize all transverse beam vibration modes. The overall vibration control consists of the inner rate feedback damping loop with an outer rotor speed control loop. Experimental frequency response and step response validate the models and show that the closed-loop damping in the first mode is three times higher than open loop with less than 1% rotor speed change for a 3% initial tip displacement. Theoretical results give good agreement with experiments. Parametric studies based on a 12 kg quadcopter indicate that if the rotor inertia is sufficiently large the proposed control can provide 8% damping with minimal impact on rotor speed.

Efficiently harvesting low-speed wind energy by a novel bi-stable piezoelectric energy harvester from vortex-induced vibration and galloping

Designing low-cost and simple harvesters to convert natural wind energy into electricity is regarded as a promising method to realize the self-powering of node sensors in the Internet of Things. However, the inherent challenge lies in the typically low and fluctuating speeds of environmental wind, making efficient energy harvesting a difficult task. To address this challenge, this study introduces a novel bi-stable wind energy harvester designed to undergo inter-well oscillations through the synergistic effects of vortex-induced vibration and galloping. The bi-stability is achieved by incorporating three magnets. To enhance the extraction of energy from low-speed wind, a square-sectioned bluff body is affixed to the cantilever beam's tip, accompanied by two foam balls. Simulations elucidate the fluid dynamics around the bluff body and foam balls, revealing that the induced vortex causes swinging in the balls, subsequently driving the piezoelectric beam to oscillate and jump. The study establishes the potential energy and force–displacement relationship of the proposed harvester to provide insights into the flow fields. A physical prototype of the harvester is fabricated and subjected to verification experiments in a wind tunnel. Results indicate that the proposed harvester exhibits snap-through or inter-well oscillations, generating a desirable energy output at wind speeds exceeding 1.3 m/s. Notably, even at very low wind speeds, the proposed harvester, despite exhibiting the same intra-well motion as its linear counterpart, achieves significantly higher output voltage due to magnetic interaction and bi-stability. Demonstrating superior performance with a voltage output of up to 10.5 V at a wind speed of 1.6 m/s, compared to the mere 0.7 V from its linear counterpart, the proposed harvester shows the advantages of bi-stability and snap-through motion in low-speed wind energy harvesting.

Enhanced two consecutive samples based de-modulation technique for atomic force microscopy application

This article investigates robust amplitude detectors suitable for atomic force microscopy (AFM) while discussing better alternatives. An AFM instrument’s measurement unit is responsible for providing the amplitude information obtained from the tip of a cantilever beam to identify the surface smoothness of a test material. Therefore, two efficient approaches are suggested to leverage Lyapunov’s theory while adhering to better noise suppression and DC-offset rejection capabilities. Nevertheless, an enhanced two samples-based Lyapunov’s demodulation approach is proposed to detect the amplitude information rapidly. Consequently, the modifications applied to the conventional method help reduce the tuning efforts and structural complications. The proposed solution remains structurally simpler and useful for high- and low-frequency probes. Furthermore, the extensive design guidelines for all techniques and the simulation results are presented. Different amplitude signals are synthetically generated from several rough pseudo-test surfaces for early verification and sent to a real-time digital controller to judge the proposal’s efficacy.

Topology Optimization of Lattice Support Structure for Cantilever Beams Fabricated Via Laser Powder Bed Fusion

Herein, a numerical scheme is presented to design, optimize, generate, and manufacture a lattice support structure that reduces thermal‐induced distortion in metallic components 3D printed by laser powder bed fusion (LPBF). The inherent strain method is implemented in the framework to fast predict the part distortion during an LPBF build, and asymptotic homogenization is used to determine the effective properties of the lattice support with a triply periodic minimum surface topology. The framework is tested on a practical case study that involves the design of the optimized gradient of a lattice that supports a cantilever beam and compares the results with benchmark designs, a lattice support structure with uniform relative density and a fully solid support. The optimized support can reduce the distortion pattern throughout the entire cantilever beam and reduces the beam tip distortion of 69% and 58% in comparison to the uniform lattice and fully solid support. To demonstrate the viability of the design workflow here presented, a proof‐of‐concept lattice support is manufactured out SS316 stainless steel via LPBF.

Influence of Retrograde Intramedullary Beam Position Within Talar Body on Radiographic Failure of Medial Column Fusion

Category: Midfoot/Forefoot; Diabetes Introduction/Purpose: Intramedullary fixation in the form of retrograde beam or bolt has developed as an intriguing treatment option for unstable midfoot collapse. This is particularly true when it is desired to minimize the length of incision or to avoid surface implants in a compromised soft tissue envelope. However, prior studies have demonstrated high rates of complications associated with intramedullary midfoot fusion constructs (Ford et al., Butt et al). The goal of this study was to create a reproducible convention of classifying position of the terminal implant within the talar body and to uncover an association of relative position of the implant at the time of surgery with an increased risk of failure. Methods: Consecutive patients treated surgically from January 2017 to September 2022 with retrograde intramedullary fusion beam were identified; 44 were included in the final analysis. Average age was 62.7 years and mean radiographic follow up measured 12.86 months. Figure 1 demonstrates our classification of relative talar position. First, a line was drawn along the axis of the talar neck and carried posteriorly dividing the talar body into dorsal and plantar hemispheres. Then, a line was drawn from the anterior articular margin of the talar body to the lateral talar process. Parallel lines were then created in an equidistant fashion to divide the talar body into equal relative quartiles. At the time of surgery, the tip of the intramedullary beam was classified into relative axial and coronal position by a single observer. Our primary outcomes were hardware failure defined by implant fracture or cutout from the bone or additional surgery. Results: Successful midfoot fusion with intramedullary beam was achieved in 77% of our cases. 10 cases demonstrated hardware failure or the need for additional surgery. Relative implant position was classified as dorsal in 43% of cases and plantar in 57% of cases. Talar quartile depth was classified as 1st in 6% cases, 2nd in 32% of cases, 3rd in 30% of cases, and 4th in 32% of cases. There was no clinical or statistically significant difference between rates of failure based on relative implant position. Conclusion: Retrograde intramedullary fusion for medial column collapse remains a viable treatment option and our data supports successful fusion in most patients but a risk of failure remains significant. In this study, the relative position of the terminal implant within the talar body did not correlate with an increased risk of failure. There are likely other patient specific, or biomechanical factors leading to hardware fracture, cut out, or return of deformity. Continued analysis as sample size increases remains paramount to forming additional conclusions.

An investigation into model extrapolation and stability in the system identification of a nonlinear structure

Estimating a nonlinear model from experimental measurements of a vibrating structure remains a challenge, despite huge progress in recent years. A major issue is that the dynamical behaviour of a nonlinear structure strongly depends on the magnitude of the displacement response. Thus, the validity of an identified model is generally limited to a certain range of motion. Also, outside this range, the stability of the solutions predicted by the model are not guaranteed. This raises the question as to how a nonlinear model derived using data from relatively low amplitude excitation can be used to predict the dynamical behaviour for higher amplitude excitation. This paper focuses on this problem, investigating the extrapolation capabilities of data-driven nonlinear state-space models based on a subspace approach. The experimental vibrating structure consists of a cantilever beam in which magnets are used to generate strong geometric nonlinearity. The beam is driven by an electrodynamic shaker using several levels of broadband random noise. Acceleration data from the beam tip are used to derive nonlinear state-space models for the structure. It is shown that model predictions errors generally tend to increase when extrapolating towards higher excitation levels. Furthermore, the validity of the estimated nonlinear models become poor for very strong nonlinear behaviour. Linearised models are also estimated to have a complete view of the performance of each candidate model for each level of excitation.

Influence of travelling waves on the fluid dynamics of a beam submerged in water

Inspired by the use of travelling waves for propulsion mechanisms adopted by many animals and organisms, this paper investigates the mechanism with which travelling waves in beam-like structures induce velocity in a surrounding fluid. This work focuses on the flow induced around the beam tip and provides an experimental characterisation of the phenomena. A test rig equipped with Laser Doppler Anemometry (LDA) is used to investigate the induced fluid velocity and its dependency on the modal response of the beam. Numerical simulations are performed to complement the experimental tests and provide further insight into the fluid–structure interaction. The numerical model also allows for the beam vibration envelope and vibration patterns to be obtained and correlated with the measured fluid velocity. Several geometrical variations are considered in the analysis over a range of frequencies that encompass resonant responses up to the fourth mode. The results showed that the fluid flow is only marginally affected by the change in the vibration pattern between the first-two resonant mode; the induced fluid velocity and, hence, the thrust are mostly driven by the tip velocity of the beam.

A semi-analytical method for determining the mixed mode I/II fracture resistance and mode mixture of ADCB laminates

The crack tip of the asymmetric double cantilever beam (ADCB) under mode-I loading is often accompanied by a proportion of mode II component, thus it is a typical mixed-mode I/II problem. Characterizing the mixed-mode I/II fracture resistance behavior and mode partition in ADCB laminates is of great significance for studying the mode mixture phenomenon. In this work, a semi-analytical method is proposed to determine the mixed-mode fracture resistance curve (R-curve) and mode mixture of ADCB composite laminates. Considering the use of the equivalent crack length related to compliance, the global crack growth rate ratio correction model is proposed. The results derived from the proposed semi-analytical method is compared with other theoretical methods to verify its effectiveness and wide applicability for ADCB laminates with various material systems and stacking sequences. In contrast, the semi-analytical method with the global crack growth rate ratio correction requires fewer measurement data and gives accurate R-curve results. In addition, it makes the mode partition during the whole delamination growth process with physical meaning.

Towards neural network‐based numerical friction models

AbstractFriction contacts can be found in almost all mechanical systems and are often of great technical importance. However, they are usually difficult to describe, and their behavior and influence on the whole system are hard to predict accurately. Modern product design and system operation strongly benefit from numerical simulation approaches today, but reliable friction models still represent a major challenge in this context.To tackle this problem, we employ neural network regression to capture the characteristics of frictional contacts and make them accessible for numerical methods in a minimal intrusive fashion. In particular, we test our approach using a Finite Element model of a 2D cantilever beam subject to stick‐slip vibrations induced by a moving conveyor belt at its free end. As a reference solution, we perform a transient analysis based on a simple analytical friction model, where the kinetic friction force only depends on the normal load and the relative sliding velocity. We take the same friction model, add some artificial noise to mimic uncertainties coming with experimental measurements, and pick a limited set of data points to train a regression neural network. The machine learning friction model is then deployed in the Finite Element code to predict the kinetic friction force acting on the beam tip during the slip phases.The deflection curves obtained by the transient numerical analysis using the new neural network friction model agree well with the reference solution based on the underlying analytical model. The results indicate that data‐driven approaches may also be capable of capturing more complex frictional contacts, including effects of temperature, humidity, and load history. The trained neural network friction models can then be employed in numerical simulations in a minimally intrusive manner. This approach opens up new possibilities to predict individual mechanical system behavior as accurately as possible.

Validation and optimization of two models for the magnetic restoring forces using a multi-stable piezoelectric energy harvester.

This article presents a tunable multi-stable piezoelectric energy harvester. The apparatus consists of a stationary magnet and a cantilever beam whose free end is attached by an assembly of two cylindrical magnets that can be moved along the beam and a small cylindrical magnet that is fixed at the beam tip. By varying two parameters, the system can assume three stability states: tri-stable, bi-stable, and mono-stable, respectively. The developed apparatus is used to validate two models for the magnetic restoring force: the equivalent magnetic point dipole approach and the equivalent magnetic 2-point dipole approach. The study focuses on comparing the accuracy of the two models for a wide range of the tuning parameters. The restoring forces of the apparatus are determined dynamically and compared with their analytical counterparts based on each of the models. To improve the model accuracy, a model optimization is carried out by using the multi-population genetic algorithm. With the optimum models, the parametric sensitivity of each of the models is investigated. The stability state region is generated by using the optimum second model.

Experimental Analysis of Hysteresis in the Motion of a Two-Input Piezoelectric Bimorph Actuator

This article presents a comparison of hysteresis courses in the motion of a two-input actuator (bimorph) and hysteresis in the motion of a single-input actuator (unimorph). The comparison was based on the results of laboratory and numerical experiments, the subject of which was an actuator built of three layers: a carrier layer from a glass-reinforced epoxy laminate and two piezoelectric layers from Macro Fiber Composite. The layers were glued together, and electrodes in the Macro Fiber Composite layers were connected to a system that included an analogue/digital board and a voltage amplifier. The main purpose of this research was to compare the characteristic points of the hysteresis curves of the displacement of the bimorph actuator with the characteristic points of the hysteresis curves of the unimorph actuator. Based on the research results, it was noticed that, in the bimorph, the maximum hysteresis and mean hysteresis values increase faster than the maximum displacement of a beam tip. However, values of characteristic input voltages for hysteresis loops—voltage corresponding to a maximum displacement of the actuator beam tip and voltage corresponding to maximum hysteresis—are almost the same for the bimorph and unimorph. From a practical point of view, it was noticed that the unimorph is a better choice compared to the bimorph in applications in which high changes in frequencies of input voltages appear.

Design and investigation of a quad-stable piezoelectric vibration energy harvester by using geometric nonlinearity of springs

In this paper, a quad-stable piezoelectric vibration energy harvester induced by the geometric nonlinearity of springs is designed and investigated. The novelty is that by replacing the permanent magnets with a combination of springs, the system can be effectively protected from electromagnetic interference in the working environment. The innovative design of three hinged springs attached to the tip of the cantilever beam makes the stiffness of the structure inherently nonlinear, which can induce the multi-stability of the system. The Euler-Lagrange equations are applied to establish the governing equation of the energy harvester. The static bifurcation analysis reveals the evolution process of multi-stability. The complex dynamic frequency (CDF) method, an efficient approach to solving strongly nonlinear dynamic problems with multi-well systems, is then applied to deduce the system's amplitude-frequency response. Combinations of theoretical and numerical results show that among a wide frequency bandwidth, the system can exhibit such as single-, double- and quadruple-well periodic motions. Finally, experiments are set up to verify the advantage of inter-well motion on harvesting power. Result shows that geometric nonlinearity can effectively make the energy harvester exhibit multi-stability, generate different movement patterns, and obtain high harvesting power.

Experimental Study on Seismic Behavior of Coupled Steel Plate and Reinforced Concrete Composite Wall

The coupled steel plate and reinforced concrete (C-SPRC) composite wall is a new type of coupled-wall system consisting of steel coupling beams (SCBs) that join two SPRC walls where the steel plate shear wall (SPSW) is embedded in the RC wall. Although the C-SPRC wall has been extensively constructed in high-rise buildings in seismic regions, research on its behavior has rarely been reported. No code provisions are available for directly guiding the preliminary design of such coupled-wall systems. In the research, three 1/3-scaled C-SPRC wall subassemblies including one-and-a-half stories of SPRC walls and a half-span of SCB were tested under simulated earthquake action, considering the fabrication method of the embedded SPSW and the shear-span ratio of the SPRC walls as two test variables. The prime concern of the research was to evaluate the influences of those popular design and construction parameters on the seismic behavior of the C-SPRC wall. Deviating from the beam tip loading method used in conventional subassembly tests, the lateral cyclic load in this research was applied at the top of the wall pier so that the behaviors of both walls and SCBs could be examined. The test results exhibited the great seismic performance of the subassemblies with the coupling mechanism fully developed. The energy dissipation capacity and inter-story deformation capacity of the subassembly with the assembled SPSW were roughly 9.4% and 13.2% greater than those with the conventional welded SPSW. Compared with the subassembly with the shear-span ratio of 2.2, the interstory-deformation capacity of the one with the shear-span ratio of 2.0 was increased by approximately 13.4%, while the energy dissipation capacity was decreased by 10.9%. The test results were further compared with the simulation results using the proven-reliable finite element analysis with respect to the hysteretic curves, skeleton curves, energy dissipation capacities and failure patterns.

Experimental investigation on internal offset crack of PMMA beam using caustics

In this paper, the dynamic stress intensity factor (DSIF) at the crack tip of a PMMA beam containing an internal offset crack under impact loading was investigated by using a transmission digital caustic test system combined with high-speed camera. Firstly, the stress intensity factor, as well as velocity, of the mixed-mode crack tip under static and dynamic loading were derived based on the transmission caustic method; secondly, a drop hammer loading test was conducted on the different specimens with biased cracks in the beam using the transmission caustic test system to obtain the dynamic fracture mechanics parameters of internal crack initiation and expansion; then, the crack initiation angle and expansion path analysis of the impact-generated expansion cracks were performed based on the theoretical analysis and the differences between the fracture process and that of the specimens containing internal symmetric cracks were discussed. The results show that the different locations of the internal off-set cracks make the stress redistribution process inside the beam and the stress state at the crack tip during the crack extension process different, and the fracture process and fracture mechanics parameters are different from those of the specimens with internal symmetric cracks, the results of the caustic test are in good agreement with the numerical analysis. The research results can provide guidance for the study of the fracture process of brittle materials such as PMMA containing internal defects.

Performance enhanced piezoelectric rotational energy harvester using reversed exponentially tapered multi-mode structure for autonomous sensor systems

Piezoelectric energy harvesting from rotational motion has recently been found to be a promising way to power wireless autonomous sensor systems. In the reported studies, a piezoelectric energy harvester (PEH) structure with a high strain concentration, an inward configuration, and varied rotation axis alignments is shown to play an important role in enhancing the harvester's vibration amplitude and performance. In this paper, a novel rotation-based PEH is proposed to harvest energy from rotational motion using a multi-mode structure (mounted in an inward configuration) consisting of a reversed exponentially tapered beam (primary beam element) and six branched beams (secondary beam elements) attached with a flange to the free end of the primary beam. The beam tip mass axis does not coincide with the rotation axis along its length to improve harvester vibration amplitude. When the harvester spins at a constant speed, the gravitational force acting on the primary and branched beams causes continuous oscillations in the transverse direction. As a result, the primary beam with a piezoelectric patch continually deforms and generates electrical energy. The harvester is theoretically modeled using the Euler-Bernoulli beam theory, and its dynamic equations are derived using the Lagrangian formulation. The proposed harvester is fabricated, and its performance is evaluated through experimentation at a rotating frequency ranging from 1.5–9.5 Hz (90–570 rpm). The harvester offers greater design adaptability in tuning structural parameters to achieve the desired frequencies. An energy management system was designed after investigating the charging behavior of the capacitor with the harvester, and it was found that the proposed harvester was suitable to source wireless autonomous sensor systems.