As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-ofplane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.
Topological insulators (TIs) are recently discovered high‐tech materials where their potential use in nanoelectronic devices such as spintronics and quantum computers, due to their unique electronic features, can be a solution to the emerging need for high‐bit data processing. Yet their mechanical properties are not well understood for their use in practical applications. With the objective of exploiting the nanomechanical behaviour of TIs, bulk single‐crystal Bi2Se3 TI is grown by using the Bridgeman–Stockbarger method and mechanically characterised by the nanoindentation method. The Young's modulus and hardness were extracted from the load‐displacement data by using Oliver and Pharr's standard method. Further, fracture toughness of the material was reported for the first time after comprehensive research of indentation crack length (ICL) methods. The grown Bi2Se3 exhibits hardness and Young's modulus as 323 MPa and 6.018 GPa at nanoscale, respectively. Fracture toughness of the TI was evaluated at 0.034 MPa m1/2 and elastic recovery was around 60% after the full unloading process.
This paper presents a comprehensive investigation of the free vibrations of stepped straight and curved beams with different shapes and different materials. The beams are assumed to be Euler-Bernoulli type, and Finite Element Displacement Method (FEDM) is used as a computational approach. In-plane and out-of-plane vibration analyses are handled with stepped straight and curved beams at different end conditions. Material pairs of the stepped curved beam are considered as (i) steel-steel, (ii) steel-aluminum, (iii) steel-brass and (iv) steel-araldite. Results are given in tabular form and compared with those in literature and computations obtained by Ansys. The effects of beam shape and different material type on the vibration characteristics are also investigated.
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