Double-clamped Beam Research Articles

Snap-through mechanism of a thin beam confined in a curved constraint

In this work, a novel snap-through mechanism of a thin beam confined in a curved constraint and driven by local loading curvature is investigated. The movable boundaries of the buckled thin beam enable it to output snap-through rotation at a lower energy input than the double-clamped beam structure. A theory is proposed to reveal the snap-through mechanism of the proposed structure based on the principle of minimum potential energy and saddle-node bifurcation, which uncovers the influences of loading positions, length ratio and constraint radius on the critical loading. Both theoretical and experimental results show that the large loading position and small constraint radius correspond to a large critical loading, while the length ratio hardly affects the critical loading. In addition, an experimental device is designed to output linear displacement based on the proposed snap-through mechanism. Due to lower energy input and snap-through response characteristics, the proposed bistable mechanism exhibits great prospects in energy harvesters, actuators, motors, pumps and robots.

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.

Stress Fields Distribution and Simulation in 3C-SiC Resonators

In this paper the stress field distribution in 3C-SiC (111) resonators has been studied by micro-Raman measurements and COMSOL simulations. The measurements show that the asymmetry of the anchor points configuration produce an asymmetry in the stress filed distribution. This behavior has been confirmed also by the simulations. Furthermore, from the simulations the importance of the reduction of the under etching of the anchor points of the resonators has also been observed. In fact the reduction of this under etch produces a decrease of the stress in the double clamped beams, a small reduction of the resonance frequency, and a large reduction of the Q-factor and then of the oscillation frequency stability of the resonators in closed-loop operation.

Fabrication of Wafer-Level Vacuum-Packaged 3C-SiC Resonant Microstructures Grown on <111> and <100> Silicon

In this work, the fabrication of wafer-level vacuum packaged 3C-SiC resonators obtained from layers grown on <100> and <111> silicon is reported. The resonant microstructures are double-clamped beams encapsulated by glass-silicon anodic bonding using titanium-based vacuum gettering. Open-loop resonance frequency measurements are performed on the vacuum-packaged devices showing Q-factor values up to 292,000 for <100> and 331,000 for <111> substrates, with a maximum vacuum level around 10-2 mbar inside the encapsulations with Ti getter.

Wavelet-based numerical investigation on damage localisation and quantification in beams using static deflections and mode shapes

In this paper discrete Wavelet-based analysis (DWT) was applied to recognise, localise and quantify simulated damages in beams. The damages were simulated by reducing the Young's modulus, whose value for the healthy beam is 210 GPa. Damage beams were stepped reduced at 5% from its original value – i.e. 210 GPa – up to 50%. Both analysis, static and modal, were performed through finite elements varying, whenever it is possible, boundary conditions – i.e. double clamped, simply supported or cantilever beams, the load type (concentrated or distributed) and the local of the load and damage application. Further, the Wavelet analysis was performed through Matlab® package and two different indexes were computed: d1index and d2index. The first one was only employed to recognise and localise the damaged element, whereas the second index was invoked to quantify the damage. As the main outcomes from this paper one can cite the successful localisation and quantification of the damage through the indexes. Also, it was worth to mention the robustness of proposed indexes (d1 and d2) which their effectiveness was tested facing several changes imposed to boundary conditions of the beams, load system and the damage severity.

Multi-scale design of composite material structures for maximizing fundamental natural frequency

This study deals with the topology optimization (TO) of linear elastic composite structures considering fundamental natural frequency maximization. The concept of functionally graded structures (FGS) is used for anisotropic composite material structure design to improve the structural dynamic performance. The rational approximation of material properties (RAMP) method was employed as an alternative to the solid isotropic material with penalization (SIMP) method to improve the convergence stability for eigen-frequency problem. In the SIMP method, the occurrence of local eigen-modes at low frequencies in the void region causes ill-convergence, whereas the RAMP method prevents local eigen-modes from occurring. The method of moving asymptotes is used as an optimizer. Numerical verification was performed for three structural types: cantilever beam, double-clamped beam, and four-pinned beam structure. In addition, for cantilever beam design, bi-objective optimization for maximizing fundamental natural frequency as well as minimizing structural compliance was performed using the adaptive weighting method that quantitatively reflects the designer's preference by adjusting the weight for each objective function at each iteration.

Damage detection in variable temperature conditions using artificial intelligence

When considering damage detection using the natural frequencies of structures, small frequency drops can indicate either the presence of cracks or a temperature change. This change can lead to additional stress affecting the modal parameters for specific structures, making it much harder to detect, locate, and evaluate damage accurately. The current research aims to describe a method for detecting transverse cracks in beams, considering temperature variations. The considered beam is fixed at both ends, thus inducing axial forces when the temperature is increased. The influence of temperature is considered using adjustment coefficients developed for each vibration mode. This coefficient can be used to accurately calculate the natural frequency for an intact or damaged beam. An analytical method for determining the natural frequencies caused by the changing temperature and the presence of a transverse crack is described and used to generate data for training a feedforward artificial neural network (ANN). The ANN’s capability of determining the position of transverse cracks in double-clamped beams subjected to small temperature changes is proven by creating numerical simulations with known crack positions and thermal conditions for testing the developed method.

Angular magnetic field dependence of a doubly clamped magnetoelectric resonator

Angular dependence of magnetic field response of fully suspended resonant microelectromechanical double-clamped magnetoelectric beams was investigated as the basis for a vector magnetometer utilizing the magnetically induced change in fundamental resonance frequency. Strain-coupled magnetostrictive iron cobalt (FeCo) and piezoelectric aluminum nitride layers together constitute a magnetoelectric heterostructure with a high magnetic field sensitivity of 70 Hz/mT along the beam axis and a transfer function of 47 V/T at 10 Hz. The fundamental frequency shift to an external magnetic field is found to be strongly anisotropic with a relative variation of more than 3% between perpendicular and parallel field orientations with respect to the long axis of the beam at a field of 100 mT. This design can form the basis for an on-chip high sensitivity vector magnetometer operating with ultra-low power when multiplexed with two or more resonators.

Correlation between Q-Factor and Residual Stress in Epitaxial 3C-SiC Double-Clamped Beam Resonators

In this work, we investigate the correlation between tensile residual stress and Q-factor of double-clamped beams fabricated on epitaxial 3C-SiC layers grown on both <100> and <111> silicon substrates, using a completely optical measurement setup to measure the Q-factor of the resonators and the residual stress of the layers by means of purposely designed micromachined test structures. From the measurements, a clear correlation appears between the residual stress of the SiC layer and the Q-factor of the resonators, with Q-factor values above half a million for resonators fabricated on <111> substrates, showing residual stress around 1 GPa.

Equilibrium and transient response of photo-actuated Liquid Crystal Elastomer beams

Light actuation is one of the preferred and advantageous approaches to remotely induce and control deformations in soft materials such as photoactive Liquid Crystal Elastomers (LCEs). Various experimental and numerical works have been carried out in the literature to study the actuation of photoactive LCE sheets under illumination. In this study, we have developed a reduced multi-physics model to predict the equilibrium and dynamic response of photoactive LCE beams under illumination. We test our model against an experiment in which a double-clamped thin nematic LCE beam is subjected to UV light, and the stress is generated in the beam due to induced contraction under illumination. Our numerical results demonstrate reasonable agreement with the experiment regarding stress evolution trend and saturation time. We also investigate the bending response of a photoactive LCE beam subjected to UV light. Based on our parameters, we observe that the nematic beam bends towards the light only due to the photochemical strain gradient along the thickness. Finally, to test our model in a dynamic situation, we perform the simulation for the self-oscillations of an LCE beam under illumination. We show that the alternate activation of the top and bottom surfaces of the LCE beam by uniform steady illumination can pump energy into the system, resulting in the phenomenon of self-oscillations.

Micro 3D Printing Elastomeric IP-PDMS Using Two-Photon Polymerisation: A Comparative Analysis of Mechanical and Feature Resolution Properties.

The mechanical properties of two-photon-polymerised (2PP) polymers are highly dependent on the employed printing parameters. In particular, the mechanical features of elastomeric polymers, such as IP-PDMS, are important for cell culture studies as they can influence cell mechanobiological responses. Herein, we employed optical-interferometer-based nanoindentation to characterise two-photon-polymerised structures manufactured with varying laser powers, scan speeds, slicing distances, and hatching distances. The minimum reported effective Young's modulus (YM) was 350 kPa, while the maximum one was 17.8 MPa. In addition, we showed that, on average, immersion in water lowered the YM by 5.4%, a very important point as in the context of cell biology applications, the material must be employed within an aqueous environment. We also developed a printing strategy and performed a scanning electron microscopy morphological characterisation to find the smallest achievable feature size and the maximum length of a double-clamped freestanding beam. The maximum reported length of a printed beam was 70 µm with a minimum width of 1.46 ± 0.11 µm and a thickness of 4.49 ± 0.05 µm. The minimum beam width of 1.03 ± 0.02 µm was achieved for a beam length of 50 µm with a height of 3.00 ± 0.06 µm. In conclusion, the reported investigation of micron-scale two-photon-polymerized 3D IP-PDMS structures featuring tuneable mechanical properties paves the way for the use of this material in several cell biology applications, ranging from fundamental mechanobiology to in vitro disease modelling to tissue engineering.

Study of the splicing/coupling influence of cabling to fibers test links measurements

Abstract This article has analyzed the splicing and coupling influence of cabling to fibers test links measurements. The simulative study for different free/forced vibration mechanics in MEMS is performed. Relative amplitude frequency plot for a cantilever beam, a double clamped beam (DCB), a cantilever beam with end mass, normal vibration of a clamped beam mass, a double clamped beam with axial force, normal vibration of a clamped beam mass are demonstrated by using MEMSolver simulation version 3.3. The frequency shift for DCB with axial force is clarified. The lowest modal frequencies of a square and round diaphragm are also reported. The lowest modal frequency of a bent beam suspension is simulated also. The dependence of mid-section of the folded beam on the resonance frequency and on the short leg of the serpentine beam are clarified. The displacement plot for a structure under free vibration with damping, the displacement plot for vibration under a step force with damping, amplitude frequency plot for vibration under harmonic force with damping and amplitude frequency plot for the vibration driven by the base excitation are also outlined in this work.

Simulative study on integrated optical multimode waveguides with guided beams based on the system standardization of elements

Abstract This study has outlined simulative study on integrated optical multimode waveguides with guided beams based on the system standardization of elements. Deflection of a cantilever are clarified with a point force at the free end, due to the distributed weight at the beam, with a mass at the free end, and at the free end under acceleration. The bending of a double clamped beam under its distributed weight, deflection with the central mass double clamped beam under its weight, the buckling of a double clamped beam due to a compressive stress, out of plane deflection (OPD) of a bent beam suspension, OPD of a folded beam suspension, and OPD of a serpentine beam suspension are also clarified and reviewed. Dependence of cross section of beam on torsion constant is outlined. The stiffness ratio of lateral to vertical motion of hammock suspension is also clarified. The design of a crab-leg suspension and the dependence of the stiffness on thigh section of the crab leg flexure and the design of a folded flexure suspension and the dependence of stiffness on ratio of column beam lengths are also reported.

A low-frequency vibration acceleration sensor based on a long-period fiber grating and a double-clamped beam

We have designed, fabricated and characterized a low-frequency vibration acceleration sensor. The sensor consists of a double-clamped beam and a long-period fiber grating (LPFG) that inscribed in a single mode fiber (SMF) by femtosecond laser. The LPFG was glued tightly to the beam top surface. Its transmission spectrum changes with beam bending, enabling vibration acceleration measurements. The experimental results display that the sensor has an accurate and steady frequency response over the frequency range of 1.5 ∼ 10 Hz with a maximum frequency response error of 4.4 %. The maximum measurable acceleration is 0.3 g, and the maximum acceleration sensitivity is 2.8 mW/g with a linearity greater than 99.6 %. The temperature drift of the sensor is less than 0.001 g/℃. The sensor has good immunity to electromagnetic interference and reliability.

Residual Stress Measurement by Raman on Surface-Micromachined Monocrystalline 3C-SiC on Silicon on insulator

In this work, we investigate, by μ-Raman spectroscopy the distribution of stress field on a micro-machined structures. They were realized on a 3C-SiC substrate, grown on a Silicon On Insulator (SOI) wafer, after lithography and etching processes. Various structures, such as strain gauge, single and double clamped beams, were analyzed, showing different stress distributions. All the structures show an intense variation of stress close to the undercut region.

A Low Frequency Fiber Vibration Acceleration Sensor Based on Long Period Fiber Grating and Double-Clamped Beam

A Low Frequency Fiber Vibration Acceleration Sensor Based on Long Period Fiber Grating and Double-Clamped Beam

Thermal tuning of mechanical nonlinearity in GaAs doubly-clamped MEMS beam resonators

We report the thermal tuning of the mechanical nonlinearity in GaAs double-clamped MEMS beam resonators for sensitive thermal sensing applications. We have estimated the mechanical nonlinearity in GaAs MEMS beam resonator by measuring its resonance frequency as a function of oscillation amplitude. The MEMS resonator shows a hardening nonlinearity with a small linear oscillation range of ∼30 nm. When electrical heat is applied to the MEMS beam, we have observed a significant reduction in the mechanical nonlinearity of MEMS resonators near the buckling point of the MEMS beam. The decrease in the mechanical nonlinearity originates from the bending of the MEMS beam, which gives a softening nonlinearity term and, hence, compensates the total nonlinearity. With the thermal tuning effect, MEMS resonator can maintain a very large quasi linear oscillation amplitude of ∼300 nm, which is ∼10 times larger than the linear oscillation range without the control of nonlinearity.

Measurement of Residual Stress and Young's Modulus on Micromachined Monocrystalline 3C-SiC Layers Grown on and Silicon.

3C-SiC is an emerging material for MEMS systems thanks to its outstanding mechanical properties (high Young’s modulus and low density) that allow the device to be operated for a given geometry at higher frequency. The mechanical properties of this material depend strongly on the material quality, the defect density, and the stress. For this reason, the use of SiC in Si-based microelectromechanical system (MEMS) fabrication techniques has been very limited. In this work, the complete characterization of Young’s modulus and residual stress of monocrystalline 3C-SiC layers with different doping types grown on <100> and <111> oriented silicon substrates is reported, using a combination of resonance frequency of double clamped beams and strain gauge. In this way, both the residual stress and the residual strain can be measured independently, and Young’s modulus can be obtained by Hooke’s law. From these measurements, it has been observed that Young’s modulus depends on the thickness of the layer, the orientation, the doping, and the stress. Very good values of Young’s modulus were obtained in this work, even for very thin layers (thinner than 1 μm), and this can give the opportunity to realize very sensitive strain sensors.

Vibration monitoring based on optical sensing of mechanical nonlinearities in glass suspended waveguides.

Vibration monitoring plays a key role in numerous applications, including machinery predictive maintenance, shock detection, space applications, packaging-integrity monitoring and mining. Here, we investigate mechanical nonlinearities inherently present in suspended glass waveguides as a means for optically retrieving key vibration pattern information. The principle is to use optical phase changes in a coherent light signal travelling through the suspended glass waveguide to measure both optical path elongation and stress build-up caused by a given vibration state. Due to the intrinsic non-linear mechanical properties of double-clamped beams, we show that this information not only offers a means for detecting excessive vibrations but also allows for identifying specific vibration patterns, such as positive or negative chirp, without the need for any additional signal processing. In addition, the manufacturing process based on femtosecond laser exposure and chemical etching makes this sensing principle not only simple, compact and robust to harsh environments but also scalable to a broad frequency range.

1:1 internal mode coupling strength in GaAs doubly-clamped MEMS beam resonators with linear and nonlinear oscillations

We have investigated the 1:1 internal mode coupling strength in a GaAs doubly-clamped MEMS beam resonator by thermally tuning the frequencies of two neighbored resonant modes. The anti-crossing of the resonant frequencies indicates that the two modes couple with each other, and the mode coupling strength was estimated by the splitting of the anti-crossed frequencies of the two modes. When the oscillation amplitudes were tuned from the weakly-driven linear regime to the strongly-driven nonlinear regime, we observed slightly increased frequency splitting, indicating that the nonlinear oscillation only makes a very small contribution to the mode coupling strength.