Natural Frequencies of Beams with Axial Material Gradation Resting on Two Parameter Elastic Foundation

Free vibration analysis is carried out on axially inhomogeneous beams resting Winkler-Pasternak elastic foundation. The material properties of the beam like Young’s modulus, modulus rigidity and density are considered to be varying along length direction following constant, linear exponential models. subjected different combinations clamped simply supported boundary conditions. formulation based Timoshenko theory energy method with Hamilton’s principle used derive governing equations. effect gradation 2 parameters foundation natural frequencies studied in detail. present results validated by comparing them established ones satisfactory matching observed.
 HIGHLIGHTS
 
 behavior functionally graded investigated
 Three models three conditions considered
 Effect two parameter Rayleigh Ritz employed
 It found that stiffness significantly affects frequency beam
 GRAPHICAL ABSTRACT