On the vibrations of axially graded Rayleigh beams under a moving load

Ebrahimi-Mamaghani, Ali; Sarparast, Hoda; Rezaei, Masoud

doi:10.1016/j.apm.2020.04.002

Cited by 52 publications

(11 citation statements)

References 55 publications

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“…Chen et al used the global modal method to study the U-shaped composite beam structure, obtained the frequency equation of the U-shaped beam structure, and obtained the natural frequency and global mode of the system [6]. Ebrahimi-Mamaghani derived the governing equations of the plane motion of the Z-shaped composite beam structure and the boundary conditions of the system by using the Hamilton's principle and theoretically obtained the natural frequency of the Z-shaped composite beam structure and the modal mode shape of the analytical form [7]. Tk et al considered the bending and torsional deformation of the rod and the bending deformation of the beam.…”

Section: Literature Reviewmentioning

confidence: 99%

Application of the Lagrange Equation for Intelligent Sensor Vibration Control for Power Network Monitoring

Cheng

2022

International Transactions on Electrical Energy Systems

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Objective. In order to control the vibration of the beam structure more effectively and improve the safety and availability of the beam structure, an application study of the Lagrange equation for vibration control of smart sensors for power grid monitoring is proposed. The vibration of the beam structure, the displacement of the beam structure under the excitation of seismic acceleration, the response analytical electrical formula, and the displacement response formula of the beam structure under the action of the kinematic force are deduced. The optimal parameters of the beam-TMDI system are given, and the parameter sensitivity analysis is carried out. Then, the control effect of the TMDI system is studied by numerical analysis, and the vibration reduction effect of the TMDI system and the tuned mass damper (TMD) system is compared. Experimental results show that when the mass ratio μ of the TMDI system and the TMD system are both set to a fixed value of 0.005, and the parameter β of the TMDI system is set to 0, namely β = b = 0 , at this time, the TMDI system degenerates into a TMD system. The TMD natural frequency is 14.179 rad/s and the damping ratio is 0.0432 by the DH optimization method, while the TMD natural frequency is 14.1812 rad/s, and the damping ratio is 0.0436 by the augmented Lagrangian optimization algorithm. Conclusion. The vibration displacement response spectrum of a beam structure obtained by the frequency domain method can effectively reflect electricity in the displacement response of a beam structure. The parameters that minimize the vibration response of the beam structure can be accurately obtained by using the augmented Lagrangian parameter optimization method. The sensitivity of the TMDI system is controlled by the inertial device, and the inertial device has a significant impact on its robustness. The vibration reduction performance of the TMDI system is obviously better than in the conventional TMD systems.

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Section: Literature Reviewmentioning

confidence: 99%

Application of the Lagrange Equation for Intelligent Sensor Vibration Control for Power Network Monitoring

Cheng

2022

International Transactions on Electrical Energy Systems

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“…Functionally graded (FG) materials are an advanced class of composite materials whose thermomechanical properties vary smoothly and continuously in a preferred direction of the structure [16][17][18][19][20][21][22][23]. Compared with homogeneous and conventional laminated materials, FG materials display unique features such as higher fracture toughness, lower stress concentration, better corrosion and thermal resistance.…”

Section: Introductionmentioning

confidence: 99%

Vibration of viscoelastic axially graded beams with simultaneous axial and spinning motions under an axial load

Ebrahimi-Mamaghani¹,

Forooghi

Sarparast

et al. 2021

Applied Mathematical Modelling

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“…The results show that this analytical expression can approximate the exact solution of the whole amplitude range and reduce the corresponding error of angular frequency relative to Hamiltonian. Ali 11 established a mechanical model to analyze the free nonlinear vibration and forced nonlinear vibration of axially moving beams. The mechanical properties of the Rayleigh beam and the Euler Bernoulli beam under moving load are analyzed, such as moment of inertia, velocity, and gradient.…”

Section: Introductionmentioning

confidence: 99%

Modal analysis and experimental investigation into vibration of the diamond-beaded rope based on lumped mass

Zhang

Wang

2021

Journal of Low Frequency Noise, Vibration and Active Control

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The natural vibration characteristics of the diamond-beaded rope (DBR) based on lumped mass are analyzed both theoretically and experimentally. The dynamic model of the DBR is established by means of the multi-body dynamics theory. According to Lagrange’s equations, the control equation of the DBR is derived. It mainly analyzes the influence of the parameters, such as the motion velocity of the DBR, the tension of the DBR, the length of diamond beads, the quality of diamond beads, and their position in the DBR, on the natural vibration characteristics for the DBR are studied. The results show that the natural frequencies and the corresponding vibration shapes of the DBR based on lumped mass change significantly when the variations of the above parameters are considered. In the process of the movement of the DBR, the random impact force of diamond beaded is the key factor that causes the natural frequency of the DBR to fluctuate., In the high-order modal analysis, the natural frequency and vibration mode of the DBR fluctuate more obviously. The relative error of the result between the calculated and the measured is less than 10%, which validates the proposed method.

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On the vibrations of axially graded Rayleigh beams under a moving load

Cited by 52 publications

References 55 publications

Application of the Lagrange Equation for Intelligent Sensor Vibration Control for Power Network Monitoring

Application of the Lagrange Equation for Intelligent Sensor Vibration Control for Power Network Monitoring

Vibration of viscoelastic axially graded beams with simultaneous axial and spinning motions under an axial load

Modal analysis and experimental investigation into vibration of the diamond-beaded rope based on lumped mass

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