Vibration Of Beam Research Articles

Robot vision-based control strategy to suppress residual vibration of a flexible beam for assembly

PurposeIndustrial robots are extensively used in the robotic assembly of rigid objects, whereas the assembly of flexible objects using the same robot becomes cumbersome and challenging due to transient disturbance. The transient disturbance causes vibration in the flexible object during robotic manipulation and assembly. This is an important problem as the quick suppression of undesired vibrations reduces the cycle time and increases the efficiency of the assembly process. Thus, this study aims to propose a contactless robot vision-based real-time active vibration suppression approach to handle such a scenario.Design/methodology/approachA robot-assisted camera calibration method is developed to determine the extrinsic camera parameters with respect to the robot position. Thereafter, an innovative robot vision method is proposed to identify a flexible beam grasped by the robot gripper using a virtual marker and obtain the dimension, tip deflection as well as velocity of the same. To model the dynamic behaviour of the flexible beam, finite element method (FEM) is used. The measured dimensions, tip deflection and velocity of a flexible beam are fed to the FEM model to predict the maximum deflection. The difference between the maximum deflection and static deflection of the beam is used to compute the maximum error. Subsequently, the maximum error is used in the proposed predictive maximum error-based second-stage controller to send the control signal for vibration suppression. The control signal in form of trajectory is communicated to the industrial robot controller that accommodates various types of delays present in the system.FindingsThe effectiveness and robustness of the proposed controller have been validated using simulation and experimental implementation on an Asea Brown Boveri make IRB 1410 industrial robot with a standard low frame rate camera sensor. In this experiment, two metallic flexible beams of different dimensions with the same material properties have been considered. The robot vision method measures the dimension within an acceptable error limit i.e. ±3%. The controller can suppress vibration amplitude up to approximately 97% in an average time of 4.2 s and reduces the stability time up to approximately 93% while comparing with control and without control suppression time. The vibration suppression performance is also compared with the results of classical control method and some recent results available in literature.Originality/valueThe important contributions of the current work are the following: an innovative robot-assisted camera calibration method is proposed to determine the extrinsic camera parameters that eliminate the need for any reference such as a checkerboard, robotic assembly, vibration suppression, second-stage controller, camera calibration, flexible beam and robot vision; an approach for robot vision method is developed to identify the object using a virtual marker and measure its dimension grasped by the robot gripper accommodating perspective view; the developed robot vision-based controller works along with FEM model of the flexible beam to predict the tip position and helps in handling different dimensions and material types; an approach has been proposed to handle different types of delays that are part of implementation for effective suppression of vibration; proposed method uses a low frame rate and low-cost camera for the second-stage controller and the controller does not interfere with the internal controller of the industrial robot.

Feedback control of actuation‐constrained moving structure carrying Timoshenko beam

AbstractThis article deals with tracking control and active vibration suppression of a hybrid rigid‐elastic vibrational mobile system with a nonlinear elastic foundation in the presence of actuator bandwidth limitation and control input saturation. The system consists of a rigid rectilinearly mobile frame on an elastic foundation, and a flexible Timoshenko beam clamped to it with a heavy attached concentrated mass. The hybrid partial differential equation (PDE)‐ordinary differential equation (ODE) system of the plant is obtained using Hamilton's principle and then is converted to a system of ODEs using the assumed mode method (AMM). Next, the model will be discretized in the time domain using the two‐step Adams‐Bashforth technique. Considering the first‐order dynamics to cover the bandwidth limitation of the actuator, a discrete‐time sliding mode controller (DSMC) is designed based on a positive definite Lyapunov functional. Following that, an innovative optimal predictive algorithm is proposed to compensate for the effects of input saturation. The proposed algorithm is based on a positive definite cost function and using an intelligent regime of optimizations and decisions, minimizes the cost function in a predefined prediction horizon. The vibratory behavior of the system also is included in the mentioned cost function. Consequently, the overall control scheme called optimal rigid‐elastic interaction control (OREIC) will be able to follow the desired tracking trajectory, suppress the beam vibrations, and compensate for the effect of bandwidth limitation as well as the effect of input saturation. The performance of the OREIC algorithm is compared with a saturated DSMC controller and the simulation results demonstrate the efficiency of the method in vibration control of mobile rigid‐elastic systems subjected to actuator bandwidth frequency and saturation limitations.

Dynamic response of FG-CNTRC beams subjected to a moving mass

This article presents the forced vibration of composite beams reinforced by single-walled carbon nanotubes (SWCNTs) and subjected to a moving mass. Considering the distribution of carbon nanotubes such as uniform (UD-CNT), functionally graded Λ (FGΛ-CNT) and X (FGX-CNT), three different beams are studied. Based on a third-order shear deformation theory (TSDT), the motion equations of the beams are derived using Hamilton's principle. Including mass interaction forces, the motion equations are transformed into a finite element equation in which a two-node beam element with eight degrees of freedom is utilized. To improve the efficiency of the beam element, the transverse shear rotation is employed as an independent variable in the derivation of the beam element. The vibration characteristics, including the dynamic magnification factors and the time histories for mid-span deflections are computed by using the Newmark method. Numerical result reveal that the vibration of the beams is clearly influenced of the CNT reinforcement, and the dynamic magnification is significantly decreased by increasing the CNT volume fraction. It is also shown that the FGX-CNT beam is the best in dynamic resistance in terms of the lowest dynamic deflection and dynamic magnification factors. The effects of the total volume fraction and the moving load velocity on the dynamic behaviour of the functionally graded carbon nanotube reinforced composites (FG-CNTRC) beams are examined in detail and highlighted.

Scanning and separating vertical and torsional–flexural frequencies of thin-walled girder bridges by a single-axle test vehicle

An effective procedure is proposed for scanning and separating the vertical (flexural) and torsional–flexural frequencies of thin-walled girder bridges by a moving single-axle test vehicle, modeled as a two degree-of-freedom (DOF) system to account for the vertical and rocking motions. The response of the vehicle is not directly used, since it may mask the bridge frequencies by self frequencies. Instead, the wheel-bridge contact responses are used for being free of vehicle’s frequencies. To start, closed-form solutions are derived for the vertical, lateral, and torsional vibrations of the mono-symmetric beam. Then, the contact responses are calculated from the vehicle responses, considering the discrete nature of field data. The vertical and torsional–flexural frequencies of the bridge are separated by using the vertical and rocking motions derived from the contact responses without prior knowledge of the mode shapes. The proposed technique is numerically validated with the following conclusions: (1) the wheels’ contact responses outperform the vehicle response in that more high frequencies of the bridge can be detected; (2) the torsional–flexural​ frequencies can better be detected from the wheel closer to the bridge edge; and (3) the vertical and torsional–flexural frequencies of bridges can be successfully separated by the proposed procedure even in the presence of pavement roughness, which is helpful for field applications.

Research on coal gangue recognition based on multi-layer time domain feature processing and recognition features cross-optimal fusion

Accurate and rapid recognition of coal gangue is an important link to realize automatic mining, which is helpful to improve the efficiency of coal mining and the safety of mining workers. Relevant studies have confirmed the effectiveness of coal gangue recognition based on tail beam vibration signal, but the recognition accuracy of a single point source vibration signal of tail beam is slightly low. In order to improve the practicability of coal gangue recognition method based on tail beam vibration signal, this paper takes the single source tail beam vibration signal as the object, improves the coverage of tail beam vibration characteristics by conducting experiments and extracting multiple vibration signals at different positions, and conducts the research on coal gangue recognition technology by multi-layer time domain feature processing and cross-optimal fusion of multiple signals. Firstly, through analysis of classification algorithm ability and coal gangue recognition principle, the coal gangue recognition process is formulated and the classification model is constructed. Then, based on the two data samples of a single signal eigenvector and multi-signal eigenmatrix obtained by Direct Data Statistics (DDS), the recognition research is carried out, and the recognition effectiveness of the eigenmatrix is verified. Based on this conclusion, the three-layers eigenmatrix data samples of DDS, EMD Data Statistics (EDS) and HHT Data Statistics (HDS) are obtained by multi-layer time domain feature processing, and the coal gangue recognition based on multi-layer eigenmatrix is carried out respectively. DDS is the most accurate signal processing method. On this basis, the construction method of DDS + EDS and DDS + HDS recognition eigenmatrix based on array series is studied, and the recognition ability of DDS + HDS recognition eigenmatrix construction method and Logic Regression algorithm is proved. Recognition accuracy based on DDS + HDS recognition eigenmatrix and Logic Regression algorithm is up to 95.25 %. Finally, in order to further improve the recognition accuracy and response speed, this paper proposes a method of feature fusion based on cross-optimal selection (FFCOS). Features of DDS and HDS are sorted by recognition sensitivity, and then cross-selected and fused according to this sort. The results show that the recognition accuracy of the serial construction method of DDS + HDS recognition eigenmatriX array and the Logistic Regression algorithm can reach 97 %, which proves the effectiveness of the FFCOS method and realizes the accurate recognition of coal gangue based on the vibration signal of single source tail beam.

Effect of two-dimensional material distribution on dynamic and buckling responses of graded ceramic-metal higher order beams with stretch effect

The contribution provided in this article is to examine free vibration and stability response of bidirectional graded material beams (BDFB) considering different boundary conditions. The stretch effect by means of a normal deformation in conjunction with the shear deformation influence are integrated for accurate results. The beam materials features are expected to depend on gradation pattern over the length and transverse directions via power law form. Lagrange’s principle is employed in order to extract the governing equations of motion. A novel approach namely differential quadrature-based Galerkin method (DQGM) is used as an effective and accurate semi-analytical tool to compute the critical stability loads and natural frequencies of (BD-FG) beam for the first time. The approach takes features from simplicity and reduced computational cost of the DQ in combination with the efficacy of the Galerkin method for its analytical aspect and easy dealing with mixed boundary conditions resulting in more accurate results. The correctness of the results obtained from the present approach for two-directional functionally graded materials (FGMs) beams have been verified. Finally, the impacts of design parameters such as material grading exponent distributions, length to thickness ratios, porosity amount, and end support types on the natural frequencies and maximum of stability loads related to the present 2D-FGM beams are examined.

Finite Element Analysis of Continuous Beam Vibration under Pedestrian Loading Considering Moving Mass Effect

Finite Element Analysis of Continuous Beam Vibration under Pedestrian Loading Considering Moving Mass Effect

Investigation of fluid viscosity and density on vibration of nano beam submerged in fluid considering nonlocal elasticity theory

Predicting the dynamical behavior of nanostructures in contact with fluid is of paramount importance owing to their vast range of applications in civil engineering, aerospace, etc. Therefore, the free vibration of a nonlocal Euler-Bernoulli beam in contact with fluid is studied in this research. Using the Navier-Stokes relation, the interaction forces between the fluid and nanobeam are obtained. The equation of motion is solved using the Galerkin method of weighted residuals, and the natural frequency values in different fluids are presented, considering the viscosity effect. Further, the fluid-solid interaction model on a macroscopic scale is compared with the finite element analysis results. By considering the fluid parameters to be zero, the results of the nonlocal beam have been validated with past research. According to the obtained results, when studying the vibration of nanobeams, while density has a remarkable impact on the reduction of nanobeam natural frequencies, the fluid viscosity can be neglected. The fluid has the greatest impact on lower modes, whereas the nonlocal parameter exerts the biggest influence on higher modes. Moreover, in all vibration modes, with the increase of the nonlocal parameter, the effect of the fluid on the reduction of the natural frequencies increases, and in the nanoscale, it has a more significant role in changing the vibrational behavior of the system compared to the classical condition.

Nonlinear free vibration and flexural analysis of hyperelastic beam utilizing a meshless method based on radial basis function

This paper investigates nonlinear free and flexural analysis of hyperelastic beams. The constitutive relations of the hyperelastic beam were derived using the neo-Hookean strain energy function and Timoshenko beam theory. Also, the nonlinear governing equations and nonlinear natural boundary conditions were derived using Hamilton’s principle. The meshless collocation method based on the multiquadric radial basis function (MQ-RBF) was utilized to discretize the nonlinear governing equations. Also, the arc-length algorithm was used to solve the nonlinear system of equations. To validate the results of the meshless method, different boundary conditions (clamped–clamped, simply supported–simply supported, clamped–simply supported, and clamped-free) were examined, and the results obtained from the meshless method were compared with those of the finite element method in Abaqus finite element software. The results show that the maximum and minimum differences between meshless and finite element methods occur in clamped and free-boundary conditions, respectively. The results also show that the meshless method based on the MQ-RBF has good accuracy compared to the finite element method for bending and free vibration analysis of hyperelastic beams.

On uncertainty modeling of thermoelastic vibration for porous nanosandwich beams with gradient core based on nonlocal higher order beam model

In the present paper, the size-dependent random thermoelastic vibration analysis of porous nanosandwich beams with gradient core are demonstrated based on the nonlocal higher order beam model. The nonlocal elasticity theory incorporation with the higher order shear deformation theory is used to describe the kinematic and constitutive relations. The governing equations are obtained from minimum potential energy principle. The finite element method is used to solve the governing equations. Three types of the FG sandwich nanobeams with three types of porous cores are taken into account, and the influences of these structures and porosity types on the deterministic and stochastic behavior of sandwich beams are thoroughly discussed. Initially convergence and validation study is preformed to validate the present theoretical model by comparing the present results with the several previous works and Monte Carlo Simulation (MCS). Further, a comprehensive parametric study is performed to demonstrate the influence of the length to thickness ratio, degree of uncertainty in the material properties, nonlocal parameter, porosity distribution type, porosity volume fraction, temperature change, and gradation of material on the deterministic and stochastic behaviors of the FG nanosandwich beams. The developed model and computed results may be useful in the precise and reliable design of the components of nanodevices and systems.

The 100th Anniversary of the Timoshenko–Ehrenfest Beam Model

The 100th Anniversary of the Timoshenko–Ehrenfest Beam Model

Exact Frequencies for Free Vibration of Exponential and Polynomial AFG Beams with Lumped End Masses and Elastic Supports

Exact Frequencies for Free Vibration of Exponential and Polynomial AFG Beams with Lumped End Masses and Elastic Supports

Linear and nonlinear vibrations of strain gradient beams with rough surface

This paper aims to study the effect of surface roughness on the linear and nonlinear free vibration behaviors of microbeams based on the strain gradient theory. Linear and nonlinear equations of motion and boundary conditions are derived by using the Hamilton’s principle. A closed-form solution of strain gradient beams (SGBs) is obtained by solving a general sixth-order differential equation. Furthermore, by utilizing the linear mode and Galerkin’s method, an exact solution for nonlinear vibration is also obtained for SGBs. A detailed parametric study is performed to study the influences of surface roughness, scale parameter, beam thickness, and boundary condition on the linear and nonlinear vibration behaviors of SGBs. The present study may provide help for optimal designing and fabricating micro-/nano-resonators.

Effect of temperature and magnetoelastic loads on the free vibration of a sandwich beam with magnetorheological core and functionally graded material constraining layer

Effect of temperature and magnetoelastic loads on the free vibration of a sandwich beam with magnetorheological core and functionally graded material constraining layer

Vortex-induced piezoelectric cantilever beam vibration for ocean wave energy harvesting via airflow from the orifice of oscillation water column chamber

Micro piezoelectric generators have attracted immense interest to convert mechanical vibrations into electric energy for ultralow power wireless sensors. Herein, an ocean wave vortex-induced vibration piezoelectric energy harvester(Wavee-VIVPEH) is proposed to extract wave energy. The renewable and sustainable ocean environment energy harvesting device consists of an oscillating water column(OWC) air chamber, wind tunnel, and piezoelectric energy converter. A fixed bluff body in the vent tunnel induces airflow vortexes and excites the piezoelectric cantilever vibration converting up the ultralow frequency of ocean waves. The novel Wave-VIVPEH is a complex multi-physics system requiring feasible methodologies to enhance its performance. The theoretical models are derived to systematically investigate and optimize the operation. The flume and wind tunnel experiments and the related fluid-solid electric coupling simulations are carried out to verify the concept's feasibility. The aerodynamic kinetic performance in the OWC chamber is characterized by the models. The instantaneous maximum exhalation airspeed reaches 16.55 m/s with the air pressure of 349.97 Pa and the wave period of T = 2.5 s. In this wave condition, the results are well agreed with the simulation values of wind speed of 17.96 m/s, and air pressure of 382.55 Pa. The output power characteristics of the piezoelectric energy harvester are analyzed for the distance of the vortex wake between the piezoelectric cantilever beam and the bluff body. With the bluff body diameter of 25 mm and distance of d/dD= 4, the theoretical results on the maximum peak voltage and output power are 10.46 V, 3.26 mW agree with the simulation optimized values of the maximum peak voltage of 10.85 V and the output power of 3.55 mW. When the wind speed is 15 m/s, the theoretical voltage of 8.62 V approaches the experimental result of 8.47 V. Especially, the comparisons of the theoretical power and voltage to experimental and simulational results indicate that the ingenious Wave-VIVPEH has great potential in ocean wave energy harvesting applications to supply power for intelligent buoys.

Softening-spring nonlinearity in large amplitude vibration of unsymmetric double-layer lattice truss core sandwich beams

In recent years, many novel sandwich structures with multilayer or graded lattice truss cores that exhibited superior structural performance have been proposed. However, only limited works have studied the nonlinear behavior of sandwich structures with unsymmetric lattice truss cores. This paper aims to provide an analytical study on the nonlinear vibration of the unsymmetric double-layer lattice truss core sandwich beams (LTCSBs). The double-layer LTCSB is designed to be unsymmetric and possesses varying material property and structural geometry in each layer. In this study, six unsymmetric cases of LTCSB classified as two categories according to the midplane locations are considered. Subsequently, an analytical model for the unsymmetric double-layer LTCSB is developed based on the Allen’s model and von Kármán nonlinear theory. The axial displacement of the midplane of LTCSB is considered in the analytical model, therefore the proposed model is more generalized compared with previous models for the symmetric double-layer LTCSB. The Ritz method with a direct iterative procedure is applied to solve the nonlinear governing equations and determine the nonlinear frequencies for the unsymmetric double-layer LTCSB. Finally, the effects of six unsymmetric cases of LTCSBs on the nonlinear frequency ratio versus amplitude curve under three different types of boundary conditions are discussed detailly. An interesting phenomenon of softening-spring nonlinearity is found for hinged–hinged and clamped–hinged sandwich beams with large bending–extension coupling.

Free vibration and stability analysis of inclined pipes conveying gas-liquid slug flow

In this paper, the free vibration and stability of inclined pipes conveying gas-liquid slug flow are investigated, by considering the intermittency of slug flow and gravity effects of the system. A new lateral motion model has been established based on the stable slug flow dynamics model and the Euler–Bernoulli beam vibration model and is then truncated by the Galerkin approach. The natural frequencies, critical gas velocities, and responses to flow conditions are comprehensively investigated to show the basic dynamic characteristics of inclined pipes. The results show that the gravity effects caused by the inclined angle have a significant effect on the vibration characteristics. The system is less stable with lower critical gas velocity and natural frequency with the increase of inclined angle, due to the gravity-induced compression. For a given inclined angle, the system dynamic responses to superficial gas/liquid velocities are directly related to the mass of liquid per unit length. In addition, the fluctuation of natural frequency caused by the intermittency of slug flow decreases with the increase of inclined angle. This study contributes to understanding the complex dynamic behavior of inclined pipes conveying slug flow and promoting pipeline safety.

Estimation of Natural Frequencies of Cantilever Beam with Open Inclined Edge Crack

This paper presents an estimation of natural frequencies for free vibration of a cantilever beam in the presence of an inclined edge crack using linear elastic fracture mechanics. The Strain Energy Release Rate (SERR) approach is employed to compute the compliance coefficients for the edge crack inclined to the longitudinal axis at an arbitrary angle. A full compliance matrix under the general loading is presented and corresponding definitions of the compliance coefficients are given. Calculations of natural frequencies are carried out for both Timoshenko and Euler-Bernoulli beams under the influence of load P1, P3, and P5. Contribution to strain energy coming from various modes of fracture is accounted for by using stress intensity factors obtained numerically using ABAQUS 6.14 software. The effect of the crack on transverse and longitudinal natural frequencies is studied for different crack locations, depths, and inclination angles. Experiments are performed on short and long beams for a set of parameters for comparison purposes. It is found that the natural frequencies estimated by the proposed method compare well with the frequencies obtained experimentally for both beams.

Free Vibration of a Cantilever Euler-Bernoulli Beam Carrying a Point Mass by Using SEM

The objective of this research is to study the free vibration of a cantilever Euler-Bernoulli beam carrying a point mass with moment of inertia at the free end using the spectral element method (SEM). Typically, the shape (or interpolation) functions used in the Spectral element method are derived from exact solutions of the governing differential equations of motion in the frequency domain. The beam was discretized by a single spectral element which was connected by a point mass at the free end. The dynamic stiffness matrix of the beam is formulated in frequency domain by considering compatibility conditions at the additional mass position. Then, the first three natural frequencies of the cantilever beam are determined. After the validation of the spectral element method, the influence of the non-dimensional mass parameter and the non-dimensional mass moment of inertia on the first three natural frequencies and shape mode are examined.

Effects of surface unevenness on energy harvesting from beam vibration subjected to a moving mass

Effects of surface unevenness on energy harvesting from beam vibration subjected to a moving mass