Abstract
The differential transformation method (DTM) is applied to investigate free vibration of functionally graded beams supported by arbitrary boundary conditions, including various types of elastically end constraints. The material properties of functionally graded beams are assumed to obey the power law distribution. The main advantages of this method are known for its excellence in high accuracy with small computational expensiveness. The DTM also provides all natural frequencies and mode shapes without any frequency missing. Fundamental frequencies as well as their higher frequencies and mode shapes are presented. The significant aspects such as boundary conditions, values of translational and rotational spring constants and the material volume fraction index on the natural frequencies and mode shapes are discussed. For elastically end constraints, some available results of special cases for isotropic beams are used to validate the present results. The new frequency results and mode shapes of functionally graded beams resting on elastically end constraints are presented.
Highlights
A new class of composite materials, called functionally graded materials (FGMs), is considered in this paper
The differential transformation method (DTM) is applied to investigate free vibration of functionally graded beams supported by arbitrary boundary conditions, including various types of elastically end constraints
Yang and Chen [9] provided analytical solution based on classical beam theory (CBT) for investigating natural frequencies and critical buckling load of FG beams with edge cracks
Summary
A new class of composite materials, called functionally graded materials (FGMs), is considered in this paper. The Lagrange multiplier method was used to solve the fundamental frequency of FG beams based on different higherorder beam theories in the study of Simsek [5]. Wattanasakulpong et al [7] used an improved third order shear deformation theory to analyze free vibration of FG beams using the Ritz method. Yang and Chen [9] provided analytical solution based on classical beam theory (CBT) for investigating natural frequencies and critical buckling load of FG beams with edge cracks. UNGBHAKORN vious study on free vibration of FG beams supported by elastically end constraints in the open literature. The effective tool, DTM, is implemented to analyze free vibration of FG beams with arbitrary boundary conditions, including various types of elastically end constraints.
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