Thin Cantilever Beam Research Articles

Large deformation theory of thin steel cantilever beams under free end load cases

Large deformation theory of thin steel cantilever beams under free end load cases

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.

Harmonic Response of a Highly Flexible Thin Long Cantilever Beam: A Semi-Analytical Approach in Time-Domain With ANCF Modeling and Experimental Validation

Abstract The main objective of this work is to use the time variational method (TVM), a semi-analytical approach to evaluate steady-state responses in the time-domain for absolute nodal coordinate formulation (ANCF) modeled systems. The gradient-deficient ANCF beam element's performance is demonstrated for a highly flexible cantilever beam under gravity and impulse loading, with comparisons to experiments. The damping behavior is compared for the Rayleigh proportional and the Navier–Stokes (NS) damping model for a gradient-deficient ANCF beam element. Classical finite element method (FEM) beam formulation's shortcomings in predicting large deflections of thin, flexible cantilever beams are highlighted. Unlike the harmonic balance method (HBM), TVM reduces the computational time for harmonic response evaluation compared to numerical integration techniques and handles nonlinear forces in the time-domain. The harmonic response is evaluated by exciting the cantilever beam in the linear region for both experiments and TVM computations.

Hydrodynamic forces in higher modes of a thin cantilever beam resonator

The hydrodynamic force in a thin uniform beam cantilever is essential quantity for designing a resonator. We obtained the hydrodynamic drag forces in a uniform cantilever vibrating at the first four transverse modes using a semi-analytical boundary element method (BEM) and finite element method (FEM) in ANSYS. The present three-dimensional (3D) BEM inertial and damping forces are compared with FEM over a frequency range with less than 9.5% deviation until frequency parameter of 100; thereafter, it deviates numerically due to neglecting the non-linear convective forces. Considering the hydrodynamic damping force, the quality factor is estimated for the first four transverse modes of a uniform cantilever beam. As a result, the present 3D BEM model behaves well at the first bending mode compared to FEM. We also study the effect of the aspect ratio (ratio of width to length) of the beam for all four modes. However, the first mode quality factor sufficiently correlates with the numerical value for all aspect ratios. For uniform beams operating with higher modes, the influence of nonlinear and resonance frequency by the numerical model is more pronounced at smaller lengths. Hence, the 3D BEM approach can estimate the hydrodynamic forces on cantilever-based resonators, for example, atomic force microscopy and biosensors.

Geometrically nonlinear analysis of functionally graded composite shells using MITC4 and MITC9 elements

In this paper, the geometrically nonlinear behaviors of functionally graded composite shells under large displacements and large rotations are analyzed. Instead of constructing conventional layer-wised models, equivalent single-layer composite shell elements based on general displacement fields are developed to model the inhomogeneity of composite materials. The mixed interpolation of tensorial components technique is used to eliminate membrane locking and shear locking phenomena. The assumed covariant strain fields are initially constructed before being used to evaluate the second Piola–Kirchhoff stress and construct stiffness matrices in local Cartesian coordinates. The standard full Newton–Raphson method is utilized to solve a system of nonlinear equations. Geometrically nonlinear analyses are performed on different thin-walled composite structures including thin cantilever beams, slit annular plates, pinched cylindrical shells, and hemispherical shells. Obtained results demonstrate good convergence characteristics and modeling capability of the developed quadrilateral composite shell elements in analyzing thin-walled composite structures.

Non-linear finite-amplitude oscillations of the large beam arrays oscillating in viscous fluids

Over the past decade, several studies have been conducted on a single and multiple oscillating thin cantilever beams in an unbounded viscous fluid. With an increase in the applications of large array oscillators in a fluid environment for fields like medicine, biology, and energy harvesting devices, it is crucial to understand the nature of the surrounding fluid dynamics. In this present study, we perform a two-dimensional computational fluid dynamics (CFD) analysis of an array of beams oscillating in an unbounded viscous fluid. The two-dimensional Navier Stokes and continuity equations are solved to investigate the hydrodynamic forces exerted on the array members from interaction with the fluid environment. A complex hydrodynamic function is proposed here to represent the distributed hydrodynamic loading experienced by the oscillating beams. Results suggest that there is an increase in viscous damping with an increase in the size of the array. In addition, the nonlinearities become dominant when an array of beams is subjected to large amplitude oscillations. The number of beams in an array determines the overall hydrodynamics and the array effect. CFD analysis can predict the non-linearities unlike boundary integral method (BIM) approach, which is limited for low amplitudes. The results from the full Navier–Stokes simulations compared favorably with results using the BIM for the time-harmonic linearized Stokes equations.

Analytical Modeling of a Soft Pneu-Net Actuator Subjected to Planar Tip Contact

Soft actuators are compliant structures that are generally made of elastomers and generates large deformation. The behavior of these structures cannot be estimated accurately using infinitesimal strain theories. The objective of soft robotics applications is the controlled large deformation of these structures. In this article, we propose an analytical model for a pneu-net soft actuator. The model is based on the Euler–Bernoulli finite strain hyperelastic thin cantilever beam theory. The deformation of the air chambers is modeled using finite strain membrane theory. The analytical model is developed for two different states of the actuator: 1) free space; and 2) when the actuator was subjected to tip contact. The proposed theoretical model predicts the deformation and force characteristics of the actuator for the grasping state. The theoretical formulation of the developed model is different from previously developed infinitesimal strain models for the actuator, as it considers the axial stretch and forces applied to the actuator. In addition, it can be theoretically implemented on similar structured actuators for various applications. The theoretically calculated deformation and force characteristics of different actuators are compared with the finite element (FE) model and experimental characteristics. The results suggest that the proposed model can predict the actuator deformation and force characteristics as accurately as the FE model, but the computation time of the proposed model is less than 1% that of the FE model. The proposed model is further implemented on a three-finger gripper to predict the air pressure required for a stable grasp of different objects and is validated experimentally.

Thin-Film PZT-Based Multi-Channel Acoustic MEMS Transducer for Cochlear Implant Applications

This paper presents a multi-channel acoustic transducer that works within the audible frequency range (250-5500 Hz) and mimics the operation of the cochlea by filtering incoming sound. The transducer is composed of eight thin film piezoelectric cantilever beams with different resonance frequencies. The transducer is well suited to be implanted in middle ear cavity with an active volume of 5 mm <inline-formula> <tex-math notation="LaTeX">$\times5$ </tex-math></inline-formula> mm <inline-formula> <tex-math notation="LaTeX">$\times0.62$ </tex-math></inline-formula> mm and mass of 4.8 mg. Resonance frequencies and piezoelectric outputs of the beams are modeled with Finite Element Method (FEM). Vibration experiments showed that the transducer is capable of generating up to 139.36 mV<inline-formula> <tex-math notation="LaTeX">$_{{\mathrm {pp}}}$ </tex-math></inline-formula> under 0.1 g excitation. Test results are consistent with the FEM model on frequency (97&#x0025;) and output voltage (89&#x0025;) values. Device was further tested with acoustic excitation on an artificial tympanic membrane and flexible substrate. Under acoustic excitation, 50.7 mV<inline-formula> <tex-math notation="LaTeX">$_{{\mathrm {pp}}}$ </tex-math></inline-formula> output voltage generated under 100 dB Sound Pressure Level (SPL). Output voltages observed in acoustical and mechanical characterizations are the highest values reported to the best of our knowledge. Finally, to assess the feasibility of the transducer in daily sound levels, it was excited with a speech sample and output signal was recovered. Time-domain waveforms of the recorded and recovered signals showed close patterns.

Экспериментальное и аналитическое исследование геометрически-нелинейного изгиба консоли под действием распределенной нагрузки гравитационного типа

This paper describes an approximate analytical solution for the geometrically nonlinear bending of a thin elastic cantilever beam under a uniformly distributed gravity load. The solution is based on the linearized Euler-Bernoulli equation of mechanics of materials. Traditionally, such a linear approach is used for small (geometrically linear) deflections. The authors have modified the original equation with an arc-length preservation condition. The modified solution allows one to obtain bending shapes, deflection, and axial displacement in the range of loads corresponding to geometrically nonlinear bending of a beam (large deflections). An experimental study is conducted to verify the proposed solution. A thin steel band bent by gravity is used as a sample. Changes in the length of the bent sample part allow one to obtain various dimensionless load parameters. The deflections and axial displacements averaged on experimental statistics are determined. Bending shapes are obtained by the least square method of 5th order. Experimental and theoretical data are shown to be in good agreement. This fact confirms that the approximate analytical solution can be applied to solve large deflection problems in a wider range of loads than normally considered in the original linear theory.

A parametric study of the effect of self-oscillating trailing-edge flaplets on aerofoil self-noise

This paper presents an acoustic study of a standard NACA 0012 aerofoil with additional self-oscillating passive flaplets deployed from the trailing edge for self-noise reduction, putting special emphasis on the potential reduction of tonal noise generated by the periodic shedding of vortices from the trailing edge. The flaplets protruding out of the trailing edge act as rectangular thin cantilever beams exited by the surrounding flow to oscillate in their dominant flexural bending mode. The noise attenuation performance is studied for different deployment length, width and inter-spacing to find the most dominant contributions at chord based Reynolds numbers Rec from 100,000 to 900,000 and three geometric angles of attack αg=0°,10° and 15°. It was observed that all flaplet configurations oscillate and thereby reduce the tonal noise. The range of the highest noise reduction in the low frequency range scales with the Strouhal number based on chord length, whereby this range can be set specifically by how far the flaplets protrude out of the trailing edge. This determines the free vibrating length and therefore the natural frequency of the oscillators. Laser-based measurements of the flaplet oscillations confirm the occurrence of a lock-in mechanism observed in previous studies, which effectively describes the oscillating flaplets as pacemaker to keep the fundamental instabilities of the flow in their linear state. It is concluded that this contributes mainly to the tonal noise reduction while the more broadband noise reduction stems from the geometry of the flaplets acting as ‘slitted-serrations’. A larger width of the flaplets is most effective in the low-frequency range, while narrower flaplets are best addressing high-frequency noise components. The results further show that a smaller inter-spacing also benefits the noise reduction. The study paves the way for novel morphing techniques to target specific noise ranges during different flight manoeuvres.

Finite element analysis of beam with different loading condition

Abstract This examination researches the diversion and the stressful appropriation in a length, thin cantilever beam or bar light emission rectangular cross section segment made of straight versatile the material behavior and mechanical properties that are homogeneous mixture. The redirections of a beam are basically a modeling of 3D issue. A flexible extending one way is joined by a pressure in opposite ways. This undertaking, structural and dynamic examination is a cycle to decide the stress, strain and distortion. Shaking qualities of a formation or a machine segment while it is being planned. It was gotten a significant choice to give an accommodating commitment in understanding control of numerous vibration wonders which experienced practically speaking. In present work we thought about the pressure and regular recurrence for various material have identical cross sectional area of the shafts are T, I and C shaft. The beam is planned and dissected in ANSYS 14.0 software. The beam shaft is fixed toward one side is vibrate to acquire the normal recurrence, modal shape in addition to redirection by the various segments and equipment.

Stability of Thin Web Composite Cantilever Beams of Random Lamination

This study addresses the analytical treatment of a closed-form buckling equation for lateral-torsional stability of thin web composite cantilever beams under mid-height tip force. The beam is composed of random ply fiber orientations. Classical lamination theory is embedded into the Vlasov plate formulation to make up the framework of the analytical treatment. A closed-form solution is realized when an innovative dimensional reduction is extended to the 3D constitutive stiffness matrix. This was made possible through a two-step process in which the shear strain, lateral curvature, and twisting curvature are retained first. By condensing the shear strain variable, effective lateral, torsional, and coupling stiffness terms were formulated. Applying the equilibrium conditions in the deformed configuration, two differential equations are obtained in terms of the lateral curvature and twisting angle. Eliminating the lateral curvature, the twisting angle differential equation with nonconstant coefficients is generated. This equation is solved using a hybrid numerical-analytical approach yielding an analytical buckling expression. Finite element results are generated to verify the accuracy of the buckling load predictions indicating very good correlation with the buckling equation results regardless of the random lamination applied.

Modal characteristics of a cantilever beam with the free-end immersed in a magnetorheological fluid

This paper presents modal characteristics of a flexible cantilever beam with its free-end immersed in a magnetorheological (MR) fluid. Immersing the beam in MR fluid allows to change boundary conditions of the free-end by controlling the magnetic field intensity across MR fluid. Hence, the modal characteristics of the beam, such as natural frequency are varied as a function of the magnetic field applied to MR fluid domain. First, a thin cantilever beam was manufactured according to a design comprising a macro fiber composite (MFC) actuator for the beam excitation. Then, the dynamic responses of the beam were measured under two conditions: the free-end vibrating in air and the free-end immersed in MR fluid with different magnetic field intensities. The changes in the dynamic characteristics, such as resonance frequency, damping ratio, and resonant amplitude were evaluated and compared for various conditions. A significant reduction in the natural frequency was observed when the free-end of the beam was immersed in MR fluid and changed further when coil current was applied. In addition, the multiphysics simulation of the system was performed using finite element method. The numerical results of the dynamic response of the system showed good agreement with experimental results.

Non‐contact method based on intensity modulation of light for measurement of vibration of a thin cantilever beam

A non-contact method based on intensity modulation of light for measurement of vibration of a thin cantilever beam (CB) is presented in this study. The system consists of a laser source, a photo-detector-based signal conditioning and comparator circuit, an ATmega8 microcontroller based data acquisition system and an interface with personal computer. The sensing principle is based on modulation of intensity of light falling laterally on a vibrating CB. The photo-detector detects the modulated light and generates pulses, which is processed by signal conditioning and comparator circuit. The output of the comparator consists of alternative high and low transistor–transistor logic pulses, interfaced to two pins of the microcontroller simultaneously; one to external event counter and the other to input wave capture. The microcontroller is used to measure the frequency, width of high and low pulses. The system is calibrated using a Tektronix AFG3251C Arbitrary Function Generator. The % error in measurement of width of pulses is found to be within the range +0.12 to −0.41%, whereas 0% measurement error is observed in the measurement of frequency. Experimental results obtained under free vibration tests of two samples of thin CB of 0.4 and 0.5 mm thickness are also presented.

A Hybrid Stress Plane Element with Strain Field

In this paper, a plane quadrilateral element with rotational degrees of freedom is developed. Present formulation is based on a hybrid functional with independent boundary displacement and internal optimum strain field. All the optimality constraints, including being rotational invariant, omitting the parasitic shear error and satisfying Fliepa’s pure bending test, are considered. Moreover, the static equilibrium equations are satisfied in this scheme. Authors’ element has only four nodes and twelve degrees of freedom. For the boundary displacement field, Alman’s second-order displacement function is employed. The validities of the proposed element are demonstrated by eleven numerical examples: thick curved beam, thin cantilever beam, Cooke’s skew beam, thin curved beam, cantilever beam with distortion parameter, high-order patch test, cantilever beam with five and four irregular mesh, Mc Neal’s thin cantilever beam and cantilever shear wall with and without openings. When utilizing the coarse and irregular meshes, numerical tests show the high accuracy, rapid convergence and robustness of the suggested element. Less sensitivity to distortion is another property of the new element.

Three-dimensional analysis of hydrodynamic forces and power dissipation in shape-morphing cantilevers oscillating in viscous fluids

In this paper, we investigate flexural vibrations of a thin sharp-edged cantilever beam submerged in a quiescent, Newtonian, incompressible, viscous fluid. We study the three-dimensional fluid–structure interaction problem in the presence of shape-morphing deformation of the beam cross section, imposed by specifying a periodic chordwise maximum curvature along the axis of the structure, coupled with the flexural motion of the beam occurring along a structural mode. This actuation strategy, resulting into anticlastic curvature for the beam, is investigated as a possible means to actively control fluid–structure interaction mechanisms by modifying the hydrodynamic interactions in the vicinity of the submerged structure. We focus on the linear vibration problem for the beam, whereby the fluid flow is well described by three-dimensional unsteady Stokes hydrodynamics. Using the hypothesis of imposed harmonic motion for the submerged structure, we solve the linear hydrodynamics problem in the frequency domain by employing a semianalytical method based on oscillating Stokeslets. The resulting integral equations are solved via a boundary element technique and our results are validated against findings from the literature. The efficacy of the proposed shape-morphing strategy on the propulsion performance is assessed by studying thrust production, lift forces, and hydrodynamic power dissipation for a range of prescribed dynamic and geometric conditions, including vibration frequency, amplitude of imposed chordwise curvature, and beam aspect ratio. Our results indicate that thrust forces and power dissipation can be simultaneously modulated via the shape-morphing strategy. We theoretically predict and numerically confirm the existence of extremal points that result into an optimal compromise between thrust forces and power dissipation. Such optimal solutions are of direct interest to the design of cantilever-based underwater biomimetic propulsion systems, where it is crucial to control and modulate oscillation quality factors, hydrodynamic forces, and power losses.

The vibrating piezoelectric cantilevered generator under vortex shedding excitation and voltage tests

A renewable electricity harvesting system consisting of a bluff body, a thin piezoelectric cantilever beam and a fixing base plate has been developed and attachable with running cars. The polymer cantilever beam with an optimum piezoelectric layer vibrates in a vortex street whose frequency is tuned to the natural frequency of the beam structure for maximum outputs. Computational fluid dynamic analyses were done to obtain the vortex shedding frequency of 15.7 Hz and to determine the efficient cross-sectional shape of bluff bodies in an air stream. The optimum shape of a piezoelectric material layer that is a small rectangle near a beam wall was obtained by the topology optimization method with frequency constraints. In addition, finite element analyses were applied for combined substrate and piezoelectric materials of harvesting beams in order to calculate their natural frequencies and voltage outputs generated from bending vibrations in an air flow. The PMN-PT harvesting polymer beams were fabricated and tested by a shaker and a wind tunnel (1.89 V) with a bluff body to validate the analytic results (2.11 V). Analytic and experimental results showed reasonably good agreement with approximately 10% error.

Measurement of mechanical properties using slender cantilever beams

The measurement of mechanical properties of materials only available in the form of thin sheets requires the use of load cells and displacement sensors of high sensitivity at low applied loads. These are available in testing platforms such as instrumented nano-indenters. In the current work, the elastic modulus and fracture toughness of thin cantilever beams of a representative brittle thin sheet material (300μm thick NiO/YSZ support for a solid oxide fuel cell) were measured using a micro-/nano-indenter. The Young’s modulus and KIC were determined to be 139±4GPa and 2.13±0.27MPam0.5 respectively using this method.

非整数階微分を用いた振動制御

Achieving active wave control is both an old and a new problem. A vibration suppression problem for a thin cantilevered beam is presented as an example for discussion. Results clarified that the active wave controller includes √s and √s terms. Those terms are realized as a 1/2-order derivative and 3/2-order derivative using fractional calculus. The active wave controller is realized as connected using fractional calculus, which is shown to be an important step for analysis. Results show that the control effect is extremely high when both a shear-force actuator and a bending-moment actuator are applied. However, the control effect is degraded considerably when only the bending-moment actuator is used because it is not called perfect active-wave-control anymore. As a subject for future work, the realization of the perfect active wave control supplemented with a shear-force actuator can be pointed out. A noncontact-type shear-force actuator using an electromagnet and so on will be required.

Three-dimensional piezoelectric vibration energy harvester using spiral-shaped beam with triple operating frequencies.

This work has demonstrated a novel piezoelectric energy harvester without a complex structure and appended component that is capable of scavenging vibration energy from arbitrary directions with multiple resonant frequencies. In this harvester, a spiral-shaped elastic thin beam instead of a traditional thin cantilever beam was adopted to absorb external vibration with arbitrary direction in three-dimensional (3D) spaces owing to its ability to bend flexibly and stretch along arbitrary direction. Furthermore, multiple modes in the elastic thin beam contribute to a possibility to widen the working bandwidth with multiple resonant frequencies. The experimental results show that the harvester was capable of scavenging the vibration energy in 3D arbitrary directions; they also exhibited triple power peaks at about 16 Hz, 21 Hz, and 28 Hz with the powers of 330 μW, 313 μW, and 6 μW, respectively. In addition, human walking and water wave energies were successfully converted into electricity, proving that our harvester was practical to scavenge the time-variant or multi-directional vibration energies in our daily life.