Large amplitude forced vibration analysis of an axially functionally graded tapered beam resting on elastic foundation

Lohar, Hareram; Mitra, Anirban; Sahoo, Sarmila

doi:10.1016/j.matpr.2017.12.114

Cited by 3 publications

(1 citation statement)

References 15 publications

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“…Calim [21] studied the dynamic behavior of AFG thick beams. Lohar et al [7,22] performed large amplitude dynamic analysis on AFG non-uniform thin and thick beams utilizing Hamilton's principle. Trabelssi et al [23] investigated the dynamics of a nonlocal thick FG nanobeam to obtain the free vibrational frequencies and frequency-dependent responses of the system.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear free vibration analysis of non-uniform axially graded beam on variable elastic foundation

Lohar¹,

Mitra²

2022

FME Transactions

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The present work investigates the nonlinear free vibration of an axially functionally graded (AFG) beam supported on the variable foundation. The beam geometry is non-uniform, with a linear cross-section variation along the length. The beam material is graded along the axial direction following the power-law relation. A Winkler type of variable elastic foundation is taken, in which variation of stiffness is considered along the length of the foundation. Geometrical nonlinearity produced by the beam's large-amplitude deflection is also considered. To attain the desired objectives, the problem is divided into two parts. The static problem is solved first, then a subsequent free vibration analysis is executed on the statically deformed beam configuration. The governing differential equations of the system are derived using suitable energy methods. A numerical technique of direct substitution with relaxation is utilized to obtain the solution of the derived nonlinear differential equations. A suitable validation study is presented to ensure the appropriateness of the present methodology. Benchmark results are also presented by means of natural frequency, backbone curve, and mode shape plot to investigate the influences of elastic foundation, material gradation, and non-uniform geometry on nonlinear vibration.

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Section: Introductionmentioning

confidence: 99%

Nonlinear free vibration analysis of non-uniform axially graded beam on variable elastic foundation

Lohar¹,

Mitra²

2022

FME Transactions

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Analytical solution for vibration of functionally graded beams with variable cross-sections resting on Pasternak elastic foundations

Huang

2021

International Journal of Mechanical Sciences

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Effect of Boundary Conditions and Taper Patterns on Geometrically Nonlinear Frequency Response of Axially Graded Beams on Elastic Foundation

Lohar

Mitra

Sahoo³

2021

Handbook of Research on Advancements in Manufacturing, Materials, and Mechanical Engineering

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Forced vibration analysis is performed on a tapered axially functionally graded beam resting on elastic foundation under externally applied harmonic excitations to present the effect of boundary conditions and taper patterns on the frequency response. The elastic foundation is modelled in the present analysis as Winkler foundation. A displacement based semi-analytical method is adopted for mathematical formulation and the derivation of governing equations is carried out following Hamilton's principle. Von Karman nonlinear strain-displacement relation employed to incorporate geometric nonlinearity. Broyden method is adopted to solve the nonlinear set of equations. Frequency response curves are plotted in non-dimensional frequency-amplitude plane to represent nonlinear forced vibration characteristic of the system. New benchmark results are also provided for different combination of system parameters (i.e., excitation amplitudes, foundation stiffness values, material models, taper patterns, and flexural boundary conditions). Operational deflection shapes (ODS) are also presented.

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Large amplitude forced vibration analysis of an axially functionally graded tapered beam resting on elastic foundation

Cited by 3 publications

References 15 publications

Nonlinear free vibration analysis of non-uniform axially graded beam on variable elastic foundation

Nonlinear free vibration analysis of non-uniform axially graded beam on variable elastic foundation

Analytical solution for vibration of functionally graded beams with variable cross-sections resting on Pasternak elastic foundations

Effect of Boundary Conditions and Taper Patterns on Geometrically Nonlinear Frequency Response of Axially Graded Beams on Elastic Foundation

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