Nonlinear dynamic response of an edge-cracked functionally graded Timoshenko beam under parametric excitation

Yan, T.; Yang, Jie; Kitipornchai, S.

doi:10.1007/s11071-011-0003-9

Cited by 27 publications

(8 citation statements)

References 40 publications

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“…Compared with the forced vibration, the parametric excitation is more complex and has a greater impact on the FCRM system (Yan et al, 2012). Thus, the parametric excitation, caused by the axial movement disturbance of the base, of the FCRM system is investigated.…”

Section: Nonlinear Dynamic Modellingmentioning

confidence: 99%

Nonlinear modelling and dynamic stability analysis of a flexible Cartesian robotic manipulator with base disturbance and terminal load

Fan

et al. 2017

Mech. Sci.

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Abstract. The flexible Cartesian robotic manipulator (FCRM) is coming into widespread application in industry. Because of the feeble rigidity and heavy deflection, the dynamic characteristics of the FCRM are easily influenced by external disturbances which mainly concentrate in the driving end and the load end. Thus, with the influence of driving base disturbance and terminal load considered, the motion differential equations of the FCRM under the plane motion of the base are constructed, which contain the forced and non-linear parametric excitations originated from the disturbances of base lateral and axial motion respectively. Considering the relationship between the coefficients of the motion differential equations and the mode shapes of the flexible manipulator, the analytic expressions of the mode shapes with terminal load are deduced. Then, based on multiple scales method and rectangular coordinate transformation, the average equations of the FCRM are derived to analyze the influence mechanism of base disturbance and terminal load on the system parametric vibration stability. The results show that terminal load mainly affects the node locations of mode shapes and mode frequencies of the FCRM, and the axial motion disturbance of the driving base introduces parametric excitation while the lateral motion disturbance generates forced excitation for the transverse vibration model of the FCRM. Furthermore, with the increase of the base excitation acceleration and terminal load, the parametric vibration instability region of the FCRM increases significantly. This study will be helpful for the dynamic characteristics analysis and vibration control of the FCRM.

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Section: Nonlinear Dynamic Modellingmentioning

confidence: 99%

Nonlinear modelling and dynamic stability analysis of a flexible Cartesian robotic manipulator with base disturbance and terminal load

Fan

et al. 2017

Mech. Sci.

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“…To the author's best knowledge, the researches regarding non-linear forced vibration responses of cracked FGB are very limited. Yan et al studied the non-linear dynamic response of FG Timoshenko beam with an edge crack under a parametric excitation, combining a static compressive load and a harmonic excitation force [21]. Panigrahi and Pohit studied the non-linear dynamics of a FG cracked Timoshenko beam under an excitation force using the harmonic balance method in conjunction with an iterative technique [22].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Chajdi¹,

Adri²,

Bikri³

et al. 2021

Diagnostyka

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Geometrically non-linear vibrations of functionally graded Euler-Bernoulli beams with multi-cracks, subjected to a harmonic distributed force, are examined in this paper using a theoretical model based on Hamilton's principle and spectral analysis. The homogenisation procedure is performed, based on the neutral surface approach, and reduces the FG beams analysis to that of an equivalent homogeneous multi-cracked beam. The so-called multidimensional Duffing equation obtained and solved using a simplified method (second formulation) previously applied to various non-linear structural vibration problems. The curvature distributions associated to the multi-cracked beam forced deflection shapes are obtained for each value of the excitation level and frequency. The parametric study performed in the case of a beam and the detailed numerical results are given in hand to demonstrate the effectiveness of the proposed procedure, and in the other hand conducted to analyse many effects such as the beam material property, the presence of crack, the vibration amplitudes and the applied harmonic force on the non-linear dynamic behaviour of FG beams.

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“…Lellep et al [35,36,37] focused on the problem of vibration and optimization of elastic solids with and without a crack. Yang and his co-workers [38,39,40,41] investigated the free and nonlinear vibration, buckling and post-buckling of a cracked FGM beam and discussed the effect of cracks on the mechanical behavior of a FGM beam in detail. However, to the best of the authors’ knowledge, no previous work has been done on cracked graphene reinforced nanocomposite structures, including any of its mechanical characteristics.…”

Section: Introductionmentioning

confidence: 99%

Vibration and Buckling Characteristics of Functionally Graded Graphene Nanoplatelets Reinforced Composite Beams with Open Edge Cracks

et al. 2019

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This paper investigates the free vibration and compressive buckling characteristics of functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) beams containing open edge cracks by using the finite element method. The beam is a multilayer structure where the weight fraction of graphene nanoplatelets (GPLs) remains constant in each layer but varies along the thickness direction. The effective Young’s modulus of each GPLRC layer is determined by the modified Halpin-Tsai micromechanics model while its Poisson’s ratio and mass density are predicted according to the rule of mixture. The effects of GPLs distribution pattern, weight fraction, geometry, crack depth ratio (CDR), slenderness ratio as well as boundary conditions on the fundamental frequency and critical buckling load of the FG-GPLRC beam are studied in detail. It was found that distributing more GPLs on the top and bottom surfaces of the cracked FG-GPLRC beam provides the best reinforcing effect for improved vibrational and buckling performance. The fundamental frequency and critical buckling load are also considerably affected by the geometry and dimension of GPL nanofillers.

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Nonlinear dynamic response of an edge-cracked functionally graded Timoshenko beam under parametric excitation

Cited by 27 publications

References 40 publications

Nonlinear modelling and dynamic stability analysis of a flexible Cartesian robotic manipulator with base disturbance and terminal load

Nonlinear modelling and dynamic stability analysis of a flexible Cartesian robotic manipulator with base disturbance and terminal load

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Vibration and Buckling Characteristics of Functionally Graded Graphene Nanoplatelets Reinforced Composite Beams with Open Edge Cracks

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