Porosity, mass and geometric imperfection sensitivity in coupled vibration characteristics of CNT-strengthened beams with different boundary conditions

Khaniki, Hossein Bakhshi; Ghayesh, Mergen H.; Hussain, Shahid; Amabili, Marco

doi:10.1007/s00366-020-01208-3

Cited by 21 publications

(6 citation statements)

References 63 publications

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“…The results showed that for the case of Axially FG (AFG) CNT beam, geometrical imperfection alters the nonlinear behavior from hardening to softening. In another study, (Khaniki et al, 2020) discussed the effect of porosity, mass, and geometric imperfections in the coupled vibration behavior of AFG CNT strengthened beam structures. The equations of motion were derived using Hamilton’s principle and the von Kármán geometrical nonlinearity and were solved using a semi-analytical modal decomposition technique.…”

Section: Introductionmentioning

confidence: 99%

Free and forced nonlinear vibrations of Bi-Directional functionally graded Euler–Bernoulli porous beams

Sari

Al‐Dahidi

Hammad

2022

Journal of Vibration and Control

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In this study, the free and forced vibrations of a bi-directional functionally graded porous beam are investigated. The governing equations of motion are derived by Hamilton’s principle, and the reduced temporal equation of motion with cubic and quintic nonlinear terms is obtained using the Galerkin approach. Analytical solutions for the nonlinear natural frequencies in addition to the primary resonance response curves are established by the method of multiple scales. The effects of the axial and transverse functionally graded indexes, initial amplitude, porosity parameter, and the elastic and mass density ratios on the nonlinear frequencies and the forced responses are examined.

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Section: Introductionmentioning

confidence: 99%

Free and forced nonlinear vibrations of Bi-Directional functionally graded Euler–Bernoulli porous beams

Sari

Al‐Dahidi

Hammad

2022

Journal of Vibration and Control

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“…At present, the potential energy principle proposed by Yang and Lin 6 in 1987 and the improvements based on this method 7,8 are the most frequently used analytical methods to solve the TVMS of healthy or unhealthy gears, where the gear tooth is modeled as a cantilever nonuniform beam. The vibrations of beams have been discussed by many scholars 9–12 . In earlier studies, 13–15 the gear tooth is simplified as a variable cross‐section cantilever beam starting from the base circle.…”

Section: Introductionmentioning

confidence: 99%

“…The vibrations of beams have been discussed by many scholars. [9][10][11][12] In earlier studies, [13][14][15] the gear tooth is simplified as a variable cross-section cantilever beam starting from the base circle. In fact, for a real gear tooth, the base circle and the root circle are not exactly coincident.…”

mentioning

confidence: 99%

Mesh stiffness calculation and vibration analysis of the spur gear pair with tooth crack, considering the misalignment between the base and root circles

Hou

Yang

et al. 2021

Int Journal of Mech Sys Dyn

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An improved variable cross-section cantilever beam model for evaluating the timevarying mesh stiffness (TVMS) of the perfect gear tooth is developed in which the tooth number of driving gear is less than 42 and that of driven is more than 42. The TVMS obtained by the proposed method is compared with the result without considering the misalignment between the base circle and gear root. Four types of root crack models and changes in TVMS of 13-crack levels are presented. The fault vibration characteristic of a single-stage spur gear reducer with root crack is analyzed and the correctness is qualitatively verified by the vibration signals of an experimental gearbox with crack or missing failure. The results presented in this paper are of great significance for a deep understanding of the possible causes of vibration and noise of gears and provide a theoretical foundation for the fault diagnosis of the gearbox. K E Y W O R D S backlash, gear, potential energy method, time-varying mesh stiffness (TVMS), tooth crack 1 | INTRODUCTION Spur gear transmission system has been used in various mechanical fields, 1-3 because of some characteristics, for example, simple structure, reliable operation, long service life, no axial forces, and so on during meshing. A great deal of research has been made on the dynamics of a pair of healthy spur gears. Amabili and Rivola 4 investigated the steady-state response and stability of a single degree of freedom (DOF) model with time-varying mesh stiffness (TVMS) and damping coefficient. Later, Amabili and Fregolent 5 proposed a new method for identifying the gear error and modal parameters,where the nonlinear meshing stiffness, mesh damping, and excitation caused by gear errors are taken into account. However, tooth crack, pitting, spalling may develop in gears for overload, harsh operating conditions, manufacturing errors, and so forth. Therefore, it is of great significance to study the mechanism and vibration characteristics of spur gear systems with faults for further understanding the causes of gear vibration and noise, as well as for gear fault diagnosis.

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“…With the development of nonlinear theory, researchers already proposed nonlinear detection methods in which nonlinear systems are used to detect weak signals 8–25 . This type of signal detection method extracts the characteristics of weak signals, not by eliminating or suppressing noise, but by using the characteristics of some nonlinear systems to detect weak signals in strong noise.…”

Section: Introductionmentioning

confidence: 99%

“…With the development of nonlinear theory, researchers already proposed nonlinear detection methods in which nonlinear systems are used to detect weak signals. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] This type of signal detection method extracts the characteristics of weak signals, not by eliminating or suppressing noise, but by using the characteristics of some nonlinear systems to detect weak signals in strong noise. In the early weak fault detection methods of rolling bearings, the stochastic resonance [26][27][28] and the chaotic oscillator 8 are widely used.…”

mentioning

confidence: 99%

Periodic‐phase‐diagram similarity method for weak signal detection

Tian

Zhang

Yang

et al. 2021

Int Journal of Mech Sys Dyn

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The periodic‐phase‐diagram similarity method is proposed to identify the frequency of weak harmonic signals. The key technology is to find a set of optimal coefficients for Duffing system, which leads to the periodic motion under the influence of weak signal and strong noise. Introducing the phase diagram similarity, the influences of strong noise on the similarity of periodic phase diagram are discussed. The principle of highest similarity of periodic phase diagram with the same frequency is detected by discussing the persistence of similarity of periodic motion phase diagram under the strong noise and the periodic‐phase‐diagram similarity method is constructed. The weak signals of early fault and strong noise are input into Duffing system to obtain the identified system. The stochastic subharmonic Melnikov method is extended to obtain the conditions of the optimal coefficients for the identified system. Based on the results, the constructed frequency conversion harmonic weak signals are considered to form a datum periodic system. With the change of frequency in the datum periodic system, the phase diagram similarity of the two constructed systems can be calculated. Based on the periodic‐phase‐diagram similarity method, the frequency of weak harmonic signals can be identified by the principle of highest similarity of periodic phase diagram with the same frequency. The results of numerical simulation and the early fault diagnosis results of actual bearings verify the feasibility of the periodic‐phase‐diagram similarity method. The accuracy of the detection effect is 97%, and the minimum signal‐to‐noise ratio is −80.71 dB.

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Porosity, mass and geometric imperfection sensitivity in coupled vibration characteristics of CNT-strengthened beams with different boundary conditions

Cited by 21 publications

References 63 publications

Free and forced nonlinear vibrations of Bi-Directional functionally graded Euler–Bernoulli porous beams

Free and forced nonlinear vibrations of Bi-Directional functionally graded Euler–Bernoulli porous beams

Mesh stiffness calculation and vibration analysis of the spur gear pair with tooth crack, considering the misalignment between the base and root circles

Periodic‐phase‐diagram similarity method for weak signal detection

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