Mode switching phenomenon in geometrically nonlinear free vibration analysis of in-plane inhomogeneous plates on elastic foundation

Lohar, Hareram; Mitra, Anirban; Sahoo, Sarmila

doi:10.1515/cls-2018-0012

Cited by 4 publications

(2 citation statements)

References 43 publications

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“…One of the most frequent non-conventional dynamic characteristics of flexible members is the mode interaction phenomenon. 70 The curvature of initially curved beams, slenderness ratio, prescriptions of loading, and boundary conditions are the main factors for the appearance of such mode interaction phenomena. 71 Despite frequent applications of the practical curved beam-like structures vibrating around statically loaded configurations under continuous excitation, most of the reported studies focus on the dynamics of such flexible structures around the initial configuration.…”

Section: Introductionmentioning

confidence: 99%

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Theoretical analysis and a parametric study on forced vibration of large statically deformed curved beam with rigid links and moving support

Ghuku,

Mitra,

Sahoo

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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Forced vibration characteristics around large statically deformed configuration of curved beam system with rigid links and moving support are analyzed. In addition, the paper also investigates various parametric effects of height to span ratio and roller radius to height ratio coupled with support connection mechanism and profile shape, on dynamic characteristics of the curved beam system. The subject problem includes two interrelated problems: determining deformed configuration under static load and dynamic response of the loaded beam under harmonic excitation. The static problem is analyzed incrementally through the variational principle-based energy method in body-embedded curvilinear frame considering geometric nonlinearities due to combined bending-stretching and non-uniform initial curvature. In each incremental step, the nonlinear governing equation is solved iteratively, and kinematic constraints due to interactive deformation of the flexible curved beam with rigid links are imposed to obtain the global solution. Concerning the statically deformed configuration, governing equation for forced vibration is derived through Hamilton’s principle in curvilinear frame. Nonlinear effects caused by combined bending-stretching modes of vibration, non-uniform curvature, and lumped mass of the dead static load are considered. The set of inhomogeneous governing equations is solved through Broyden’s method. A direct substitution technique through successive relaxation is also employed to obtain an initial guess solution. Besides the forced vibration, free vibration analysis at static deformed configuration is also carried out for the completeness of the study. The theoretical model is validated through comparisons of loaded natural frequency results with finite element package. After the validation study, the effects of the mentioned geometric parameters on the dynamic response of the curved beam system are investigated and presented suitably. The physically insightful framework along with the parametric study may facilitate simulation and design of several practical structures involving moving support and rigid links subjected to continuous excitation around large statically deformed configurations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theoretical analysis and a parametric study on forced vibration of large statically deformed curved beam with rigid links and moving support

Ghuku,

Mitra,

Sahoo

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

Self Cite

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Optimization and Uncertain Nonlinear Vibration of Pre/post-buckled In-Plane Functionally Graded Metal Nanocomposite Plates

Hussein¹

2023

J. Vib. Eng. Technol.

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Purpose This paper studies the nonlinear free and forced vibration of in-plane bi-directional functionally graded (FG) metal nanocomposite plates considering uncertain material elastic properties in the pre/post buckling states. Initially, the distribution of the nano-reinforcement volume fraction is designed through an optimization process to minimize the amount of the reinforcement in case of simply supported and clamped plates. Methods The elastic modulus of the nanocomposite is modeled as a non-stationary random field using the Karhunen–Loève expansion (KLE) technique while the uncertain output variables are modeled using the polynomial chaos expansion (PCE). The considered plates are thin, so the classical plate theory with the von Kármán nonlinear strain field is used for the analysis. The harmonic balance method and the fourth-order Runge Kutta method are used to estimate the vibration responses. Results The in-plane optimization process of the nonreinforcement volume fraction distribution yielded a 14% and 70% saving in the reinforcement amount in the case of the simply supported plate and the clamped plate respectively. The uncertainty in the vibration amplitude in the pre-buckled state can be multiples of the uncertainty in the elastic modulus and follows near normal distributions. In the post-buckled state, the nature of the probability distribution depends on the excitation force and frequency. In general, the FG plates can have similar or more uncertainty levels compared to the equivalent homogenous plates. Conclusion The uncertainty in the nonlinear vibration of in-plane functionally graded plates depends on the boundary conditions, modeling definition of the input uncertainty, the excitation force and frequency.

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Static and dynamic analysis of thin functionally graded shell with in-plane material inhomogeneity

Wang

Liu

Zhou

et al. 2021

International Journal of Mechanical Sciences

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Mode switching phenomenon in geometrically nonlinear free vibration analysis of in-plane inhomogeneous plates on elastic foundation

Cited by 4 publications

References 43 publications

Theoretical analysis and a parametric study on forced vibration of large statically deformed curved beam with rigid links and moving support

Theoretical analysis and a parametric study on forced vibration of large statically deformed curved beam with rigid links and moving support

Optimization and Uncertain Nonlinear Vibration of Pre/post-buckled In-Plane Functionally Graded Metal Nanocomposite Plates

Static and dynamic analysis of thin functionally graded shell with in-plane material inhomogeneity

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