Abstract
BackgroundThe geometrically non-linear formulation based on Von-Karman’s hypothesis is used to study the free vibration isosceles triangular plates by using four types of mixtures of functionally graded materials (FGMs - AL/AL2O3, SUS304/Si3N4, Ti- AL-4V/Aluminum oxide, AL/ZrO2). Material properties are assumed to be temperature dependent and graded in the thickness direction according to power law distribution.MethodsA hierarchical finite element based on triangular p-element is employed to define the model, taking into account the hypotheses of first-order shear deformation theory. The equations of non-linear free motion are derived from Lagrange's equation in combination with the harmonic balance method and solved iteratively using the linearized updated mode method.ResultsResults for the linear and nonlinear frequencies parameters of clamped isosceles triangular plates are obtained. The accuracy of the present results are established through convergence studies and comparison with results of literature for metallic plates. The results of the linear vibration of clamped FGMs isosceles triangular plates are also presented in this study.ConclusionThe effects of apex angle, thickness ratio, volume fraction exponent and mixtures of FGMs on the backbone curves and mode shape of clamped isosceles triangular plates are studied. The results obtained in this work reveal that the physical and geometrical parameters have a important effect on the non-linear vibration of FGMs triangular plates.
Highlights
The geometrically non-linear formulation based on Von-Karman’s hypothesis is used to study the free vibration isosceles triangular plates by using four types of mixtures of functionally graded materials (FGMs - AL/ AL2O3, SUS304/Si3N4, Ti- AL-4V/Aluminum oxide, AL/ZrO2)
functionally graded Materials (FGMs) clamped isosceles triangular plates was analyzed by a triangular p-element
The material properties of the functionally graded triangular plate assumed to be graded only in the thickness direction according to a b simple power law distribution in terms of the volume fraction of the constituents
Summary
The geometrically non-linear formulation based on Von-Karman’s hypothesis is used to study the free vibration isosceles triangular plates by using four types of mixtures of functionally graded materials (FGMs - AL/ AL2O3, SUS304/Si3N4, Ti- AL-4V/Aluminum oxide, AL/ZrO2). Material properties are assumed to be temperature dependent and graded in the thickness direction according to power law distribution. The geometrically non-linear vibration of functionally graded Materials (FGMs) for different structures has acquired great interest in many researches. FGMs are composite materials which are microscopically inhomogeneous. The mechanical properties of FGMs are expressed with mathematical functions, and assumed to vary continuously from one surface to the other. Since the variation of mechanical properties of FGM is nonlinear, studies based on the nonlinear deformation theory is required for these type of materials.
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