Geometrically nonlinear free vibration analysis of axially functionally graded taper beams

Kumar, Saurabh; Mitra, Anirban; Roy, Haraprasad

doi:10.1016/j.jestch.2015.04.003

Cited by 49 publications

(17 citation statements)

References 44 publications

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“…(1 À ). The higher-order functions are generated using Gram-Schmidt orthogonalisation procedure explained in detail by Kumar et al 35 which take care of the higher-order vibration modes. The above functions are numerically described at the computational points and by ordered multiplication of beam functions in two orthogonal directions the plate functions are obtained.…”

Section: Static Analysismentioning

confidence: 99%

Large amplitude free vibration study of non-uniform plates with in-plane material inhomogeneity

Kumar

Mitra

Roy

2016

Proceedings of the Institution of Mechanical Engineers, Part L:

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Free vibration study of non-uniform plates with in-plane material inhomogeneity is carried out in the present work considering geometric nonlinearity. Inhomogeneous plates where the material properties vary along only x-axis (unidirectional) and along both x-and y-axis (bidirectional) are considered. The analysis is performed for two boundary conditions namely clamped and simply supported at all edges, under the action of a transverse uniformly distributed load. The large amplitude problem is formulated using nonlinear strain-displacement relations along with a variational form of energy method. A two-step solution procedure is utilised where, in the first part the static problem is solved and undetermined coefficients are found, subsequently the dynamic problem is taken up on the basis of previously determined coefficients. Validity of the results is successfully confirmed by comparison with the works of other researchers. The analysis reveals that the amplitude and taper parameter affect the loaded natural frequencies significantly. Threedimensional mode shapes for linear and nonlinear cases are presented along with their respective contour plots.

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Section: Static Analysismentioning

confidence: 99%

Large amplitude free vibration study of non-uniform plates with in-plane material inhomogeneity

Kumar

Mitra

Roy

2016

Proceedings of the Institution of Mechanical Engineers, Part L:

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“…Furthermore the studies have been extended in mechanical analysis of small-sized structures [23][24][25][26][27][28][29][30][31]. Studies on non-uniform FG beams can also be found in literature [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47], while studies on non-uniform FG beams with an imperfection are scarce.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of cracked functionally graded non-uniform beams

Shabani

Cunedioĝlu

2020

Mater. Res. Express

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This paper presents the free vibration analysis of an edge cracked non-uniform symmetric beam made of functionally graded material. The Timoshenko beam theory is used for the finite element analysis of the multi-layered sandwich beam and the cantilever beam is modeled by 50 layers of material. The material properties vary continuously along the thickness direction according to the exponential and power laws. A MATLAB code is used to find the natural frequencies of two types of non-uniform beams, having a constant height but an exponential or linear width variation along the length of the beam. The natural frequencies of the beam are verified with ANSYS software as well as with available literature and good agreement is found. In the study, the effects of different parameters such as crack location, crack depth, power-law index, geometric index and taper ratio on natural frequencies are analyzed in detail.

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“…On the other hand, research effort devoted to AFG beams is quite limited and only recently researchers have taken interest into this domain. Various approaches have been adopted for investigating the static/buckling and dynamic behaviours of non-uniform AFG beams on the basis of Euler-Bernoulli beam model [12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear response of axially functionally graded Timoshenko beams on elastic foundation under harmonic excitation

Lohar

Mitra

Sahoo³

2019

Curved and Layered Structures

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Forced vibration of non-uniform axially functionally graded (AFG) Timoshenko beam on elastic foundation is performed under harmonic excitation. A linear elastic foundation is considered with three different classical boundary conditions. AFG materials are an advanced class of materials that have potential for application in various engineering fields. In the present work, variation of material properties along the longitudinal axis of the beam are considered according to power-law forms. Five values of material gradation parameter provides different functional variation and their effect on the frequency response of the system is studied. The present approximate method is displacement based and Von-Karman type of geometric nonlinearity is considered with rotational component to incorporate transverse shear. Hamilton’s principle is used to derive nonlinear set of governing equation and Broyden method is implemented to solve the nonlinear equations numerically. The results are successfully validated with previously published article. Frequency vs. amplitude curve corresponding to different combinations of system parameters are presented and are capable of serving as benchmark results. A separate free vibration analysis is undertaken to include backbone curves with the frequency response curves in the non-dimensional plane.

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Geometrically nonlinear free vibration analysis of axially functionally graded taper beams

Cited by 49 publications

References 44 publications

Large amplitude free vibration study of non-uniform plates with in-plane material inhomogeneity

Large amplitude free vibration study of non-uniform plates with in-plane material inhomogeneity

Free vibration analysis of cracked functionally graded non-uniform beams

Nonlinear response of axially functionally graded Timoshenko beams on elastic foundation under harmonic excitation

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