Statistical properties of nonlinear mode spectrum for large amplitude forced vibration systems

Ma, Aijun; Chen, Suhuan; Liu, Zhong‐Sheng

doi:10.1016/0045-7949(94)00582-n

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…Mei and Decha-Umpkai (1985) used the finite element method for nonlinear forced vibration analysis of beam structures subjected to harmonic excitation. The statistical properties of a geometrically nonlinear mode spectrum for large amplitude forced vibration systems had been estimated by Ma et al (1995a) using the finite element method. Ma et al (1995b) used the matrix perturbation method for the large amplitude forced vibration analysis of beams, incorporating longitudinal inertia in the formulation.…”

Section: Introductionmentioning

confidence: 99%

A numerical analysis of large amplitude beam vibration under different boundary conditions and excitation patterns

Das

Sahoo

Saha

2011

Journal of Vibration and Control

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Large amplitude forced vibration behavior of thin beams under harmonic excitation is studied, incorporating the effect of geometric nonlinearity. Large amplitude free vibration analysis of the same system is also carried out to obtain the backbone curves. When a very small loading is considered, the system response becomes almost identical to the backbone curve, which confirms the validity of the large amplitude study. The sets of governing equations for both forced and free vibration problems are obtained using Hamilton’s principle, whereas the same for the static problem are obtained by applying the variational form of the energy principle. The solution of the static problem provides system stiffness as a function of deflection and it becomes an input to the corresponding free vibration problem. The results are presented in the nondimensional frequency–amplitude plane in the form of response curves, and the related backbone curves are shown to represent the complete system behavior. Results for different combinations of classical flexural boundary conditions and loading patterns are reported.

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Section: Introductionmentioning

confidence: 99%

A numerical analysis of large amplitude beam vibration under different boundary conditions and excitation patterns

Das

Sahoo

Saha

2011

Journal of Vibration and Control

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“…Chen et al (1994) devised a computational method for design sensitivity analysis of a nonlinear mode spectrum for forced vibrations of beams. Ma et al (1995a) estimated the statistical properties of a geometrically nonlinear mode spectrum for large amplitude forced vibration systems using finite element method. The same authors (1995b) presented combined mode superposition of modal perturbation and matrix perturbation method for large deflection forced vibration of beams subjected to periodic loading incorporating both longitudinal displacement and longitudinal inertia in the formulation.…”

Section: Introductionmentioning

confidence: 99%

Large amplitude forced vibration analysis of cross-beam system through energy method

Mitra¹,

Sahoo²,

Saha³

2010

Int. J. Eng. Sci. Tech

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Large amplitude forced vibration behaviour of cross-beam system under harmonic excitation is studied, incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way, in which the dynamic system is assumed to satisfy the force equilibrium condition at peak load value, thus reducing the problem to an equivalent static case. The two beams of the system are solved individually either by a direct substitution method employing successive relaxation technique or a multi-dimensional secant method, known as Broyden's method. An iterative scheme, based on the reaction force between the two beams of the system and equality of vibration amplitude at the contact of two beams, is developed to obtain the response of the system under external harmonic excitation. The present method is validated through results generated in ANSYS 11.0. The system response is studied for various loading type and contact location of the beams. The results are presented in terms of plots of vibration amplitude of the contact point versus frequency of forcing excitation in dimensional plane.

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Finite element analysis of nonlinear shell structures with uncertain material property

Chang

Liu

Chang

2008

Thin-Walled Structures

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Statistical properties of nonlinear mode spectrum for large amplitude forced vibration systems

Cited by 3 publications

References 8 publications

A numerical analysis of large amplitude beam vibration under different boundary conditions and excitation patterns

A numerical analysis of large amplitude beam vibration under different boundary conditions and excitation patterns

Large amplitude forced vibration analysis of cross-beam system through energy method

Finite element analysis of nonlinear shell structures with uncertain material property

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