Cantilever Beam Configuration Research Articles

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.

Modeling and Design Parameter Optimization to Improve the Sensitivity of a Bimorph Polysilicon-Based MEMS Sensor for Helium Detection.

Helium is integral in several industries, including nuclear waste management and semiconductors. Thus, developing a sensing method for detecting helium is essential to ensure the proper operation of such facilities. Several approaches can be used for helium detection, including based on the high thermal conductivity of helium, which is several times higher than air. This work utilizes the high thermal conductivity of helium to design and analyze a bimorph MEMS sensor for helium sensing applications. COMSOL Multiphysics software (version 6.2) is used to carry out this investigation. The sensor is constructed from poly-silicon and SiO2 materials with a trenched cantilever beam configuration. The sensor is electrically heated, and its morphed displacement depends on the surrounding gas's composition, which decreases in the presence of helium. Several factors were investigated to probe their effect on the sensor's sensitivity to helium, including the thickness of the poly-silicon layer, the configuration of the trench, and the thickness and location of SiO2 layer. The simulations showed that the best performance, up to 2 ppm helium detection level, can be achieved with thinner beams and medium trench lengths.

On micropolar elastic foundations

The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar elasticity. Conversely, elastic foundation theory is widely employed in fracture mechanics and the analysis of delamination propagation in composite materials. This study aims to amalgamate these two frameworks, enhancing the elastic foundation theory to accommodate materials exhibiting micropolar behaviour. Specifically, we present a novel theory of elastic foundation for micropolar materials, employing stress potentials formulation and a unique normalisation approach. Closed-form solutions are derived for stress and couple stress reactions inherent in such materials, along with the associated restoring stiffness. The validity of the proposed theory is established through verification using the double cantilever beam configuration. Concluding our study, we elucidate the benefits and limitations of the developed theory by quantifying the derived parameters for materials known to exhibit micropolar behaviour. This integration of micropolar elasticity into the elastic foundation theory not only enhances our understanding of material responses but also provides a versatile framework for the analysis of heterogeneous materials in various engineering applications.

Introducing an innovative FRF-based method for identification of an adhesive joint characteristics

An energy harvesting system can be attached to the host structure using adhesive joint with viscoelastic behavior. Adhesive joints having nonlinear properties, significantly alter the dynamics of a piezoelectric energy harvesting system and, as a result, have the potential to dramatically alter the output voltage. In this paper, an innovative FRF-based method is introduced to identify adhesive joint characteristics of a piezoelectric energy harvester in cantilever beam configuration which is jointed to a base structure in root. To this end, a novel viscoelastic model is considered for the adhesive joint, which consists of two longitudinal and torsional springs and two longitudinal and torsional dashpots. Additionally, the system is analytically modeled using Euler-Bernoulli beam theory, strain rate damping and the piezoelectric constitutive relations. The adhesive joint characteristics are identified through Genetic Algorithm method employing experimental tests data and model updating. The identified nonlinear pre-strain-dependent characteristics verify both the proposed analytical model and the joint identification method. Furthermore, the effects of the adhesive joint's thickness and pre-strain loading on its characteristics are investigated.

Lengthwise Fracture Analysis of Inhomogeneous Viscoelastic Cantilever Beam Subjected to Sinusoidal Strains

This paper describes a research of lengthwise fracture in a viscoelastic inhomogeneous cantilever beam under strain that is a sinusoidal function of time. The beam mechanical behavior is investigated by a model having two linear springs and a linear dashpot. The beam material is continuously inhomogeneous along thickness. Therefore, the modules of elasticity of the springs and the coefficient of viscosity of the dashpot vary smoothly in the thickness direction. The compliance method is applied to derive the strain energy release rate (SERR) for the lengthwise crack in the beam structure. The integral J is applied for verification. The stress-strain-time dependence of the viscoelastic model is used for describing the behavior of the beam when obtaining solutions of the SERR and the J-integral. Solutions are derived for both positive and negative rotation angle of the lower crack arm end (when the angle is positive, the upper crack arm is load free, while at negative angle both crack arms are loaded). The effects of various factors including the sign of the angle of rotation on the SERR are analyzed.

Electro-mechanical behavior of multi-functional glass fiber composites under dynamic Mode-I fracture loading

An experimental study was performed to investigate damage sensing and fracture toughness of multifunctional conductive glass fiber composites under dynamic mode-I fracture loading. Carbon nanotubes (CNTs) were dispersed within the epoxy matrix using a shear mixing and sonicating process. An electrostatic wet flocking process was used to reinforce milled short PAN-based carbon fibers onto each of the layers of glass fiber fabric along the thickness direction in the composites. These layers of flocked fabric were stacked, and a vacuum infusion process was employed to fabricate the composites. The parametric study consisted of two carbon fiber lengths (80 μm and 150 μm) and two fiber densities (1000 fibers/mm2 and 2000 fibers/mm2) and was performed to investigate the damage sensing capabilities of a three-dimensional conductive network generated through CNTs and carbon fibers. A double cantilever beam (DCB) configuration was considered, and a modified Hopkinson pressure bar setup along with a high-speed camera was used to investigate dynamic fracture toughness of the composites. The piezo-resistance response of the composites during dynamic fracture was measured using a modified system of four probes. For comparison, composites were also characterized for fracture toughness and piezo-resistance under quasi-static fracture loading conditions. The addition of short, milled PAN-based carbon fibers significantly increased the fracture toughness of glass/epoxy composites. The piezo-resistance response of the composites was easily correlated with instances of sudden crack growth during static fracture loading.

Snap-through Crack Propagation in Architected Bonded Interfaces Analyzed Using a Mechanoluminescent SAO/E Coating.

We investigate the mechanics of crack propagation in architected adhesive joints whose adherends are inspired to the base plate of the barnacle Amphibalanus (=Balanus) amphitrite, and feature an array of buried hollow cylindrical channels located perpendicularly to the direction of crack growth. Selective laser sintering is used to obtain the adherends that are subsequently bonded in the double cantilever beam configuration to ascertain the mechanics of crack growth. Finite element (FE) simulations are deployed to determine the strain energy release rate (ERR) and to elucidate the salient features of the fracture process. It is shown that the channels induce a modulation of the ERR and enable a crack tip shielding mechanism. Besides, FE simulations based on a cohesive zone approach indicate the occurrence of crack pinning/depinning cycles that are validated via experiments. A highlight of the present study is the use of a mechanoluminescent (ML) coating to unravel the evolution of the transient stress field in the crack tip region. The coating comprises an optical epoxy resin loaded with doped strontium aluminate phosphors (SrAl2O4/Eu2+) and converts mechanical energy into light emission with intensity proportional to the magnitude of mechanical stress. By combining the ML emission patterns with the stress distribution obtained from FEA, we unveil interesting details of snap-through cracking in architected bio-inspired adhesive joints.

Experimental Detection of Nonlinear Dynamics Using a Laser Profilometer

This paper investigates a cantilever beam nonlinear dynamic behaviour, on which the nonlinearity is introduced with permanent magnet interactions or with a non-holonomic contact. The experimental time domain responses obtained from non-zero initial conditions are measured using a laser profilometer, conventionally adopted for product shape detections in online industrial applications. The Fourier transform, Continuous Wavelet transform, and Hilbert transform are used to investigate nonlinear phenomena in the frequency content, highlighting advantages and drawbacks of the three methods in catching instantaneous phenomena. Then, a Multi-Phi approach is proposed to describe the time evolution of nonlinear systems by means of a discrete number of linearised systems. Therefore, two linearised models have been developed and tuned to describe the dynamic behaviour of different Euler–Bernoulli cantilever beam configurations. The experimental data of nonlinear systems are compared with the corresponding ones of the linear system to evaluate the effects of introduced nonlinearities on the overall dynamic properties.

Fracture toughness determination and mechanism for mode-I interlaminar failure of 3D-printed carbon-Kevlar composites

Additive manufacturing for continuous fiber composite exhibits great potential for the fabrication of sophisticated structural components. Nevertheless, interlaminar characteristics of printed parts have remained an open research question. This study aims to evaluate the mode-I interlaminar fracture property of 3D-printed continuous fiber reinforced composites with different interlaminar interfaces adopting carbon and Kevlar fiber. Three different double cantilever beam (DCB) configurations are considered, including carbon/carbon, Kevlar/Kevlar and carbon/Kevlar hybrid interface. It is observed that the interlaminar failure of carbon fiber was seriously affected by the void defects caused by 3D-printed. It is further found that Kevlar fiber could greatly improve the interlaminar fracture toughness attributed to the better bonding of interlayers and the denser bridging fiber. Finally, a novel idea for the hybrid interface is provided based on the characterization study of the carbon-Kevlar composites.

Design of a composite sub-structural beam specimen for investigating tunneling cracks under cyclic loading

The design of a thin-walled composite beam is presented whose purpose is to facilitate the study of intra-laminar tunneling cracks at the sub-structural length-scale. The beam utilizes a variable thickness reinforcement in the longitudinal direction to develop a gauge zone of near-uniform strains when loaded in a cantilever beam configuration. The beam is manufactured from E-glass fibers and epoxy resin and is tested under static and cyclic multi-axial loading. The results presented include experimental strain measurements at the gauge zone, which agree with numerical strain predictions, and observations of the developed tunneling cracks.

Closed-form solution for interfacially cracked layered beams with bending-extension coupling and hygrothermal stresses

This paper investigates the problem of the mechanical behavior of an interfacially cracked layered beam with possible bending-extension coupling (BEC) and residual hygrothermal stresses (RHTS), as well as shear deformations and crack-root rotations. The paper presents a mechanical model of a beam that results by assembling two sublaminates by a semi-rigid interface. The beam is clamped at its one end and interfacially cracked and generally loaded at the other. First, the mathematical problem is formulated and analytically solved in terms of the internal forces, strains, displacements, and interfacial stresses. Novel closed-form expressions are derived regarding these quantities and thoroughly reported in tables. The proposed expressions stand out for their generality; they apply to beams with arbitrary layers of random thicknesses and materials and consider general loading, BEC, and RHTS. Next, we highlight some specific cases by appropriately reducing the general expressions. As an example, we investigate the mechanical responses of composite laminates with possible BEC and RHTS using the double cantilever beam configuration. Lastly, the paper discusses new ways to deepen our knowledge of additional aspects of the fracture response of interfacially cracked beams with BEC and RHTS.

Electrical Properties of Aluminum Nitride Thick Films Magnetron Sputtered on Aluminum Substrates.

The realization of a c-axis oriented aluminum nitride thick film on aluminum substrates is a promising step in the development of transducers for applications with a working temperature up to about 600 °C. The present paper deals with the realization of AlN thick films by means of reactive magnetron sputtering with a pulsed DC power supply, operating in continuous mode for 50 h. Two values (0.4 and 0.8) of nitrogen concentration were used; operative pressure and power were set at 0.3 Pa and 150 W, respectively. The thickness of the obtained aluminum nitride films on the aluminum substrate, assessed with a profilometer, varied from 20 to 30 µm. The preferential orientation of AlN crystals was verified by X-ray diffraction. Finally, as the main focus of the investigation, the films underwent electrical characterization by means of an LCR-meter used on a parallel plate capacitor set-up and a test system based on a cantilever beam configuration. AlN conductivity and ε33 permittivity were derived in the 100 Hz–300 kHz frequency range. Magnetron sputtering operation with nitrogen concentration equal to 0.4 resulted in the preferred operative condition, leading to a d31 piezoelectric coefficient, in magnitude, of 0.52 × 10−12 C/N.

An Atlas of Piezoelectric Energy Harvesters in Oceanic Applications.

Nowadays, a large number of sensors are employed in the oceans to collect data for further analysis, which leads to a large number of demands for battery elimination in electronics due to the size reduction, environmental issues, and its laborious, pricy, and time-consuming recharge or replacement. Numerous methods for direct energy harvesting have been developed to power these low-power consumption sensors. Among all the developed harvesters, piezoelectric energy harvesters offer the most promise for eliminating batteries from future devices. These devices do not require maintenance, and they have compact and simple structures that can be attached to low-power devices to directly generate high-density power. In the present study, an atlas of 85 designs of piezoelectric energy harvesters in oceanic applications that have recently been reported in the state-of-the-art is provided. The atlas categorizes these designs based on their configurations, including cantilever beam, diaphragm, stacked, and cymbal configurations, and provides insightful information on their material, coupling modes, location, and power range. A set of unified schematics are drawn to show their working principles in this atlas. Moreover, all the concepts in the atlas are critically discussed in the body of this review. Different aspects of oceanic piezoelectric energy harvesters are also discussed in detail to address the challenges in the field and identify the research gaps.

Online Frequency Estimation on a Building-like Structure Using a Nonlinear Flexible Dynamic Vibration Absorber

The online frequency estimation of forced harmonic vibrations on a building-like structure, using a nonlinear flexible vibration absorber in a cantilever beam configuration, is addressed in this article. Algebraic formulae to compute online the harmonic excitation frequency on the nonlinear vibrating mechanical system using solely available measurement signals of position, velocity, or acceleration are presented. Fast algebraic frequency estimation can, thus, be implemented to tune online a semi-active dynamic vibration absorber to obtain a high attenuation level of undesirable vibrations affecting the main mechanical system. A semi-active vibration absorber can be tuned for application where variations of the excitation frequency can be expected. Adaptive vibration absorption for forced harmonic vibration suppression for operational scenarios with variable excitation frequency can be then performed. Analytical, numerical, and experimental results to demonstrate the effectiveness and efficiency of the operating frequency estimation, as well as the acceptable attenuation level achieved by the tunable flexible vibration absorber, are presented. The algebraic parametric estimation approach can be extended to add capabilities of variable frequency vibration suppression for several configurations of dynamic vibration absorbers.

Enhancement of the adhesion energy between monolayer graphene and SiO2 by thermal annealing

Because graphene is placed on a rigid or flexible substrate for future applications such as transparent or flexible electronic devices, the interfacial characteristics between graphene and the underlying substrate are of great importance for developing mechanically and electrically reliable devices. In this work, the interaction strength of large-area monolayer graphene transferred on SiO2/Si was adjusted by thermal treatments, and its adhesion energy was measured by mode I fracture tests using a double cantilever beam (DCB) configuration with a laminated composite (Si/SiO2/graphene/epoxy/SiO2/Si). Mechanical delamination of monolayer graphene from SiO2 showed an adhesion energy of 1.5 ± 0.15 J/m2. It was found that thermal annealing of graphene on SiO2 at 300 and 450 °C increased the adhesion energy to 2.2 ± 0.20 and 4.6 ± 0.31 J/m2, respectively. Characterization of graphene on SiO2 using atomic force microscopy and Raman spectroscopy revealed that the enhanced adhesion energy was attributed to the improved conformal contacts of monolayer graphene with corrugated SiO2 surfaces.

Effect of thermal treatment on fracture behavior of solder joints at various strain rates: Comparison of cyclic and constant temperature

Fracture tests on Sn93Pb37 solder joints in a double cantilever beam (DCB) configuration were performed at two different strain rates of 10−5 and 0.03 s−1 under mode I loading conditions. In each case, the critical strain energy release rate for crack initiation, Jci, was obtained. Effects of storing specimens at a constant temperature of 75 °C and cyclic temperature varying between 32 and 75 °C were examined at these strain rates. In the strain rate of 0.03 s−1, storing samples in a constant or cyclic temperature caused the fracture energy to decrease significantly with respect to the specimens maintained in ambient temperature. The significant reduction in fracture energy by placing the samples at high temperatures in the intermediate strain rate was due to the considerable rise in IMC layer thickness. Also, in this strain rate, the decrease in fracture energy under the constant thermal condition was greater in comparison to the thermal cycling case. This behavior was attributed to microstructural differences in the solder layer of samples; in the specimens aged at a constant temperature of 75 °C, Cu6Sn5 and Cu3Sn phases were observed in the solder joint microstructure. No such phases formed in the samples experienced the thermal cyclic profile. In quasi-static loading conditions, however, the fracture energy in cyclic and constant thermal conditions was approximately equal with the fracture energy of the sample stored in ambient temperature. In both thermal conditions, fracture energy increased significantly by rising the strain rate from quasi-static (i.e. 10−5 s−1) to 0.03 s−1. Moreover, the influence of strain rate was greater in cyclic thermal condition compared to constant thermal condition.

Mode III numerical analysis of composite laminates with elastic couplings in split cantilever beam configuration

This paper presents numerical analysis of the mode III strain energy release rate (SERR, GIII) distributions along delamination front in carbon fiber reinforced plastic (CFRP) and hybrid fiber reinforced plastic (HFRP) laminates exhibiting elastic couplings. The beam models were analyzed by using the split cantilever beam (SCB) tests configuration. Influence of elastic coupling phenomenon on mode III SERR distributions was investigated numerically in Abaqus/CAE software environment by using the virtual crack closure technique (VCCT). In addition, two different boundary conditions (BCs) were considered. Results revealed, that critical strain energy release rates distributions obtained for bending-twisting (BT) and bending-extension (BE) elastically coupled laminates were found to be strongly irregular and skewed which is not desirable in the point of view of experimental determination of mode III fracture toughness. On the other hand, application of different materials compositions in the form of HFRP laminates slightly decreased negative effect of elastic couplings on mode III SERR widthwise distributions but this field have to be more developed and explored.

Fracture analysis of a nonhomogeneous beam with two concentric cylindrical longitudinal cracks

This paper is concerned with the analysis of the fracture behaviour of a nohomogeneous cantilever beam with two concentric longitudinal cracks. The beam has a circular cross-section with linearly varying radius along the beam length. Moreover, the beam exhibits continuously varying material inhomogeneity in the radial direction. The fracture is analyzed in terms of strain energy release rate assuming nonlinear mechanical behaviour of the material. For this purpose, solutions for the strain energy release rate are derived by considering the energy balance. Two cantilever beam configurations with different lengths of longitudinal cracks are analysed. Moreover, the two cracks are arranged arbitrarily in the radial direction. The longitudinal fracture behaviour of the beam is also analysed by considering the complementary strain energy for verification. The strain energy release rate solutions are used to investigate the influence of varying radius of the cross section along the length of the beam on the longitudinal fracture behaviour. The effects of crack lengths and the location of the two concentric cracks in the radial direction on fracture are also studied. The influences of the loading conditions of the beam and the inhomogeneity of the material in the radial direction on the fracture behaviour are also evaluated.

Mode-I interlaminar fracture behavior of laminated bamboo composites

Mode-I interlaminar fracture behavior of laminated bamboo composites was characterized by mechanical testing in a bonded double cantilever beam configuration. No obvious fiber bridging was observed during the test. At the front of crack tip, nonlinear response was relatively small and negligible. The failure mode of laminated bamboo composites was mainly governed by brittle fracture. Mode-I interlaminar fracture toughness ([Formula: see text]) calculated using the modified beam theory was 501.08 J/m2. Besides, numerical simulation combined with cohesive elements was used to simulate the mode-I interlaminar fracture behavior. A direct method for the determination of cohesive parameters without recourse to iterative fitting was presented in detail. The applicability and effectiveness of this method for interpretation of the fracture behavior of laminated bamboo composites were verified by comparing numerical predictions with experimental results.

A cohesive zone model to predict fatigue-driven delamination in composites

A cohesive zone model is proposed to analyse composite delamination propagation under high-cycle fatigue loading. A new method to compute the strain energy release rate at any point within the element fatigue life cycle range is presented. The proposed scheme is based on the J-integral method evaluated at an estimated position of the crack-tip within the element, instead of the element integration points. Furthermore, a new fatigue damage evolution law is proposed to account for the unwanted quasi-static damage during the element fatigue degradation process. The model prediction capabilities were verified against experimental data available in the literature and theoretical solutions using a double cantilever beam configuration for mode I loading, four-point end-notched flexure configuration for mode II loading, and mixed-mode bending configuration for mixed-mode loading. The simulations were performed at both constant and variable amplitude loading. The numerical predictions obtained using the proposed model correlated very well with literature’s experimental data.