Fixed-fixed Beam Research Articles

Innovative computational model for optimal deep coal mining under large-scale crustal stress conditions.

Understanding and controlling the ground stress in deep coalfield mining is crucial for ensuring mine safety and efficiency. This study aims to address two unresolved scientific issues in ground stress research: the selection of optimal excavation plans and the large-scale rapid acquisition of ground stress data. A novel computational model is proposed for key rock layer control under different crustal stress conditions. The model considers the complexity and uncertainty of ground stress distribution by simplifying the key rock strata into a fixed-fixed beam model and calculating their safety through mechanical methods. Introducing an innovative approach for acquiring large-scale stress fields using GPS data. By inverting large-scale strain fields in the coalfield area, combined with World Stress Map (WSM) and measured data, accurate stress fields are obtained. The proposed optimal excavation plan can be applied to various coalfield locations worldwide, providing a scientific basis for safe and efficient mining operations. Additionally, the innovative use of GPS data in obtaining large-scale stress fields offers a valuable tool for assessing ground stress variation.

Identification of excitation frequencies of a vibrating beam using Dynamic Mode Decomposition

Identifying modal parameters for the different vibrational conditions for any structure or machine is very important for its structural health monitoring. Researchers have proposed different methodologies to determine that structure’s excitation or natural frequency. In the initial design phase, researchers have to rely on building the FE model and then analyze its natural and excitation frequencies. However, for the complex structure, it is difficult to handle a huge dataset of the vibrational information of the mesh for multi-frequency excitations and it becomes computationally expensive to analyze the system’s performance. This work presents the data-driven technique called Dynamic Mode Decomposition (DMD) which addresses this problem by discovering the system’s dynamics using system’s high-dimensional spatiotemporal data. The present work studies the FE vibration of fixed-fixed beams with single and multi-frequency harmonic forcing functions with and without noise for real-time scenarios. Here, DMD is applied to the sequential spatiotemporal data of displacement of the vibrating beams, and dominant frequencies and corresponding mode shapes are identified to predict the actual time dynamics of the system under different conditions in simulation and experimental conditions. This study also involves the failure of the DMD to capture the periodic oscillation (standing wave) in the beam and proposes the application of the Hankel matrix (time-delay coordinate) to capture the actual dynamical parameters of the system. The resulting predicted frequencies match the actual excitation frequencies, and the accuracy is improved with a number of stackings of the given time series data through the Hankel matrix at different rank truncations.

High Isolation, Double-Clamped, Magnetoelectric Microelectromechanical Resonator Magnetometer.

Magnetoelectric (ME)-based magnetometers have garnered much attention as they boast ultra-low-power systems with a small form factor and limit of detection in the tens of picotesla. The highly sensitive and low-power electric readout from the ME sensor makes them attractive for near DC and low-frequency AC magnetic fields as platforms for continuous magnetic signature monitoring. Among multiple configurations of the current ME magnetic sensors, most rely on exploiting the mechanically resonant characteristics of a released ME microelectromechanical system (MEMS) in a heterostructure device. Through optimizing the resonant device configuration, we design and fabricate a fixed-fixed resonant beam structure with high isolation compared to previous designs operating at ~800 nW of power comprised of piezoelectric aluminum nitride (AlN) and magnetostrictive (Co1-xFex)-based thin films that are less susceptible to vibration while providing similar characteristics to ME-MEMS cantilever devices. In this new design of double-clamped magnetoelectric MEMS resonators, we have also utilized thin films of a new iron-cobalt-hafnium alloy (Fe0.5Co0.5)0.92Hf0.08 that provides a low-stress, high magnetostrictive material with an amorphous crystalline structure and ultra-low magnetocrystalline anisotropy. Together, the improvements of this sensor design yield a magnetic field sensitivity of 125 Hz/mT when released in a compressive state. The overall detection limit of these sensors using an electric field drive and readout are presented, and noise sources are discussed. Based on these results, design parameters for future ME MEMS field sensors are discussed.

A Gaussian multi-scale space difference method to multiple slight damage localization based on strain modes

PurposeIn structural health monitoring, localization of multiple slight damage without baseline data is significant and difficult. The purpose of this paper is to discuss these issues.Design/methodology/approachDamage in the structure causes singularities of displacement modes, which in turn reveals damage. Methods based on the displacement modes may fail to accurately locate the slight damage because the slight damage in engineering structure results in a relatively small variation of the displacement modes. In comparison with the displacement modes, the strain modes are more sensitive to the slight damage because the strain is the derivative of the displacement. As a result, the slight variation in displacement data will be magnified by the derivative, leading to a significant variation of the strain modes. A novel method based on strain modes is proposed for the purpose of accurately locating the multiple slight damage.FindingsIn the two bay beam and steel fixed-fixed beams, the numerical simulations and the experimental cases, respectively, illustrate that the proposed method can achieve more accurate localization in comparison with the one based on the displacement modes.Originality/valueThe paper offers a practical approach for more accurate localization of multiple slight damage without baseline data. And the robustness to measurement noise of the proposed method is evaluated for increasing levels of artificially added white Gaussian noise until its limit is reached, defining its range of practical applicability.

Establishment of theoretical models for beam structures with particle impact damper

Over the past few decades, research on impact dampers has grown significantly, leading to numerous analytical and experimental investigations in that field. Vibrations can harm industrial equipment and cause process errors. Particle impact damper has a significant impact on lowering vibration and has been broadly implemented in various engineering applications. This work deals with the theoretical modeling for cantilever beam and fixed-fixed beam attached with a cylindrical enclosure filled with particles. Transient and forced excitations are considered to trace the motion of the primary mass with respect to time. Also, theoretical modeling of particle arrangement in enclosure, condition for particles to detach from base or ceiling of enclosure, motion of particle after detachment from enclosure, and mechanism of collision and friction of particles are discussed and presented in detail. Theoretical models proposed in this study can be used to generate theoretical readings for practical engineering applications.

Mathematical validation of spring constant of a varying section fixed-fixed beam RF MEMS switch and effects of spring constant on the switching parameters

Mathematical validation of spring constant of a varying section fixed-fixed beam RF MEMS switch and effects of spring constant on the switching parameters

Analytical Study of Lateral Buckling of Pipelines with Initial Imperfection Based on Fixed-Fixed Beam Model

The beam analysis model and the initial imperfection are predominant factors in analyzing the lateral buckling behavior of submarine pipelines under high temperature. However, the existing beam models do not consider the inhibition provided by the virtual anchor point of the pipeline. In this study, a fixed-fixed beam model is introduced to simulate the lateral buckling response of a submarine pipeline. This model considers the suppression tension provided by the virtual anchor point during the pipeline feeding-in process, which better reduces the buckling response phenomenon of the pipeline. Based on the assumption of rigid-plastic pipe-soil interaction, the analytical solution of the buckling development of pipeline under full-contact repetitive cosine imperfection is derived. The effectiveness of the fixed-fixed model is verified by comparing with the analytical solutions in other literature. The influence of the imperfection model, the temperature difference, and the soil resistance on the pipeline buckling is investigated. Finally, the size effect of the pipeline on the effective axial force development is discussed. The results show that the pipeline undergoes stress vibration under tensile force, and the frequency and density of the pipeline stress vibration increase with the increase of the initial defect amplitude. Increasing the diameter–thick ratio will significantly increase the bending amplitude and bending stress of the pipeline. Attention should be paid to the fatigue damage caused by continuous stress mutations during pipeline buckling, which could further lead to the structural destruction of the pipeline.

Analisa Getaran Pada Balok Jepit Bebas dan Jepit-Jepit dengan Variasi Posisi Motor Penggetar

This study aims to determine the difference in vibration produced when the position of the vibration source is placed in a different position on the cantilever beam which is supported by fixed-fixed and free-fixed supports. This research used 6061 series aluminum beam with a size of 32 mm x 32 mm x 600 mm. Variations the placement of the exciter of fixed-fixed beams was in the 15 cm, 30 cm, and 45 cm positions, while the fixed-free beams was in the 10 cm, 20 cm, 30 cm, 40 cm, and 50 cm positions. The results of the research on fixed-fixed beams showed that the maximum displacement value was at a position of 30 cm with a value of 0.097 mm, the minimum displacement at 45 cm with a value of 0.04 mm. The maximum velocity value was at a position of 15 cm with a value of 0.653 cm/s, the minimum velocity was at a position of 45 cm with a value of 0.397 cm/s. The maximum acceleration value was at a position of 15 cm with a value of 12.16 m/s², the minimum acceleration was at a position of 45 cm with a value of 8.33 m/s². While the fixed-free beam showed that the maximum displacement value was at a position of 50 cm with a value of 0.197 mm, the minimum displacement at a position of 10 cm with a value of 0.097 mm. The maximum velocity value was at a position of 30 cm with a value of 1.138 cm/s, the minimum velocity at a position of 10 cm with a value of 0.670 cm/s. The maximum acceleration value was at a position of 30 cm with a value of 21,833 m/s², the minimum acceleration was at a position of 10 cm with a value of 9.95 m/s².Keywords: vibration, displacement, velocity, acceleration, aluminum

To investigate the electrical properties of boron nitride nanosheet under tensile loading effect

In the present work, an attempt is made to investigate the electrical properties of the boron nitride under the application of tensile load, theoretically. The tensile load is ranging from 0.8 nN to 44 nN to the boron nitride nano sheet. The boron nitride (BN) sheet is supported at its two ends with graphene substrate and hence considered a fixed-fixed beam. The size of the BN sheet is 500 nm × 100 nm. A constant temperature is considered for the present investigation. The results state that the surface density of the lattice cell has minimal changes under the application of load varying in the given range which results in the minimal variation in the charge carrier density under stretched condition. The stretching of the BN sheet results in the reduction of the energy band gap of the material from 5.2 eV to 1.16 eV.

The static and dynamic behavior of a simple parallel-plate capacitor with Casimir force

The static and dynamic behavior of a fixed-fixed beam under the effect of Casimir force is studied. Two different corrections are studied: the effect of real conductor (in contrast to the ideal conductor) on the Casimir force, and the effect of electrode roughness on the electric and Casimir forces. The bifurcation diagrams and the phase portraits are presented and compared. The chaotic behavior of the system is studied for the case a harmonic voltage is added to the dc voltage, and there is a damping force. It is shown that for autonomous systems (no ac voltage and no damping), the stable region is enlarged when real conductor corrections are applied, applying both the real conductor and roughness corrections shrinks the stable region (compared to applying only the real conductor corrections). Finally, the appearance of chaotic behavior is investigated and the threshold values of the control parameters are found, in the perturbative limit (small values of the harmonic and damping forces). The chaotic regions are compared for the flat ideal, flat real, and rough real cases.

Studying the Critical Buckling Load of FG Beam Using ANSYS

In this article, the critical buckling load of functionally graded beam is calculated using ANSYS APDL Software (version 17.2) under mechanical and thermal load. In mechanical load, the effects of length to thickness ratio, power law index and mode number on the non-dimension critical buckling load of fixed-fixed and fixed-free FG beam. The results show that the length to thickness ratio is not effect on the non-dimension critical buckling load while the power law index and mode number effect on the non-dimension critical buckling load. In thermal load, the critical buckling load for fixed-fixed and pinned-pinned FG beam depend on length to thickness ratio, power law index and mode number. The results show that the critical buckling load increases with decreasing length to thickness ratio.

Optimized vertical RF-MEMS switch design with a small actuation voltage

A vertical RF-MEMS (Radio Frequency Micro ElectroMechanical Switch) switch design is proposed in this work that features a shunt capacitive configuration and can operate at a very low actuation voltage. Besides operating on a low switching voltage, the switch behold a small value of insertion loss in Up (ON) state and offers a towering isolation factor in Down (OFF) state. A horizontal structure of bridge membrane is used in the proposed design and the switch function (with ON and OFF operating states) is provided by the vertical movement of this membrane structure that is controlled by the electrostatic actuation technique. The actuation pad is centrally fed by a Coplanar Waveguide structure. The switch performance has been analysed over a wide frequency range from 1 to 40 GHz. For obtaining a 1.5 μm vertical displacement of the bridge membrane, a sheer 3.0 Volts of pull-in voltage (VPI) is required. CoventorWare and HFSSv13 tools are used in this work for designing and analysing the proposed switch. The use of fixed-fixed flexure beam configuration is chosen for switch design. Simulation results showcase excellent RF characteristics with isolation factor of −47 dB (at 32.5 GHz) and insertion loss in range of −0.01 to −1.10 dB (for 1−40 GHz frequency).

Transverse Vibration Energy Harvesting of Double Elastic Steel

This study uses the piezoelectric technology to collect vibration energy from the fixed-fixed nonlinear elastic beams attached with the piezo-patch between the two ends. Both single elastic steel sheet (SESS) and double elastic steel sheet (DESS) systems are investigated and correlated. To simulate the power generation of the vibration energy harvester (VEH) of both the SESS and the DESS in different engineering elements, the simple harmonic external force generated by a shaker at the location of the piezo-patch is used as the source. With this, more vibration converted electric energy is derived from the transverse deformation and flapping from the DESS than the SESS beam. The equation of a nonlinear Euler–Bernoulli beam is coupled with the electric energy equation of the piezo-patch to simulate the SESS VEH system. The flapping force from the DESS VEH system can be considered the concentrated external load applied on the SESS beam model. The method of multiple scales (MOMS) is employed to analyze this nonlinear problem. The fixed points plots and the numerical results confirm this theory presented for the two beam systems, which can be used for evaluating similar engineering systems. Experiments are also performed in this study. The Taguchi method is used to analyze the optimum locations of the shaker and piezo-patch, as well as the confidence level of the factors. The method of nonlinear analysis presented in this study demonstrates its accuracy compared with the linear case. The transverse DESS VEH model proposed is proved to be feasible and more effective than the SESS system.

Modeling and optimization of an inertial triboelectric motion sensor

Abstract This paper aims to provide a better understanding of how the triboelectric effect could be utilized in the context of an inertial motion sensor. The device consists of a base-excited fixed-fixed beam carrying a middle mass that is brought into cyclic contact/separation with a dielectric mounted on the base. A theoretical model was developed encompassing both the electrical and mechanical phenomena. A low-cost device was designed and fabricated to experimentally validate the model. A parametric study was performed to distinguish the effects of the various device parameters. A hybrid Particle Swarm Optimization (PSO) and direct search technique was utilized for device improvement on some of the physical device parameters. The device was experimentally tested at input accelerations ranging from 0.4 g to 1.2 g and an objective function was formulated in terms of the output voltage density, i.e. peak output voltage per unit volume at different excitation frequencies for various design parameters. The usefulness and validity of the optimization techniques utilized was proved highlighting their possible usage in other applications based on the triboelectric effect.

Numerical investigation of water droplet impact on horizontal beams

Droplet impact on elastic beams is considered as a novel model of energy transfer which is a promising alternative in applications of energy harvesting. The transient impact process is dominated by the fluid–solid interaction and the capillary effect. The numerical model based on SPH method allows predicting the droplet dynamic behaviors due to super-hydrophobic (SH) surfaces. The predicted results are also compared with relevant experiments to verify the robustness and flexibility of the model. For fixed-fixed beams, typical regimes, namely spherical-shaped rebound, pancake-shaped rebound and splashing of droplet, are identified. The elasticity of beam causing the earlier lifting-off phenomenon of droplet is investigated in detail. By comparison, cantilever beams repel the droplet in a smoother way and large deformation of the beam is considered. The slipping-off phenomenon is expected to occur under specific conditions on soft cantilevers. The effect of elasticity plays a key role in the maximum deflection and oscillating frequency for both types of beams. This work examines the effectiveness of the framework based on the numerical model which provides further understandings for droplet impacts. It may lay the foundation for practical applications, such as engineering piezoelectric raindrop energy harvesters and plant leaves repelling raindrops.

A Very Simple Closed-Form Expression for Pull-In Voltage and Fundamental Frequency of Fixed-Fixed Beam

In this paper, a very simple closed-form expression for pull-in voltage and fundamental frequency of a fixed-fixed beam is presented with appropriate accuracy. We propose a model incorporating all know factors including effects of partial electrode configuration, axial stress, nonlinear stiffening, charge redistribution, and the fringing field effects. For the first time we express an analytic formulation for the pull-in deflection as a function of beam specification. We make an extensive comparison between the results of pull-in voltage obtained by our new expression and well-known approaches proposed in the literature. To do this, we calculate pull-in voltage with our expression for a wide range of beam specification and compare it with numerical, experimental and also other reported expressions. The pull-in voltage model has an average error of %1.29 in comparison to the experimental data for beams with a complete electrode, and %3.37 as compared to the 3D-coupled FEM simulation results for beams with partial electrode. Moreover, we show that the calculated fundamental frequency using proposed model is in good agreement with the experimental result from zero to near the pull-in voltages.

Damage detection in a fixed-fixed beam using natural frequency changes

This paper presents a damage detection technique which uses change in Frequency Response Function (FRF) and Modal Strain Energy (MSE) for damage detection in beam and truss like structures. It’s a robust approach for Structural Health Monitoring (SHM) using natural frequency for structural damage assessment. This technique couples FRF with Iterative Modal Strain Energy (IMSE) method to accurately localize and quantify the damage with only few frequencies, overcoming the limitation of mode shape based damage detection methods which requires mode shapes at full coordinates but damage is either over/underestimated. In the current approach, a damage detection algorithm is developed and validated by conducting numerical studies for a Fixed-Fixed beam, both noise-free and noise-effected cases are simulated. The numerical studies reveal that proposed algorithm is capable of identifying, localizing and quantifying the damage accurately at reduce computational cost.

Design and characterization of RF MEMS capacitive shunt switch for X, Ku, K and Ka band applications

In this paper, we present the design and development of a Radio Frequency Micro-Electro-Mechanical-Systems (RF-MEMS) capacitive shunt switch based on a fixed-fixed beam configuration for X (8–12 GHz), Ku (12–18 GHz), K (18–26 GHz) and Ka (26–40 GHz) band applications. The design parameters for RF switch have been taken into consideration based on in-house standard 6” CMOS foundry. Silicon substrate with high resistivity (ρ > 8 kΩ-cm, εr = 11.8, and tanδ = 0.01) has been utilized for the realization of MEMS switch. The device demonstrates the pull in voltage of 22.78 V. The measured return loss, insertion loss and isolation are better than 20 dB, 0.5 dB and 25 dB respectively, over the entire frequency band (0–40 GHz).The electromechanical and electromagnetic analyses of 3D structure were performed using Finite Element Method (FEM) & Method of Moments (MoM) based full wave simulators. Design and simulation data was further validated by measured results during DC and RF characterization of the devices.

Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model

Several studies indicate that Eringen’s nonlocal model may lead to some inconsistencies for both Euler-Bernoulli and Timoshenko beams, such as cantilever beams subjected to an end point force and fixed-fixed beams subjected a uniform distributed load. In this paper, the elastic buckling behavior of nanobeams, including both Euler-Bernoulli and Timoshenko beams, is investigated on the basis of a stress-driven nonlocal integral model. The constitutive equations are the Fredholm-type integral equations of the first kind, which can be transformed to the Volterra integral equations of the first kind. With the application of the Laplace transformation, the general solutions of the deflections and bending moments for the Euler-Bernoulli and Timoshenko beams as well as the rotation and shear force for the Timoshenko beams are obtained explicitly with several unknown constants. Considering the boundary conditions and extra constitutive constraints, the characteristic equations are obtained explicitly for the Euler-Bernoulli and Timoshenko beams under different boundary conditions, from which one can determine the critical buckling loads of nanobeams. The effects of the nonlocal parameters and buckling order on the buckling loads of nanobeams are studied numerically, and a consistent toughening effect is obtained.

Control of Beam Vibrations using Viscoelastically Damped Absorber System

The aim of this paper is to study the use of viscoelasically damped vibration absorber systems to optimally control the vibrations of a fixed-fixed beam. In this paper, a main beam with fixed-fixed boundary condition with viscoelstically damped cantilever beam as absorber is taken for the analysis. The paper includes optimum design & analysis of vibration absorber with viscoelastic damping. The equations of motion of the system have been derived to find the vibration response with absorber and used for optimization of parameters. The classical and Den Hartong optimization methods are used to optimize the design parameters and optimum values of design are found out. Theoretical calculations have been done for a fixed-fixed beam with three types of absorber beams (undamped, unconstrained treated damped absorber beam and constrained treated absorber beam). To validate the theoretical calculations, experiments have performed and deviation from theoretical data is discussed.