Cantilever Mode Research Articles

Computational homogenization for dynamic characterization of a square cellular honeycomb vibration energy harvester

The prevailing literature on homogenization of cellular structures mainly focuses on computing their effective properties, but only a few studies demonstrate their subsequent use in practical applications. Moreover, the emphasis is largely on static analysis, and dynamic studies are limited to free vibration analysis with no specific applications. Therefore, this research aims to address these gaps by assessing the effectiveness of finite element based homogenization approach in characterizing cellular vibration energy harvester. In particular, the study considers a square cellular structure in cantilever mode and demonstrates the dynamic characterization using the homogenization approach. The results from free, forced, and random vibration analysis show close conformance between cellular and homogenized models with a maximum error of less than 10%. Further, the homogenized model was used to characterize the electro-mechanical response of the square cellular vibration energy harvester, and the predicted voltages for the cellular and homogenized models were 11 V and 13.8 V, respectively, validating the accuracy of homogenized model. Also, the computational time is reduced by 50–75% when using the homogenized model, thereby providing a computationally efficient alternative to experimental and full-scale time intensive finite element simulations.

Efficacious constrained layer damping of carbon black‐reinforced nitrile butadiene rubber‐polyvinyl chloride blend vulcanizates: A comprehensive study

AbstractWe report efficacious vibration damping of carbon black reinforced nitrile butadiene rubber‐polyvinyl chloride blend (NVC) vulcanizates in a constrained layer damping (CLD) configuration. The objective is to compare numerical simulations using finite element method (FEM) and the widely used Ross‐Kerwin‐Ungar (RKU) model with the experimental results. NVC blend (50:50 by weight), was compounded with carbon black as reinforcing filler and vulcanized using a sulfur‐based curative system. Significant reinforcement and toughening were observed for the carbon black reinforced vulcanizates compared to the pristine blend. The viscoelastic properties of the vulcanizates were assessed using dynamic mechanical analysis (DMA), exploring their behavior concerning temperature variations and different frequencies to generate the Prony series coefficients for input in FEM analysis. Vibration damping experiments were conducted using the Oberst beam method in a single cantilever mode, with steel as the vibrating substrate, aluminum as the constraining layer, and the NVC vulcanizates as viscoelastic materials (VEM). Numerical simulations were performed using FEM to analyze mode shapes and frequency response function (FRF), and the RKU model was employed to quantify CLD system loss factors (SLF). The salient finding of this study was the observed SLF values in the range of 0.08–0.20 in the frequency regime of 200–2000 Hz. These values qualify the studied material as effective VEMs for CLD treatment of structural vibrations. This study supports design optimization efforts in a wide range of engineering applications where effective vibration damping is critical.Highlights Enhancement of NVC blend properties through carbon black reinforcement. Detailed analysis of viscoelastic behavior using DMA. Validation of findings through experimental modal analysis. Promising results in terms of system loss factors for CLD applications.

Enhanced feedback performance in off-resonance AFM modes through pulse train sampling.

Dynamic atomic force microscopy (AFM) modes that operate at frequencies far away from the resonance frequency of the cantilever (off-resonance tapping (ORT) modes) can provide high-resolution imaging of a wide range of sample types, including biological samples, soft polymers, and hard materials. These modes offer precise and stable control of vertical force, as well as reduced lateral force. Simultaneously, they enable mechanical property mapping of the sample. However, ORT modes have an intrinsic drawback: a low scan speed due to the limited ORT rate, generally in the low-kilohertz range. Here, we analyze how the conventional ORT control method limits the topography tracking quality and hence the imaging speed. The closed-loop controller in conventional ORT restricts the sampling rate to the ORT rate and introduces a large closed-loop delay. We present an alternative ORT control method in which the closed-loop controller samples and tracks the vertical force changes during a defined time window of the tip-sample interaction. Through this, we use multiple samples in the proximity of the maximum force for the feedback loop, rather than only one sample at the maximum force instant. This method leads to improved topography tracking at a given ORT rate and therefore enables higher scan rates while refining the mechanical property mapping.

Systematic analysis of fractured specimens of composite laminates: Different perspectives between tensile, flexural, Mode I, and Mode II test

Novel hybrid laminates consisting of carbon fiber-reinforced polymers and steel plate cold commercial (CFRP-SPCC) have been successfully manufactured and tested in the present study. Four different tests have been made i.e., tensile test, flexural test, double cantilever beam (DCB) or Mode I test, and end notched flexure (ENF) or Mode II test. After being tested, these samples need to be evaluated. Hence, an inappropriate evaluation step while identifying the cause of failure of the failed specimens can create a false conclusion. The present study aims to systematically evaluate the fractured specimens of CFRP-SPCC in different tests (tensile, flexural, DCB, and ENF test) using different tools, i.e., pocket camera, digital microscope, light microscope, and Scanning Electron Microscopy (SEM). The results showed, in terms of tensile, the highest strength occurred with 1475.4 MPa. In comparison, the highest flexural strength occurred with 1516.1 MPa, while DCB and ENF showed the highest values with 116.4 and 330 J/m2, respectively. Furthermore, the results showed that digital and light microscopes are satisfied to evaluate the specimen in tensile test. However, for the flexural test, ENF, and DCB test, besides the light microscope, further analysis using SEM-EDX is recommended to evaluate the specimen after failure.

Intermodal coupling spectroscopy of mechanical modes in microcantilevers.

Atomic force microscopy (AFM) is highly regarded as a lens peering into the next discoveries of nanotechnology. Fundamental research in atomic interactions, molecular reactions, and biological cell behaviour are key focal points, demanding a continuous increase in resolution and sensitivity. While renowned fields such as optomechanics have marched towards outstanding signal-to-noise ratios, these improvements have yet to find a practical way to AFM. As a solution, we investigate here a mechanism in which individual mechanical eigenmodes of a microcantilever couple to one another, mimicking optomechanical techniques to reduce thermal noise. We have a look at the most commonly used modes in AFM, starting with the first two flexural modes of cantilevers and asses the impact of an amplified coupling between them. In the following, we expand our investigation to the sea of eigenmodes available in the same structure and find a maximum coupling of 9.38 × 103 Hz/nm between two torsional modes. Through such findings we aim to expand the field of multifrequency AFM with innumerable possibilities leading to improved signal-to-noise ratios, all accessible with no additional hardware.

Analysis of influence of deformation modes of retaining structures on deformation of a side shield tunnel

In the process of foundation pit excavation, different retaining structures and support stiffness may lead to different deformation modes of retaining structures. The soil displacement cause by the deformation of the retaining structure is calculated by the virtual image technique. Meanwhile, the collaborative deformation model for rotation and dislocation is introduced to analyze the tunnel longitudinal deformation caused by different deformation modes as well as the tunnel maximum displacement equivalent field, and two case verifications are carried out. The study shows that there is a large difference in the size and distribution law of the soil displacement field caused by different enclosure structure deformation modes. The horizontal displacement of soil caused by the cantilever type always shows a "cantilever type" curve with increasing horizontal distance from the enclosure structure, while the composite type, inner convex type and kicker type develop from the "bow" to the "cantilever type" curve. The vertical displacement field of the soil is in the shape of a "spoon" and the soil exhibits a certain bulge deformation below the critical depth. The critical depths of the composite type and inner convex type are similar, while the kick type is the largest and the cantilever type is the smallest. The influence area of the maximum horizontal displacement of the tunnel outside the pit of the inner convex type and the composite type is basically the same. The influence area of the cantilever mode is the smallest, while the influence depth of the kick-in mode is higher than that of the other three deformation modes.

Prediction of bonded asymmetric metallic cross-tension and single lap shear joints using finite element model with material-level adhesive properties and cohesive zone method

Predictive finite element (FE) models of adhesive joints are needed to enable the design and evaluation of adhesively joined structures, particularly large-scale structures that may be costly to assess experimentally. Although models calibrated to coupon-level tests have provided an important first-step, models based on material-level characterization are needed to enable joint assessment in complex modes of loading. In the present study, a structural epoxy adhesive was characterized using rigid double cantilever (Mode I) and bonded shear (Mode II) specimens to provide material-level input properties. Three single-lap shear (SLJ) and seven cross-tension (CT) specimen configurations were fabricated with aluminum and steel sheet materials. The specimens included symmetrical (the same adherend material and thickness) and asymmetrical (dissimilar adherend material or unequal thickness) configurations, with three loading angles (0°, 45°, 90°) for the CT specimens. Finite element models of the SLJ and CT specimens were developed using Cohesive Zone Modeling for the adhesive, with properties determined from the Mode I and Mode II characterization tests. The FE models of the SLJ and CT test specimens predicted the peak load within an average difference of 2%–19%. The joint strength varied between different test configurations, owing to adherend deformation, load eccentricity and mixed-mode loading. Importantly, the model parameters were not calibrated to the SLJ and CT tests. The FE models were able to predict joint response for varying test specimen geometry, adherend thickness, adherend material, and modes of loading.

Dynamic mechanical thermal analysis of unaged and hygrothermally aged discontinuous Bouligand structured CFRP composites

A dynamic mechanical thermal analyser operating in the single cantilever mode was used to examine the dynamic mechanical properties of unaged and hygrothermally aged discontinuous asymmetric helicoidal (Bouligand) carbon fibre reinforced plastic (CFRP) composites as a function of fibre architecture. The discontinuous Bouligand was manufactured using two major pitch angles as independent variables: 90° and 120° and from each major pitch angle, minor interply pitch angles were used as independent variables ranging 5°–25°. The composites were tested as either dry unaged specimens or following hygrothermal ageing in seawater at the constant temperatures of 40 °C and 60 °C for over 2000 h. We find that the viscoelastic properties E′ and E″ are adversely affected by both hygrothermal aging and the minor pitch angle, but not the major pitch angle. Higher hygrothermal ageing temperatures and increasing minor pitch angles are found to decrease the energy absorption and dissipation capacities of discontinuous Bouligand structured CFRP composites. The tan-δ curves also indicate that hygrothermal ageing increases the heterogeneity of discontinuous Bouligand structured composites, with separate viscoelastic phases and glass transition temperatures.

Ballistic dynamics of flexural thermal movements in a nanomembrane revealed with subatomic resolution.

Flexural oscillations of freestanding films, nanomembranes, and nanowires are attracting growing attention for their importance to the fundamental physical and optical properties and device applications of two-dimensional and nanostructured (meta)materials. Here, we report on the observation of short–time scale ballistic motion in the flexural mode of a nanomembrane cantilever, driven by thermal fluctuation of flexural phonons, including measurements of ballistic velocities and displacements performed with subatomic resolution, using a free electron edge-scattering technique. Within intervals <10 μs, the membrane moves ballistically at a constant velocity, typically ~300 μm/s, while Brownian-like dynamics emerge for longer observation periods. Access to the ballistic regime provides verification of the equipartition theorem and Maxwell-Boltzmann statistics for flexural modes and can be used in fast thermometry and mass sensing during atomic absorption/desorption processes on the membrane.

Parametric Study of different Fiber Parameters and their Influence on Acoustics and Vibration Behavior of Jute Fiber/Polyester resin Composites

ABSTRACT Short natural fiber–based composites are becoming a viable alternative to short E-glass fiber–reinforced composites in a variety of applications, due to their better damping and sound absorption capabilities. Also, quasi-isotropic properties can be obtained with randomly oriented short natural fibers. However, identifying the optimum fiber length and weight content are important to obtain better mechanical properties. The effect of fiber parameters on acoustic and vibration properties of jute/polyester composites was investigated in this study. Compression molding was used to fabricate composite specimens with different fiber lengths (10, 15, 20, and 25 mm) and fiber loadings (5, 10, 15, and 20 wt%). Further, sound absorption and damping properties of composites were studied using the impedance tube method and a free vibration test in cantilever mode. The damping property increases with increasing fiber loading and decreases with increasing fiber length, according to the findings. The highest natural frequency was found with a fiber length of 5 mm and a fiber loading of 25%, but larger fibers resulted in improved sound absorption. The findings suggest that jute/polyester composites could be a more cost-effective, practical, and environmentally superior and therefore, an alternative to E-glass/polyester composites, particularly in damping-sensitive applications.

Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation

In this paper, we establish the existence and multiplicity for periodic solutions of the nonlinear system associated with a tapping mode cantilever Atomic Force Microscope (AFM) with Lennard-Jones potential and an external harmonic excitation. The technique used to solve the nonlinear system is based in the classical nonlinear technique of lower and upper solutions in reverse order. Finally, we show some numerical simulations using the Poincaré map to present regions where the existence is guaranteed.

Triangular-Shaped 5-DOF Piezoelectric Robot for Optical Lens Positioning

The paper represents numerical and experimental investigations on a 5-DOF piezoelectric robot that can provide rotary and planar motions of the payload. The design of the robot is based on a single piezoelectric ring and a triangular-shaped passive layer made from stainless steel. Six semispherical contacts of alumina oxide were used as contact points for rotary and planar motions. Finally, the top electrode of the piezo ceramic ring was divided into six equal segments to control the 3-DOF angular and 2-DOF planar motions of the payload. Two harmonic signals of different frequencies are used to drive the piezoelectric robot. The robot operation is based on the excitation of the third radial vibration mode of the ring and the first bending mode of the trapezoidal-shaped cantilever. Motion control is performed by switching electric signals between the particular segments of the piezoelectric ring. A numerical investigation was performed to validate the operation principle of the robot and to analyze electrical and mechanical characteristics. Numerical investigations showed that the first bending mode of trapezoidal cantilevers and the third radial mode of the piezo ceramic ring were obtained at a frequency of 13.79 kHz and 95.75 kHz, respectively. Moreover, it was revealed that the coupling ratio between vibration amplitudes of passive and active segments is more than 4 times. The prototype of the piezoelectric robot was made and an experimental study was performed to validate the operating principle of the robot, as well as to investigate the dynamic characteristics. The investigation showed that the highest velocity of the planar motion is 22.3 mm/s while the maximum angular motion speed is 29.3 RPM when an excitation voltage of 200 Vp-p and payload of 25.1 g was applied.

Effect of magnetorheological elastomer thickness and magnetic flux on vibrational characteristics

The maximum vibration is achieved when the natural frequency of any vibrating device reaches its resonance value. In a conventional suspension system, springs are used as vibration absorber. Since the stiffness of the spring is constant and the natural frequency of the road surface could vary at some point, the natural frequency of the spring can become the same as the natural frequency of the road. This would lead to resonance, and the vibration would be maximum and hence discomfort for the passengers. There are many active vibration absorbers under testing and development to overcome this disadvantage. In this paper, one such alternate vibration absorber is studied. The vibration absorber analyzed here is a magnetorheological elastomer (MRE). Magnetorheological materials fall under the smart material category as they could exhibit different properties under different conditions. The MRE laminate containing silicone and carbonyl iron was prepared for 6, 8, and 10 mm in thickness and was cut to the required dimension. The vibration characteristics of the vibration absorber were analyzed with and without magnetic flux. Acceleration of the MRE laminate fixed in cantilever mode as a function of natural frequency for 6, 8, and 10 mm thick with and without magnetic flux. The natural frequency increases with increasing MRF composite thickness due to the increasing stiffness of the composite. With applying magnetic flux, the rise in natural frequency has increased for all thicknesses. It shows that the increase in natural frequency achieved by applying magnetic flux to a 10 mm thick laminate is greater. The natural frequency increases as the thickness increases for modes 1 and 2. The rise in natural frequency for mode 2 compared to mode 1 has increased for all thicknesses.

Experimental study on dynamic mechanical properties of arecanut husk fiber composite

Natural fibers gain utility value by being used as reinforcing materials in the production of lightweight and inexpensive composites. Natural fibers possess considerable mechanical properties and will replace the synthetic fiber used in applications of structural elements, such as construction materials, interior components, aerospace, automotive parts, and sports goods, packaging industries, and other industries. It is necessary to investigate the viscoelastic behavior of polymer composite over increasing temperature and frequency. The present investigation focuses on the dynamic behavior to evaluate the damping factor, elastic modulus and loss modulus of AHF reinforced epoxy composite using a DMA Q800 instrument in double cantilever mode at heating rate of 3 °C per minute over ramping temperature from 28 °C to 125 °C with multi-frequency ranging from 1 to 10 Hz. The dynamic characteristics of AHF reinforced epoxy composites are impacted by frequency and temperature. The modulus values increased as the loading frequency increased, and the modulus values decreased as the temperature increased. Glass transition temperature was increased from 84 °C for untreated AHF composites to 91 °C for treated AHF composites. Treated AHF composites show improved storage and loss modulus compared to untreated AHF composites because of 6 % KOH treatment of AHF.

Decoupling competing electromechanical mechanisms in dynamic atomic force microscopy

Electromechanical coupling is ubiquitous in nature and piezoresponse force microscopy (PFM) has emerged as a powerful tool to probe electromechanical coupling with nanometer resolution. Electrostatic interference, however, is inevitable in dynamic atomic force microscopy (AFM), making the analysis and interpretation of PFM data challenging, especially in a quantitative manner. In this work, we propose a decomposition principle to quantitatively decouple intrinsic electromechanical strain from extrinsic electrostatic interaction in PFM measurement, utilizing the first two vibrational modes of AFM cantilever for which piezoelectric strain and electrostatic force show different dependence. The cantilever dynamics involving both electromechanical couplings is simulated first by finite element method (FEM), validating our decomposition principle numerically. The method is then implemented using data-intensive bimodal sequential excitation (SE) PFM and applied to periodically poled lithium niobate (PPLN), demonstrating substantial electrostatic interference that overwhelms piezoelectric strain even in the strong ferroelectric PPLN. The decomposition not only reconstructs ferroelectric domain pattern consistent with theoretical expectation, but also recovers piezoelectric coefficient accurately regardless of sample voltage applied, confirming the reliability of the method. The applicability of the decomposition in different materials is also demonstrated via PMN-PT crystal.

Fatigue tests of superelastic NiTi wires: an analysis using factorial design in single cantilever bending

This paper investigates the fatigue behavior of superelastic NiTi shape memory alloy thin wires with circular and rectangular cross-sections under single cantilever bending mode. A dynamic mechanical analyzer operating in single cantilever mode is employed as a testing machine. The fatigue life of the wires was analyzed at different strain amplitudes and loading frequencies. The simultaneous influence of these parameters was assessed through a factorial design with replication. Circular wires have higher fatigue life compared to rectangular wires. Higher strain amplitudes decrease the fatigue life of both circular and rectangular cross-section wires. On the other hand, the loading frequency strongly affected the rectangular cross-section wire, while having a significantly weaker effect on the circular wire. The NiTi wires showed fatigue lives between 103 and 105 cycles in the evaluated range of strain amplitude, which falls within the fatigue life observed for shape memory alloy (SMA) wires under similar loading conditions. Furthermore, the factorial design proved to be a valuable tool in the study of fatigue life of NiTi SMA, especially for the visualization and interpretation of the effect of the chosen variables.

Damping characteristics of pure aluminum: A comparison of microwave and conventional sintering

The current research focuses on how heating mode in powder metallurgy affects the damping properties of pure aluminum. The aluminum powder was compacted in a hydraulic press measuring 40 x 12 x 1.5mm3 and heated in a muffle furnace (conventional) and a microwave sintering furnace. The damping measurements were conducted on the samples using a dynamic mechanical analyzer under dual cantilever mode at various vibrating frequencies of 0.1, 1 and 10Hz from room temperature (RT) to 150°C at constant strain. Results demonstrated that the microwave sintered samples exhibit high storage modulus and high damping capacities compared to conventional sintered samples. The mechanisms that support this behavior are investigated and presented.

Dynamic mechanical analysis of graphene and nano silica reinforced hybrid epoxy composites under dual cantilever mode

This paper presents Dynamic mechanical behaviour of polymer Nano composites reinforced with various weight percentages of polymer and Nano particles and effect of Nano particles with polymer. The Graphene and Nano silica were used as fillers with epoxy resin. The Nano composite plates were prepared using cold compression moulding technique. Finally, the prepared composite plates were sized in laser cutting according to ASTM standards and subjected to DMA test. A series of dynamic mechanical tests were performed for prepared composites over a range of testing temperatures. Test frequency was kept constant. The dynamic mechanical properties of prepared Nano composites were studied by recording storage modulus, loss modulus, tan δ and glass transition temperature (Tg). It was found that the storage modulus (E’) recorded was decreasing with increasing temperature. The loss modulus (E”) and damping peaks (Tan δ) values were found to be increased with increasing in temperature up to certain value and beyond certain temperature it was found to be decreased. Also, the loss modulus (E”) and damping peaks (Tan δ) values were found to be reduced with increasing reinforcements whereas Tg decreases as reinforcements increase.

Visualization of Subatomic Movements in Nanostructures.

Electron microscopy, scanning probe, and optical super-resolution imaging techniques with nanometric resolution are now routinely available but cannot capture the characteristically fast (MHz-GHz frequency) movements of micro-/nano-objects. Meanwhile, optical interferometric techniques can detect high-frequency picometric displacements but only with diffraction-limited lateral resolution. Here, we introduce a motion visualization technique, based on the spectrally resolved detection of secondary electron emission from moving objects, that combines picometric displacement sensitivity with the nanometric spatial (positional/imaging) resolution of electron microscopy. The sensitivity of the technique is quantitatively validated against the thermodynamically defined amplitude of a nanocantilever's Brownian motion. It is further demonstrated in visualizing externally driven modes of cantilever, nanomechanical photonic metamaterial, and MEMS device structures. With a noise floor reaching ∼1 pm/Hz1/2, it can provide for the study of oscillatory movements with subatomic amplitudes, presenting new opportunities for the interrogation of motion in functional structures across the materials, bio- and nanosciences.

An Investigation on the Flexural and Thermo-mechanical Properties of CaCO3/Epoxy Composites

Present work focused on the flexural and thermo-mechanical characteristics of epoxy based composites filled with 3 different calcium carbonate (CaCO3) concentrations: 1.5, 3 and 5 wt.%. Composite specimens were fabricated through conventional casting method and subjected to flexural test via 3 point bending fixture. Additionally, dynamic-mechanical analyzer (DMA) with single cantilever mode was used to reval the thermo-mechanical responses of samples. The findings showed that the filler concentration increase led to the increase of storage modulus (E') for all specimens while the glass transition temperature (Tg) slightly decreased for 1.5 wt. % CaCO3 filled epoxy composite. The 5 wt.% CaCO3 loaded composite showed maximum E' and Tg values with 10% and 1.5% improvement, respectively. Based on flexural test results it was surprisingly found that, 1.5% wt. CaCO3 addition attained the highest strength with almost 27% improvement among all samples. However, 5 wt.% CaCO3 introduced composites displayed the lowest mechanical performance due to the presence of agglomerates/tactoids, which was verified from SEM images as well.