Browsing by Author "Dinckal, C."

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Citation - WoS: 16
Citation - Scopus: 15
Free Vibration Analysis of Carbon Nanotubes by Using Finite Element Method
(Springer, 2016) Dinckal, C.
In the present study, an efficient and accurate finite element model for vibration analysis of carbon nanotubes (CNTs) with both Euler-Bernoulli and Timoshenko beam theory has been presented. For this purpose, an analytical solution for the exact dynamic shape functions of CNTs based on both Euler-Bernoulli and Timoshenko beam theories has been derived. The solution is general and is not restricted to a particular range of magnitudes of the nonlocal parameters. The exact dynamic shape functions have been utilized to derive analytic expressions for the coefficients of the exact dynamic (frequency-dependent) element stiffness matrix. Numerical results are presented to figure out the effects of nonlocal parameter, mode number and slenderness ratio on the vibration characteristics of CNTs. It is shown that these results are in good agreement with those reported in the literature. Present element formulation will be useful for structural analyses of nanostructures with complex geometries, loadings, material properties and boundary conditions.
On the Properties of Piezoelectric Materials Based Upon Orthonormal Representations
(Crc Press-taylor & Francis Group, 2014) Dinckal, C.; Dinckal, C.
For piezoelectric tensor, the decomposition method based upon irreducible orthogonal representation is overviewed. Besides, orthonormal tensor basis method is improved to express any third rank tensors such as piezoelectric tensor showing the piezoelectric effect of the material properties on the structures. Numerical examples for materials from different crystal symmetry classes serve to illustrate and verify the orthonormal tensor basis method. The differences and similarities are stated by comparing the methods presented in this work and the others in literature. It is also demonstrated that for hexagonal symmetry, each decomposed parts obtained from orthonormal tensor basis method has physical meaning. Furthermore, the norm based upon orthonormal tensor basis representation of piezoelectric tensor is obtained explicitly for each crystal symmetry classes and those results are used to study the piezoelectric effect of different materials. It is also shown that one can determine in which material the piezoelectric effect is stronger by using the norm concept for any material from various crystal symmetry classes.