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

This article presents a new analysis of the vibration characteristics of open-edge cracks for graded moving beams under thermal load. The material property gradient is based on the distribution of the power law in the direction of the beam thickness. The vibration equation is obtained depending on the precept of Hamilton and resolved by the extension of Galerkin’s approach. A rotational spring is used to represent the cracking in the beam. The effects of the axial velocity, gradient index, thermal load, and cracking parameters on vibration characteristics are observed. Furthermore, the mode shapes of the simple support cracked moving graded beam are determined. The results show that the rise in the axial velocity, the crack depth, and the material property index led to a decrease in the natural frequencies, which indicates the results obtained. HIGHLIGHTS Stability and vibrations analysis of the cracked gradient beams with an axial motion under a uniform temperature rise The effect of axial velocity, gradient index, thermal load, and cracks parameter was studied Galerkin’s technique is developed for vibrational analysis of cracked graded beams with longitudinal motion The Euler-Bernoulli beam model was used taking into account the effect of rotatory inertia GRAPHICAL ABSTRACT

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“…To solve the vibration equations (22-a, and 22-b), a Galerkin's technique was used. The general form of Galerkin's equation is given as [38];…”

Section: Solution Methodsmentioning

confidence: 99%

Investigation of Transverse Vibration Characteristics of Cracked Axially Moving Functionally Graded Beam Under Thermal Load

Elaikh

Agboola²

2022

Trends Sci

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“…The strain-displacement relation for the longitudinal strain of spinning systems can be expressed as 10,63 where v and w are the displacement of the nanotube in y - and z - directions, respectively.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The strain-displacement relation for the longitudinal strain of spinning systems can be expressed as 10,63…”

Section: Potential Energymentioning

confidence: 99%

Size-dependent vibrational behavior of embedded spinning tubes under gravitational load in hygro-thermo-magnetic fields

Liu

Ruonan

Koochakianfard

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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In the present investigation, with the aim of performance improvement of size-dependent bi-gyroscopic structures, the vibrational behavior of spinning small-scale tunes conveying fluid embedded in various foundations subjected to distributed tangential load and hygro-thermo-magnetic environments by including gravitational effect is investigated. The modified couple stress theory is used to study the microscale tube, and the modified nonlocal theory is utilized to model the nanoscale tubes. A parametric investigation is also conducted to highlight the impacts of various key factors such as gravity, flow profile modification factor, fluid velocity, spinning speed, substrate coefficients, boundary conditions, size-dependent parameters, and environmental attacks on divergence and flutter thresholds of the structure. The dynamical equations are solved using Laplace transformation as well as Galerkin discretization techniques, and forward and backward frequencies are identified accordingly. Meanwhile, the instability borders of the system are obtained analytically. Campbell and stability diagrams, and the time history of the system, are acquired. The results revealed that contrary to influences of gravity, magnetization, and size-dependent parameters, the compressive tangential load and humidity have decreasing effects on the vibrational frequencies and make the system prone to experience static and dynamical instabilities. Moreover, it is determined that applying the viscous foundation eliminates the re-stabilization zone in the system stability evolution, and after the occurrence of the divergence phenomenon, the system immediately undergoes the flutter instability.

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“…Sarparast and Ebrahimi-Mamghani [36] studied the rotating beams effects considering the foundation forcing impositions. Rotating rods analysis under the effects of axial loading is reported by Ebrahimi-Mamghani et al [37]. Ebrahimi and Mokhtari [38] investigated vibration analysis of rotating porous micro-beam.…”

Section: Introductionmentioning

confidence: 98%

Free Vibration Analysis of Rotating Beams Based on the Modified Couple Stress Theory and Coupled Displacement Field

Babaei

Arabghahestani

2021

Applied Mechanics

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In this paper, transverse vibration analysis of rotating micro-beam is investigated based on the modified couple stress theory. The simply-supported micro-beam is modeled utilizing Euler-Bernoulli and Timoshenko beam theories. The system is rotating around a fixed axis perpendicular to the axial direction of the beam. For the first time, displacement filed is introduced as a coupled field to the translational field. In other words, the mentioned rotational displacement field is expressed as a proportional function of translational displacement field using first (axial), second (lateral), and third (angular or rotational) velocity factors. Utilizing Hamilton’s approach as a variational method, dynamic-vibration equations of motion of the proposed model are derived. Galerkin’s method is adopted to solve the equation corresponding to the Euler–Bernoulli and Timoshenko beams. For the case considering shear deformation effects, Navier method is chosen. For evaluation of current results and models, they are compared with those available at the benchmark. In this paper; effects of slenderness ratio, axial, lateral, and angular velocity factors, and rotations of the beam on the frequency are reported. Based on the results presented, mentioned factors should be counted in the analysis and design of such rotating micro-systems.

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

Cited by 59 publications

References 58 publications

Investigation of Transverse Vibration Characteristics of Cracked Axially Moving Functionally Graded Beam Under Thermal Load

Investigation of Transverse Vibration Characteristics of Cracked Axially Moving Functionally Graded Beam Under Thermal Load

Size-dependent vibrational behavior of embedded spinning tubes under gravitational load in hygro-thermo-magnetic fields

Free Vibration Analysis of Rotating Beams Based on the Modified Couple Stress Theory and Coupled Displacement Field

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