Sub-tangentially loaded and damped Beck's columns on two-parameter elastic foundation

Lee, Jung Hoon; Kim, Namil; Kim, Moon-Young

doi:10.1016/j.jsv.2007.06.017

Cited by 18 publications

(8 citation statements)

References 52 publications

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“…where * 1 , * 2 denote the first and second dimensionless natural frequencies of a cantilever beam, respectively, and * 1 , * 2 can be obtained by solving simultaneous equation (26). It is worth noting from (26) that * 1 , * 2 under the assumption of Rayleigh damping increase in direct proportion to the damping ratio .…”

Section: Estimation Of Damping Coefficients For Stability Analysis Ofmentioning

confidence: 99%

“…Most have investigated shear effects on the divergence and flutter loads of nonconservative systems using FE formulations, but those studies neglected the effects of damping. Some researchers [20][21][22][23][24][25][26][27] noticed that external and internal (viscoelastic) damping of nonconservative systems can be treated as Rayleigh damping and explored the destabilizing effects of internal damping using an analytical approach or FE analysis.…”

Section: Introductionmentioning

confidence: 99%

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Structural Damping Effects on Dynamic Instability of Subtangentially Loaded and Shear Deformable Beck’s Columns

Min¹,

Park

Yeon³

et al. 2016

Mathematical Problems in Engineering

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A frequency equation of externally and internally damped and shear-flexible cantilever columns subjected to a subtangentially follower force is analytically derived in a dimensionless form with relation to the linear instability theory of Beck’s columns. Some parametric studies are then performed with variation of two damping coefficients under the assumption of Rayleigh damping. Based on the analysis results, it is demonstrated that three damping cases in association with flutter loads of Beck’s columns can be selected including one case representative of structural damping. Finally, stability maps of shear-flexible and damped Beck’s columns are constructed for the three damping cases and discussed in the practical range of damping coefficients and shear parameters. In addition, flutter loads and time history analysis results are presented using dimensionless FE analysis and compared with exact solutions.

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Section: Estimation Of Damping Coefficients For Stability Analysis Ofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Structural Damping Effects on Dynamic Instability of Subtangentially Loaded and Shear Deformable Beck’s Columns

Min¹,

Park

Yeon³

et al. 2016

Mathematical Problems in Engineering

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“…Sub-tangential follower forces are found in missile applications (Pradhan and Datta 7 ). Lee et al 8 investigated sub-tangentially loaded Beck's column. Adali 9 studied the e®ect of sub-tangential follower forces on plates.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Instability Characteristics of Thin Plate Like Beam with Internal Damage Subjected to Follower Load

Subramani

Datta

2015

Int. J. Str. Stab. Dyn.

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This study investigates the vibration, buckling and dynamic instability characteristics of damaged cross-ply and angle-ply laminated plate like beam under follower loading using thē nite element approach. The damage is anisotropic in nature and parametrically incorporated into the composite using the concept of reduction in sti®ness. It has been observed that damage shows a strong orthogonality and in general deteriorates the vibration and buckling characteristics. For follower type of loading, analysis is carried out on plate like beam structure to obtain the°utter characteristics. The e®ects of damage and its location on°utter characteristics are studied. The desirable position of damage on the plate like beam structure based on di®erent stability behavior is discussed. The results show that°utter is observed as primary modes of instability when damaged plate like beam is subjected to follower loads. The behavior of°utter characteristics for di®erent damaged parameters is discussed.

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“…Amongst the analytical or numerical methods available for the dynamic stability problems, the finite element method seems to be undoubtedly the most versatile, accordingly a large amount of works (Lee et al, 2007;Ryu et al, 1998;Kim and Choo, 1998;Saje and Jelenic, 1994;Del Giudice et al, 1992) were devoted to the technical improvement of the finite elements.…”

Section: Introductionmentioning

confidence: 99%

Dynamic stability analysis for Beck’s type of inelastic Timoshenko steel columns

2015

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In this study, the dynamic stability analysis of a Beck's type of steel column subjected to a sub-tangential follower force is presented considering the effects of gradual yielding along the length of column, the shear deformation, and the rotary inertia. The nonlinear tangent modulus-stress, tangent modulus-slenderness ratio, and compressive stress-strain relationships of an inelastic column are derived from the column strength curve given in Korea Bridge Design Code (KBDC) based on the tangent modulus theory. The equations of motion of the Timoshenko inelastic column are derived from the Hamilton's principle. The finite element method using the Hermite cubic interpolation functions is employed to obtain the mass, inelastic stiffness, geometric stiffness, and load correction matrices, and the evaluation procedure for critical values of divergence and flutter of the non-conservative system is briefly described. The obtained results are compared with available results of other numerical or analytical methods. Finally, the effects of various structural parameters such as the material inelasticity, the shear deformation, the rotary inertia, the effective length factor, and the sub-tangentiality factor on the divergence and flutter behavior of non-conservative columns are parametrically investigated.

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Sub-tangentially loaded and damped Beck's columns on two-parameter elastic foundation

Cited by 18 publications

References 52 publications

Structural Damping Effects on Dynamic Instability of Subtangentially Loaded and Shear Deformable Beck’s Columns

Structural Damping Effects on Dynamic Instability of Subtangentially Loaded and Shear Deformable Beck’s Columns

Dynamic Instability Characteristics of Thin Plate Like Beam with Internal Damage Subjected to Follower Load

Dynamic stability analysis for Beck’s type of inelastic Timoshenko steel columns

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