Open AccessNatural Frequencies of Beams with Axial Material Gradation Resting on Two Parameter Elastic Foundation
Author(s) -
Saurabh Kumar
Publication year - 2022
Publication title -
trends in sciences
Language(s) - English
Resource type - Journals
ISSN - 2774-0226
DOI - 10.48048/tis.2022.3048
Subject(s) - gradation , timoshenko beam theory , vibration , axial symmetry , beam (structure) , foundation (evidence) , boundary value problem , stiffness , natural frequency , rayleigh–ritz method , rigidity (electromagnetism) , elastic modulus , material properties , constant (computer programming) , hamilton's principle , modulus , mechanics , structural engineering , materials science , mathematics , mathematical analysis , physics , engineering , composite material , acoustics , law , programming language , computer science , computer vision , political science
Free vibration analysis is carried out on axially inhomogeneous beams resting on Winkler-Pasternak elastic foundation. The material properties of the beam like Young’s modulus, modulus of rigidity and material density are considered to be varying along the length direction following constant, linear and exponential material models. The beam is subjected to different combinations of clamped and simply supported boundary conditions. The formulation is based on Timoshenko beam theory and energy method along with Hamilton’s principle is used to derive the governing equations. The effect of material gradation and the 2 parameters of elastic foundation on the natural frequencies are studied in detail. The present results are validated by comparing them with established ones and satisfactory matching is observed.
HIGHLIGHTS
Free vibration behavior of axially functionally graded beams in investigated
Three different material models and three boundary conditions are considered
Effect of two parameter elastic foundation is considered
Timoshenko beam theory and Rayleigh Ritz method are employed
It is found that the stiffness of elastic foundation significantly affects the natural frequency of the beam
GRAPHICAL ABSTRACT