Cantilever Research Articles

Reliability-based topology optimization of imperfect structures considering uncertainty of load position

In this paper, a novel optimization technique is implemented to explore the effects of considering uncertain load positions. Therefore, the integration of reliability-based design into structural topology optimization, while considering imperfect geometrically nonlinear analysis, is proposed. By comparing the results obtained from perfect and imperfect geometrically and materially nonlinear analyses, this study examines the impact of nonlinearity on probabilistic and deterministic analyses. Concerning probabilistic analysis, the originality of this research lies in its incorporation of the position of the applied load as a stochastic variable. This distinctive approach complements the consideration of other relevant parameters, including volume fraction, material properties, and geometrical imperfections, with the overarching goal of capturing the variability arising from real-world conditions. For the assessment of uncertainties, normal distribution is assumed for all these parameters. Normal distributions are chosen due to their advantages in terms of simplicity, ease of implementation, and computational efficiency. These characteristics are particularly beneficial when dealing with complex optimization algorithms and extensive analyses, as is the case in our research. The proposed algorithm is validated according to the results of benchmark problems. Structural examples like cantilever beam, pinned-shell, and L-shaped beam problems are further explored within the context of imperfect geometrically nonlinear reliability-based topology optimization, with specific regard to the probabilistic aspect of the location of the externally applied loads. Moreover, the results of the suggested approach suggest that the inclusion of a probabilistic design strategy has influenced topology optimization. The reliability index acts as a controlling constraint for the resulting optimized configurations, including the mean stress values associated with the resulting topologies.

Transverse Vibration Response and Time-Varying Analysis of Axially Moving Beams Based on Choi–Williams Distribution

Cantilever beams with axial extension and contraction functions as time-varying parameter systems have attracted extensive research due to their prevalence in engineering structures. In this paper, the dynamic characteristics of the flat-push bridge mechanism are investigated from the theoretical aspect, firstly, it is simplified into a cantilever beam model with axial motion, and the transverse vibration equations of the cantilever beam are established based on the Euler–Bernoulli beam theory and D’Alembert’s principle, and the transverse displacements of the beam are discretized using the Galerkin truncation method and solved numerically by using the Newmark-[Formula: see text] method for the second-order vibration differential equations with variable coefficients; second-order vibration differential equations were solved numerically by the Newmark-[Formula: see text] method; then the structural examples in the existing literature are verified numerically, and the calculation results are consistent with the literature results, indicating that the transverse vibration equations derived in this paper are solved effectively; then a parametric analysis of the speed of the cantilever beam during axial extension/contraction was done, which showed that the faster the speed of axial motion, the faster the rate of change of the dynamic characteristics of the beam and the more pronounced the vibration; finally, the power signal is decomposed in the time-frequency domain by using the Choi–Williams Distribution (CWD), and the time-frequency characteristics of the system under different speeds are analyzed, and the results show that the use of CWD technique can accurately reflect the system’s transient vibration frequency and vibration energy with the change rule of time and speed, and the axial motion speed of ±0.05[Formula: see text]m/s, the transient frequency of the theoretical prediction and the average relative deviation between the finite element modal frequencies are kept within 5% and the recognition accuracy is high. This analysis provides flexible technical guidance for vibration control in engineering structures.

Design of stiffness-variable dielectric elastomer wing based on seagull characteristics and its application in avian flight bionics

ABSTRACT Dielectric elastomers (DE), renowned for their lightweight, rapid response, high energy density, and efficient conversion, have garnered significant attention in the realm of avian flight bionics. However, a lack of understanding of the mechanical principles underlying flapping wing biomimetics has hindered accurate simulations of actual bird flight postures. To address this, a stiffness-variable DE-based wing (DEW) has been designed, inspired by the characteristics of seagulls, to mimic the wing deformations across different bird flight phases. The evolution of the DEW’s deformation is modeled based on the differential equation describing the bending curve of a DE cantilever beam. By applying different voltage cycles, three continuous avian flight postures have been replicated: takeoff, cruising, and hovering. The simulation results demonstrate that the stiffness-variable DEW effectively mimics the wing deformations observed in birds during different flight postures, closely resembling real-world flight conditions. This study has the potential to serve as an important reference for exploring changes in bird flight behavior, thereby advancing the application of DE materials in the field of soft robotics.

Cantilever configurations in vibration-based piezoelectric energy harvesting: A comprehensive review on beam shapes and multi-beam formations.

Abstract Vibration-based energy harvesting technology is a well-established research area that has attracted tremendous interest over the last decade. This interest is primarily owing to its extension into a wide range of engineering domains, particularly in Microelectromechanical Systems (MEMS). The cantilever beam is the most common and widely used model for vibration-based energy harvester, driven by two key factors: a) simplicity in design, and b) high output power density. Numerous studies over the years have focused on optimizing the cantilever beam design to increase output power capacity and/or widen the frequency bandwidth of the harvester. While researchers have proposed a plethora of cantilever beam configurations for specific purposes (e.g., low-frequency harvesting, multi-directional frequency harvesting, etc.), there is a notable lack of detailed literature on the types and configurations of cantilever beams. This gap hinders researchers from gaining a comprehensive understanding of the cantilever beams already introduced. Following the need, in this article a comprehensive review is made to list the types of cantilever beams proposed by the researchers over the years. This review covers the working principles of piezoelectric energy harvesting, analyses existing solutions geared towards increasing power output and widening working frequency, and discusses diverse configurations including single and multiple beam setups. The listed beams are categorized based on their structural shape and organization such that it can be helpful for a reader to anticipate which cantilever beam design can be suitable for a specific need. Power output capacity and operating frequency for every beam design are also presented in a tabular form, under each beam category. This would enable the researchers to tailor their designs for specific applications, enhance material efficiency, drive innovation, and open new application possibilities.

Damage detection and localization in a cantilever beam structure via regression-and-classification-based machine learning

Damage detection and localization in a cantilever beam structure via regression-and-classification-based machine learning

Stress relaxation and improved fracture toughness of metal bonding using flexible monolith sheets and an epoxy adhesive

AbstractWhile epoxy resins exhibit excellent mechanical and insulating properties as well as excellent stability against heat and chemicals, epoxy adhesives also have drawbacks such as brittleness and stress concentration. Rubber-based materials are often added to epoxy adhesives to increase toughness, but they are sensitive to heat and moisture, limiting their effectiveness in harsh environments. In this study, we propose a new sheet-type adhesive consisting of a conventional liquid epoxy adhesive and an epoxy monolith sheet with internal continuous pores, using the advantageous properties of the flexibility and toughness of the epoxy monolith to avoid stress concentration. We evaluated the adhesion strength for metal bonding using the sheet-type epoxy adhesives via a lap-shear tensile adhesion test at various temperatures. The total destruction energy was also estimated via a tapered double cantilever beam test. Furthermore, a heat cycle adhesion test was conducted using two types of metallic materials with different coefficients of thermal expansion to elucidate the effect of the monolith sheet on the improvement of interfacial failure induced by stress concentration.

Improved active vibration control of a cantilever beam using MFC actuators with Hammerstein model-based hysteresis modeling and VSS-FxLMS control algorithm

This study aims to enhance active vibration control in a cantilever beam using macro fiber composite (MFC) actuators. To address the challenge of accurately modeling the complex hysteresis behavior of MFC actuators, an advanced hysteresis modeling technique is employed, integrating a non-symmetric Bouc–Wen model with an Auto-Regressive model with eXogenous inputs (ARX). The parameter estimation of this model is optimized using an adaptive mutation factor, and multiple mutation strategy differential evolution (AmFMMDE) algorithm. Additionally, a Variable Step Size Filtered-x Least Mean Square (VSS-FxLMS) algorithm with step size adaptation based on normalized error change is utilized for effective vibration control. This approach shows promising potential for practical engineering applications requiring precise and efficient active vibration control.

Comparison of passive and semi-active piezoelectric transducer damping of cantilever oscillation

The aim of this work is the analysis of passive and semi-active damping methods on the model woven beam with a piezoelectric (PZ) layer. The mathematical model of the PZ layer on cantilever beam is derived. For modeling, real product parameters of PZ layer are used, and through simulation find the optimal values to dampen it. The resistive-inductance passive model, and State-Switch Damping SSD semi-active model are used in this work. The models are processed in the MATLAB Simulink environment and the results of the behavior of the models compared to each other. The program involving passive and semi-active systems, where analyze the behavior of the model for different parameters and the damping capabilities of individual methods are compared. The simulation results show the effectiveness of the semi-active system in comparison with the passive systems, also it shows the passive method is not so effective at low frequency as it in high frequency, and the semi-active method is not optimal for high frequency vibration.

Development of fiber Bragg grating vibration sensor for bidirectional monitoring of thin rod cantilever beam

Monitoring of vibration frequencies and forces in cables and suspension rods of bridges is crucial. In order to achieve high-precision and bidirectional low-frequency monitoring of cable force and suspension rod, in this work, a thin rod cantilever beam type FBG vibration sensor was developed for bidirectional monitoring based on theory, experiment, and finite element simulation. Firstly, elastic structure of the thin rod was analyzed, and the structural parameters of the sensor were optimized based on theoretical analysis and finite element simulation. Then, the frequency and sensitivity of the sensor were tested. The obtained test results showed that the resonant frequency of the sensor in the x/y direction was 48 Hz, sensitivity was 90.5/102.3 pm/g, and error in frequency was less than 2 %. Furthermore, the force in the cable measured by the sensor was verified through indoor tension tests. The test results showed that the maximum error in the force measured in the cable was 0.86 % relative to the actual tension in the cable, indicating high measuring accuracy of the developed sensor. Finally, the sensor was applied to monitor forces in actual engineering cables, where an error of 4.21 % was noticed, which further validated the accuracy and applicability of the sensor. The research results of the present would provide guidance for improving the ability of the bidirectional low-frequency FBG vibration sensors to measure low-frequency random vibrations.

A nonlinear and asymmetric monostable compliant ortho-planar spring piezoelectric vibrational energy harvester using a H-I structure

This paper proposes a compliant ortho-planar spring piezoelectric vibrational energy harvester (COPS-PVEH) using a H-I structure that exploits a nonlinearity and an asymmetric mono-stability to enhance the bandwidth of the device. The main structure is based on a double clamped beam (I-structure) coupled with four cantilever beams (H-structure) and an ortho-planar spring in the centre of the I-structure. Finite element analysis (FEA), analytical modelling, and experimentation were performed to analyse the dynamical and electrical behaviour of the harvester. The device was fabricated using polylactide (PLA). Six bimorph PZT-5H piezoelectric materials, electrically connected in parallel, were used as piezoelectric generators. The device was tested using an optimum load resistor of 90 kΩ under sinusoidal and sine sweep excitation in the gravity (vertical) direction. The pre-load (due to gravitation) causes a softening nonlinearity and an asymmetric mono-stability in the potential energy function. The results show that multiple peaks are observed in the output voltage of the harvester in the FEA, analytical modelling, and experimentation under harmonic excitation in the sub 15 Hz frequency range. Furthermore, analytical modelling and experimentation exhibit softening nonlinearity and chaotic behaviour, reaching a maximum amplitude power of 1.01 mW (at 8.3 Hz) and 1.07 mW (at 9.5 Hz) respectively under sine sweep excitation (amplitude of 0.6 g (g = 9.81 m/s2)). Experimentally, the harvester also generates an average power greater than 46 µW with a 6.8 Hz bandwidth under the same excitation. The softening nonlinearity and asymmetric mono-stability enhance the bandwidth of the harvester in the low frequency region where most broadband ambient vibrations are available in practical environments.

Optimization of the Cantilever Beam with TPMS Lattice Structure

Optimization of the Cantilever Beam with TPMS Lattice Structure

Effect of fiber orientation of adjacent plies on the mode I delamination fracture of carbon fiber reinforced polymer multidirectional laminates

AbstractThe extensive use of multidirectional composite laminates requires to understand the delamination behavior at interfaces between plies with different fiber orientations. In this study, double cantilever beam testing was performed to investigate the mode I interlaminar fracture of carbon fiber reinforced polymer laminates with different central interfaces (0//0, 0//+45 and +45//−45). X‐ray microtomography revealed the curved crack front shape that was incorporated to calculate fracture toughness. The fracture toughness varies with the crack length in a typical delamination resistance curve, which can be quantified by an empirical equation. Incorporation of variable fracture toughness into a cohesive zone model can better predict the delamination fracture of the laminate, compared to constant toughness. It was found that the delamination mechanism is independent of central interfaces. However, compared to unidirectional laminates, multidirectional laminates are less resistant to crack initiation, but more resistant to propagation with higher toughness and shorter fiber bridging zone.Highlights Mode I interlaminar fracture of CFRP laminates with different central interfaces was investigated experimentally and numerically. Curved crack front shape was incorporated to calculate fracture toughness. Incorporation of variable fracture toughness into a cohesive zone model can better predict the delamination fracture of the laminate. Multidirectional laminates are less resistant to crack initiation but more resistant to propagation with higher toughness and shorter fiber bridging zone.

Epsilon-Greedy Thompson Sampling to Bayesian Optimization

Abstract Bayesian optimization (BO) has become a powerful tool for solving simulation-based engineering optimization problems thanks to its ability to integrate physical and mathematical understandings, consider uncertainty, and address the exploitation–exploration dilemma. Thompson sampling (TS) is a preferred solution for BO to handle the exploitation–exploration trade-off. While it prioritizes exploration by generating and minimizing random sample paths from probabilistic models—a fundamental ingredient of BO—TS weakly manages exploitation by gathering information about the true objective function after it obtains new observations. In this work, we improve the exploitation of TS by incorporating the e-greedy policy, a well-established selection strategy in reinforcement learning. We first delineate two extremes of TS, namely the generic TS and the sample-average TS. The former promotes exploration, while the latter favors exploitation. We then adopt the e-greedy policy to randomly switch between these two extremes. Small and large values of e govern exploitation and exploration, respectively. By minimizing two benchmark functions and solving an inverse problem of a steel cantilever beam, we empirically show that e-greedy TS equipped with an appropriate e is more robust than its two extremes, matching or outperforming the better of the generic TS and the sample-average TS.

Numerical investigation of thermal influence on debonding behavior in composite structures through a friction and cohesive coupled model

AbstractThis study conducts an in-depth numerical analysis of debonding behavior in composite structures, with a particular focus on the critical role of thermal effects. Utilizing a frictional contact cohesive zone model, the research characterizes the debonding process while sequentially integrating thermal analysis to assess the impact of thermal loading. A thermomechanical coupled model is developed and implemented using the finite element software ABAQUS. The model's accuracy is validated through the Double Cantilever Beam (DCB) test, ensuring reliable results. The methodology involves a detailed finite element analysis, where thermal loads are applied to composite specimens, followed by mechanical loading to simulate debonding. The frictional contact cohesive zone model accurately captures the interface behavior under varying thermal conditions. Quantitative results indicate that thermal loading significantly affects the debonding process, with a noticeable increase in debonding initiation and propagation rates, highlighting the critical influence of thermal effects on structural integrity.

The influence of lumped mass deployment on the performance of a hybrid galloping energy harvester

This article delves into a hybrid galloping energy harvester featuring a longitudinally aligned triangular-shaped bluff body. Numerically, it analyzes how the position of a lumped mass influences the average output power of the harvester under concurrent base excitation and galloping. In comparison with traditional hybrid energy harvesters, the impact of three factors—low airflow velocity, small base excitation amplitude, and low frequency—is examined for each case of lumped mass deployment. The findings reveal that optimal mass positioning markedly enhances the harvester’s average power output when there are low airflow velocities, small base excitation amplitudes, and low frequencies, constituting a novel contribution to the field. Through numerous numerical simulations, it is determined that the optimal position for deploying the lumped mass is approximately 60–70% along the length of the cantilever beam substrate.

Fracture toughness in SPCC/CFRP hybrid laminates: Mode I and mode II perspectives

Hybrid composites using adhesive joints are gaining popularity in various industries as their various material combinations can create certain advantages. This research focuses on examining the mode I and mode II fracture toughness characteristics of the combined laminate between Steel Plate Cold Rolled Commercial (SPCC) metal and Carbon Fiber Reinforced Polymer (CFRP) composite processed using adhesive bonding. SPCC/CFRP hybrid laminate composites were manufactured with a variety of manufacturing options (A, B, and C) to find the most optimal method using two types of epoxy and cyanoacrylate adhesives, with two different bonding processes: secondary bonding and co-bonding. Fracture toughness values were measured through the Double Cantilever Beam (DCB) test for mode I and the End Notched Flexure (ENF) test for mode II. The test results showed that epoxy adhesives in the SPCC/CFRP adhesive joints provided better fracture toughness performance, especially when combined with the co-bonding technique. Specimens from manufacturing option C showed the highest GIC and GIIC values of 83.05 and 254.94 J/m2, respectively. These values increased by 58.98 % and 80.48 % compared to manufacturing options A and B in Mode I. Additionally, the GIIC value for manufacturing option C increased by 78.00 % and 66.76 % compared to manufacturing options A and B. The SPCC/CFRP hybrid laminates showed adhesive failure on the SPCC surface when using epoxy adhesive, whereas adhesive failure occurred on the CFRP surface with cyanoacrylate adhesive for the different manufacturing options.

Characterization of the mechanical properties of a polyurethane adhesive: Tensile strength and Fracture tests

The aim of this paper is to study the response of a polyurethane-based adhesive when subjected to different loading conditions. To achieve this, double cantilever beam (DCB) and dogbone specimens were manufactured, and tensile strength, fracture and fatigue fracture tests were performed. The results of the tensile tests revealed a tensile strength of 14.5 MPa and an elastic modulus of 0.27 GPa for the studied polyurethane adhesive. The analysis of the fatigue tests showed that fatigue crack growth starts to stabilize after 20% of the test is done, and that the adhesive used is more suitable for static loading conditions than for cyclic loading conditions, since the value of the average , 0.2 N/mm, is much lower than the value of the average , 4 N/mm.

Whale Optimization Algorithm for structural damage detection, localization, and quantification

This paper introduces an approach for vibration-based damage detection based on matrix updating aided by the Whale Optimization Algorithm (WOA). The methodology uses the Data-driven Stochastic Subspace Identification (SSI-DATA) technique to determine the modal parameters, which are compared with those obtained from both healthy and damaged conditions of the structure. The methodology’s efficacy is assessed through three distinct steps: numerical simulations, experimental data, and real-world data from a bridge. Initially, numerical analyses are conducted on a cantilever beam, a 10-bar truss, and a Warren truss subjected to environmental vibrations with varying damage cases and noise levels. Subsequently, experimental validations are performed on a test system and in the Z24 Bridge. Results from the computational simulations demonstrate the method’s promise to identify, locate, and quantify single and multiple damage cases, even amidst signal noise, variations in the first vibration mode as minimal as 0.015%, and complex structures with 54 elements. Moreover, the matrix updating method utilizing WOA showcased superior accuracy compared to existing techniques in the literature. In addition, the Z24 Bridge example validated the capability of the presented damage detection method to localize structural damage solely based on natural frequencies.

System Dynamics of the Water Droplet Impacting Flexible Cantilever Beams.

In this work, a water droplet impacting superhydrophobic flexible cantilever beams is systematically studied via experimental methods, aimed at recognizing the significance of the system dynamics that arises from the interplay between substrate oscillation and droplet impact. Influences of the substrate stiffness and the impact Weber number on the substrate oscillation and droplet impact dynamic are the focus particularly. For substrate oscillations, the beam deflection increases with the Weber number but decreases with the beam stiffness, while the oscillation period of the beam is not affected by the impact dynamic. For the droplet impact dynamic, the spreading dynamic is independent of beam oscillation, while the retraction dynamic is closely related to the surface elasticity. The effect of the cantilever beams on the droplet (i.e., promoting or inhibiting the rebound behavior) is dependent on the coupling movement of the water drop and the cantilever beam, which is varied by changing the stiffness of the cantilever beam. The findings of this work will provide a theoretical reference for the application of flexible substrates in the fields of anti-icing and self-cleaning.

Combining Magnetostriction with Variable Reluctance for Energy Harvesting at Low Frequency Vibrations

In this paper, we explore the benefits of using a magnetostrictive component in a variable reluctance energy harvester. The intrinsic magnetic field bias and the possibility to utilize magnetic force to achieve pre-stress leads to a synergetic combination between this type of energy harvester and magnetostriction. The proposed energy harvester system, to evaluate the concept, consists of a magnetostrictive cantilever beam with a cubic magnet as proof mass. Galfenol, Fe81.6Ga18.4, is used to implement magnetostriction. Variable reluctance is achieved by fixing the beam parallel to an iron core, with some margin to create an air gap between the tip magnet and core. The mechanical forces of the beam and the magnetic forces lead to a displaced equilibrium position of the beam and thus a pre-stress. Two configurations of the energy harvester were evaluated and compared. The initial configuration uses a simple beam of aluminum substrate and a layer of galfenol with an additional magnet fixing the beam to the core. The modified design reduces the magnetic field bias in the galfenol by replacing approximately half of the length of galfenol with aluminum and adds a layer of soft magnetic material above the galfenol to further reduce the magnetic field bias. The initial system was found to magnetically saturate the galfenol at equilibrium. This provided the opportunity to compare two equivalent systems, with and without a significant magnetostrictive effect on the output voltage. The resonance frequency tuning capability, from modifying the initial distance of the air gap, is shown to be maintained for the modified configuration (140 Hz/mm), while achieving RMS open-circuit coil voltages larger by a factor of two (2.4 V compared to 1.1 V). For a theoretically optimal load, the RMS power was simulated to be 5.1 mW. Given the size of the energy harvester (18.5 cm3) and the excitation acceleration (0.5 g), this results in a performance metric of 1.1 mW/cm3g2.