Exact frequency equations of free vibration of exponentially non-uniform functionally graded Timoshenko beams

Tang, A.-Y.; Wu, Jingxiang; Li, Xian-Fang; Lee, K.Y.

doi:10.1016/j.ijmecsci.2014.08.017

Cited by 101 publications

(31 citation statements)

References 31 publications

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“…Therefore, this gap is aimed to be fulfilled in this paper. However, in this study, a functionally graded Timoshenko beam with a power-law gradient is considered and the efficiency of DTM has not been examined for other gradients such as exponent gradient (Tang et al, 2014; Hao and Wei, 2016; Li et al, 2013;Wang et al, 2016). The examination of the DTM efficiency for other gradient types can be considered as a challenging future work.…”

Section: Future Workmentioning

confidence: 99%

Application of the differential transform method to the free vibration analysis of functionally graded Timoshenko beams

Őzdemir

2016

jtam

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In this study, free vibration characteristics of a functionally graded Timoshenko beam that undergoes flapwise bending vibration is analysed. The energy expressions are derived by introducing several explanotary figures and tables. Applying Hamilton's principle to the energy expressions, governing differential equations of motion and boundary conditions are obtained. In the solution part, the equations of motion, including the parameters for rotary inertia, shear deformation, power law index parameter and slenderness ratio are solved using an efficient mathematical technique, called the differential transform method (DTM). Natural frequencies are calculated and effects of several parameters are investigated.

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Section: Future Workmentioning

confidence: 99%

Application of the differential transform method to the free vibration analysis of functionally graded Timoshenko beams

Őzdemir

2016

jtam

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“…The boundary conditions for simply supported plates with immovable edges (SSI) are: Three expansions of plate displacements are used to discretize the system for the different boundary conditions. For simply supported movable (SSM) edges, the displacements u, v and w and rotations φ 1 and φ 2 are expanded by using the following expressions, which satisfy identically the geometric boundary conditions: [26][27][28][29][30] where m and n are the numbers of half-waves in the x and y directions, respectively, and t is the time; u m,n (t), v m,n (t), w m,n (t), φ 1 m,n (t) and φ 2 m,n (t) are the generalized coordinates, which are unknown functions of t. M and N indicate the terms necessary in the expansion of the in-plane displacements and, in general, are larger thanM andN , respectively, which indicate the terms in the expansion of out-of-plane displacement and rotations.…”

Section: Appendix A: Boundary Conditions and Discretizationmentioning

confidence: 99%

“…Tang et al [29] have analyzed the free vibration of nonuniform functionally graded beams via the Timoshenko beam theory. They assumed the bending stiffness and distributed mass density to obey a unified exponential law and derived exact frequency equations in closed form for various boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid

Khorshidi

Bakhsheshy

2015

Acta Mech

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This study investigates the vibration analysis of a functionally graded (FG) rectangular plate partially in contact with a bounded fluid. The material properties are assumed to vary continuously through the thickness direction according to a simple power-law distribution in terms of volume fraction of material constituents. Wet dynamic transverse displacements of the plate are approximated by a set of admissible trial functions, which are required to satisfy the clamped and simply supported geometric boundary conditions. The fluid velocity potential satisfying fluid boundary conditions is derived, and wet dynamic modal functions of the plate are expanded in terms of finite Fourier series for compatibility requirement along the contacting surface between the plate and the fluid. Natural frequencies of the plate coupled with sloshing fluid modes are calculated using the Rayleigh-Ritz method based on minimizing the Rayleigh quotient. The proposed analytical method is validated with available data in the literature. In the numerical results, the effects of boundary conditions, aspect ratios, thickness ratios, gradient index, material properties of the FG plate, depth of the fluid and dimensions of the tank on the wet natural frequencies are investigated.

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“…The exact solution to free vibration of exponentially axially graded beams was presented by Li et al (2013). Explicit frequency equations of free vibration of exponentially FG Timoshenko beams were derived by Tang et al (2014). Huang et al (2013) presented a new approach to the investigation of free vibration of axially functionally graded Timoshenko beams.…”

Section: Introductionmentioning

confidence: 99%

An approach for free vibration analysis of axially graded beams

Kukla¹,

Rychlewska²

2016

jtam

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In this study, the solution to the free vibration problem of axially graded beams with a non-uniform cross-section has been presented. The proposed approach relies on replacing functions characterizing functionally graded beams by piecewise exponential functions. The frequency equation has been derived for axially graded beams divided into an arbitrary number of subintervals. Numerical examples show the influence of the parameters of the functionally graded beams on the free vibration frequencies for different boundary conditions.

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Exact frequency equations of free vibration of exponentially non-uniform functionally graded Timoshenko beams

Cited by 101 publications

References 31 publications

Application of the differential transform method to the free vibration analysis of functionally graded Timoshenko beams

Application of the differential transform method to the free vibration analysis of functionally graded Timoshenko beams

Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid

An approach for free vibration analysis of axially graded beams

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