In the present work, a comparative study has been carried out between sandwich functionally graded beams made up of power law and exponential and sigmoidal laws under free vibration conditions. The study has been carried out using the recently proposed higher-order zigzag theory. The present formulation satisfies all important necessary conditions such as interlaminar transverse stress continuity condition at the interface. The present formulation incorporates transverse normal stress and hence is more efficient. Also, the present formulation satisfies zero transverse shear stress conditions at the top and bottom surface of the beam. Three-noded C-0 finite element having eight degrees of freedom per node is used during the study. The present formulation is free from any post-processing requirements. The efficiency of the present model has been carried out by comparing the present results for the power-law sandwich FGM beam with those available in the literature. Variation of stresses across the thickness for the first six modes in graphical form is also reported. Several new results have also been presented in the manuscript, especially for exponential and sigmoidal sandwich FGM beams, which will serve as the benchmark for future studies.

Finite Element-based Free Vibration Analysis of Power-Law, Exponential and Sigmoidal Functionally Graded Sandwich Beams

This study aims to develop the governing differential equation and to analyze the free vibration of a rotating non-uniform beam having a flexible root and setting angle for variations in operating conditions and structural design parameters.,Hamiltonian principle is used to derive the flapwise bending motion of the structure, and the governing differential equations are solved numerically by using differential quadrature with satisfactory accuracy and computation time.,The results obtained by using the differential quadrature method (DQM) are compared to results of previous studies in the open literature to show the power of the used method. Important results affecting the dynamics characteristics of a rotating beam are tabulated and illustrated in concerned figures to show the effect of investigated design parameters and operating conditions.,The principal novelty of this paper arises from the application of the DQM to a rotating non-uniform beam with flexible root and deriving new governing differential equation including various parameters such as rotary inertia, setting angle, taper ratios, root flexibility, hub radius and rotational speed. Also, the application of the used numerical method is expressed clearly step by step with the algorithm scheme.

Free vibration analysis of a rotating double tapered beam with flexible root via differential quadrature method

Buckling and free vibration characteristics of functionally graded porous metal ceramic beams subjected to mechanical and thermal loads are presented. Five-noded, beam element with ten degrees of freedom is used to analyse the buckling and vibration behaviour. The effects of porosity, porosity pattern, functional grading of material, elastic foundations, slenderness ratio and different boundary conditions are analysed for critical comparison of behaviour of the beam under thermal and mechanical load. Results revealed that buckling and dynamic behaviour of the beam under thermal load is significantly different compared to the mechanical load. It is also observed that nature of porosity distribution and its volume fraction also influences the buckling strength significantly. Beam with uniform porosity shows better thermal buckling strength likewise beam with graded porosity for mechanical buckling strength.

Buckling and Free Vibration of Porous Functionally Graded Metal Ceramic Beams under Thermal and Mechanical Loading: A Comparative Study

A flapwise vibration analysis is performed on a functionally graded tapered rotating beam with tip mass. The beam is considered as functionally graded, whose material properties varying in the direction of thickness. It is assumed as beam is a taper beam with uniform width. Using Mori Tanaka method the properties of the functionally graded material are achieved. The first three frequencies of flapwise are obtained using finite element analysis based software ANSYS. By comparing with the results in open literature, the accuracy of the results is tested. The proposed method yielded good results compared with the existing Frobenious method because of good mesh capabilities. Different parametric studies are carried out to investigate the influence of tip mass on the functionally graded (FG) rotating taper beam flapwise frequencies. The influence of rotating speed, hub radius ratio, gradient index, taper ratio and hub radius ratio on flapwise frequency are elaborated with the support of ANSYS results and analytical models. The results show that the variation in tip mass tends to depress the frequencies from 107.19 Hz to 25.31 Hz at 100 rps in fundamental frequency and in third frequency it is decreased from 336.70 to 332.13 Hz at the same rotational speed. Cite this article as: Kumar P R , Nancharaiah T, Kumar D S , K alam S A , Balakrishna G. Flapwise vibration of functionally graded rotating tapered beam with tipmass. Sigma J Eng Nat Sci 2022;40(3): 630 – 638 .

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Flapwise vibration of functionally graded rotating tapered beam with tipmass

Rotating beams are the practical application for aircraft propellers, helicopter blades, wind mill propeller, turbine blades and spinning space structures. In these structures, taper beams are preferred due to optimum weight distribution with uniform strength. Vibration behavior of tapered variable section beams subjected to centrifugal forces is important in analysis of structures. The research work deals with flapwise vibration of functionally graded (FG) rotating taper beam. The material properties of the beam change symmetrically in the direction of thickness from middle surface to the outer surfaces. Mori-Tanaka method estimates these properties of FG beam. The flapwise frequencies are obtained using Differential Transform Method (DTM). The effect of different parameters such as rotating speed, taper ratio, hub radius ratio and gradient index on flapwise frequency is discussed.

Pacharu Ravi Kumar

Papers

Effect of Taper on Free Vibration of Functionally Graded Rotating Beam by Mori-Tanaka Method