Application of the modified iteration method to nonlinear vibration of corrugated circular plates

Li, Dong; Liu, Renhuai

doi:10.1007/bf02014567

Cited by 15 publications

(6 citation statements)

References 5 publications

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“…Hence, f (ξ, τ) and g(ξ, τ) are acquired from Eqs. (19) and (20). Inner forces and displacements in shells under dynamic load can be easily obtained as long as f (ξ, τ) and g(ξ, τ) are known.…”

Section: Integral Equation and Its Solutionmentioning

confidence: 99%

“…Based on the theory of orthotropic circular plate [18−20] , selecting the maximum amplitude in the center of the corrugated circular plate as the perturbation parameter, the nonlinear natural frequency of corrugated circular plate was solved using the perturbation variation method by Wang et al [18] . The problem of nonlinear free vibration of corrugated circular plate was solved successfully by Liu and Li utilizing Galerkin method [19] and modified iteration method [20] , and the relationship between amplitude and frequency was obtained. There are four kinds of theoretical problems on nonlinear vibration of corrugated shells being worthy of further study, which are (i) nonlinear forced vibration of corrugated circular plate based on the theory of orthotropic circular plate; (ii) nonlinear free and forced vibration of corrugated circular plate based on the dynamic equations of nonlinear large deflection of shells; (iii) nonlinear free and forced vibration of corrugated shells based on the dynamic equations of nonlinear large deflection of shells; (iv) nonlinear free and forced vibration of corrugated shells based on the theory of orthotropic shells.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear vibration of corrugated shallow shells under uniform load

袁鸿

刘人怀

2007

Appl Math Mech

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Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution, the nonlinear forced vibration of a corrugated shallow shell under uniform load is investigated. The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green's function. To solve the integral-differential equations, expansion method is used to obtain Green's function. Then the integral-differential equations are reduced to the form with degenerate core by expanding Green's function as series of characteristic function. Therefore, the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic force is obtained by considering single mode vibration. As a numerical example, forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied. The obtained solutions are available for reference to design of corrugated shells

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Section: Integral Equation and Its Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of corrugated shallow shells under uniform load

袁鸿

刘人怀

2007

Appl Math Mech

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“…In this subsection, the second-order modified-iterative solution can be given. By substitution of (29) and (30) into (19), one has…”

Section: The First-order Approximate Solutionmentioning

confidence: 99%

“…When the rotational inertia is considered, the nonlinear vibration mechanical model of the Euler beam with inertial boundary conditions is established. The modified iteration method is employed to solve the motion equations and used Matlab for simulation and analysis [19,20]. Hereby, the relationships of axial velocity, tension, and rotational inertia are investigated, and the results may provide an important theoretical reference to control and analyze the vertical vibration of strip during continuous rolling process.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration Analysis of Moving Strip with Inertial Boundary Condition

Gao

Feng

et al. 2015

Mathematical Problems in Engineering

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According to the movement mechanism of strip and rollers in tandem mill, the strip between two stands was simplified to axially moving Euler beam and the rollers were simplified to the inertial component on the fixed axis rotation, namely, inertial boundary. Nonlinear vibration mechanical model of Euler beam with inertial boundary conditions was established. The transverse and longitudinal motion equations were derived based on Hamilton’s principle. Kantorovich averaging method was employed to discretize the motion equations and the inertial boundary equations, and the solutions were obtained using the modified iteration method. Depending on numerical calculation, the amplitude-frequency responses of Euler beam were determined. The axial velocity, tension, and rotational inertia have strong influences on the vibration characteristics. The results would provide an important theoretical reference to control and analyze the vertical vibration of moving strip in continuous rolling process.

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“…But little has been done to study the large amplitude vibration of sandwich plates. The present paper interestingly gets some inspiration from [1, 4,5] to look into the free axisymmetric large amplitude vibration of circular sandwich plates.…”

Section: Introductionmentioning

confidence: 99%

Large amplitude vibration of circular sandwich plates

1994

Appl Math Mech

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Application of the modified iteration method to nonlinear vibration of corrugated circular plates

Cited by 15 publications

References 5 publications

Nonlinear vibration of corrugated shallow shells under uniform load

Nonlinear vibration of corrugated shallow shells under uniform load

Nonlinear Vibration Analysis of Moving Strip with Inertial Boundary Condition

Large amplitude vibration of circular sandwich plates

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