A new approach for free vibration of axially functionally graded beams with non-uniform cross-section

The first-order shear deformation beam theory for static and free vibration of axially loaded rectangular functionally graded beams is developed. In this theory, the improved transverse shear stiffness is derived from the in-plane stress and equilibrium equation and thus, associated shear correction factor is then obtained analytically. Equations of motion are derived from the Hamilton's principle. Analytical solutions are presented for simply-supported functionally graded beams. The obtained results are compared with the existing solutions to verify the validity of the developed theory. Effects of the power-law index, material contrast and Poisson's ratio on the displacements, natural frequencies, buckling loads and load-frequency curves as well as corresponding mode shapes are investigated.

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“…( [29], [30]) investigated the vibration of axially FG Timoshenko beams with non-uniform cross-section.…”

Section: Introductionmentioning

confidence: 99%

Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory

Nguyen

Thai

2013

Composites Part B: Engineering

140

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“…Based on Rayleigh-Ritz method (Huang and Li, 2010), the longitudinal and transverse vibration of the FCRM can be obtained as:…”

Section: Nonlinear Dynamic Modellingmentioning

confidence: 99%

Nonlinear modelling and dynamic stability analysis of a flexible Cartesian robotic manipulator with base disturbance and terminal load

Fan

et al. 2017

Mech. Sci.

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Abstract. The flexible Cartesian robotic manipulator (FCRM) is coming into widespread application in industry. Because of the feeble rigidity and heavy deflection, the dynamic characteristics of the FCRM are easily influenced by external disturbances which mainly concentrate in the driving end and the load end. Thus, with the influence of driving base disturbance and terminal load considered, the motion differential equations of the FCRM under the plane motion of the base are constructed, which contain the forced and non-linear parametric excitations originated from the disturbances of base lateral and axial motion respectively. Considering the relationship between the coefficients of the motion differential equations and the mode shapes of the flexible manipulator, the analytic expressions of the mode shapes with terminal load are deduced. Then, based on multiple scales method and rectangular coordinate transformation, the average equations of the FCRM are derived to analyze the influence mechanism of base disturbance and terminal load on the system parametric vibration stability. The results show that terminal load mainly affects the node locations of mode shapes and mode frequencies of the FCRM, and the axial motion disturbance of the driving base introduces parametric excitation while the lateral motion disturbance generates forced excitation for the transverse vibration model of the FCRM. Furthermore, with the increase of the base excitation acceleration and terminal load, the parametric vibration instability region of the FCRM increases significantly. This study will be helpful for the dynamic characteristics analysis and vibration control of the FCRM.

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“…The critical buckling load is closely related to the end supports of the beam. The expressions for the cantilever beam can be presented as follows [6]:…”

Section: Numerical Examplesmentioning

confidence: 99%

Vibrations of Functionally Graded Timoshenko Beams

Lepik

Hein

2014

Mathematical Engineering

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A new approach for free vibration of axially functionally graded beams with non-uniform cross-section

Cited by 292 publications

References 27 publications

Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory

Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory

Nonlinear modelling and dynamic stability analysis of a flexible Cartesian robotic manipulator with base disturbance and terminal load

Vibrations of Functionally Graded Timoshenko Beams

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