Abstract
The nonlinear forced vibration of bidirectional functionally graded porous material beams where the material components gradient change in both thickness and axial directions are studied in this study. Combining von Karman’s geometric nonlinearity and first-order shear deformation theory, the governing equations describing the coupled deformations are formulated as a system of nonlinear partial differential equations. Utilizing the Galerkin method, the formulated continuous model is transformed to a coupled nonlinear ordinary differential dynamic system. By accomplishing bifurcation calculation for periodic response of the discrete system using pseudoarclength technique, the vibration response curves are obtained by extracting the max-min amplitude of periodic motions. To highlight the effect of nonlinearity, the linear and nonlinear dynamic responses of beam are demonstrated. It is found that the periodic motion of beam may undergo cyclic-fold bifurcation. Numerical results are presented to examine the effects of the system parameters, e.g., gradient indexes, porosity, damping coefficients, and aspect ratio.
Highlights
Graded materials (FGMs) are a class of composites which have a continuous variation of material properties in one or more directions and have the ability to lessen the phenomenon of stress concentration that is usually unavoidable in laminated composites
Adopting the differential quadrature method (DQM), Esfahani et al [3] performed thermal buckling analysis of FG beams sited on the elastic foundation with nonlinear reaction force
Considering the materials grading in thickness or axial direction, Alshorbagy et al [4] showed the vibration characteristics of FG beams employing the finite element method (FEM)
Summary
Graded materials (FGMs) are a class of composites which have a continuous variation of material properties in one or more directions and have the ability to lessen the phenomenon of stress concentration that is usually unavoidable in laminated composites. Niknam et al [2] provided the analytical solution of the nonlinear bending of tapered functionally graded beam under action of thermal and mechanical load. Considering the materials grading in thickness or axial direction, Alshorbagy et al [4] showed the vibration characteristics of FG beams employing the finite element method (FEM). Truong and co-workers [15, 16] proposed an evolution method for material optimization in the design of bending and free vibration behaviors of BDFG beam. The nonlinear forced vibration response of BDFG porous beam with different boundary conditions has not been reported. We attempt to explore the nonlinear forced vibration response of BDFG porous beam under action of lateral harmonic excitation. Numerical simulations are given to explain the influences of material, porosity, and geometrical parameters on the nonlinear primary resonance of BDFG beam
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