Browsing by Author "Inman, Daniel J."

Now showing 1 - 4 of 4

Citation - WoS: 8
Citation - Scopus: 6
Coupled Bending-Bending Vibration of a Pre-Twisted Beam With Aerofoil Cross-Section by the Finite Element Method
(Hindawi Publishing Corporation, 2003) Yardımoğlu, Bülent; Yardımoğlu, Bülent; Inman, Daniel J.; 03.10. Department of Mechanical Engineering; 03. Faculty of Engineering; 01. Izmir Institute of Technology
The present study deals with a finite element model for coupled bending-bending-torsion vibration analysis of a pretwisted Timoshenko beam with varying aerofoil cross-section. The element derived in this paper has two nodes, with seven degrees of freedom at each node. The nodal variables are transverse displacements, cross-section rotations and the shear angles in two planes and torsional displacement. The advantage of the present element is the exclusion of unnecessary derivatives of fundamental nodal variables, which were included to obtain invertable square matrix by other researchers, by choosing proper displacement functions and using relationship between cross-sectional rotation and the shear deformation. Element stiffness and mass matrices are developed from strain and kinetic energy expressions by assigning proper order polynomial expressions for cross-section properties and considering higher order coupling coefficients. The correctness of the present model is confirmed by the experimental results available in the literature. Comparison of the proposed model results with those in the literature indicates that a faster convergence is obtained. The results presented also provide some insights in the formulation by clearly indicating that higher order coupling terms have considerable influence on the natural frequencies.
Citation - WoS: 11
Citation - Scopus: 14
Coupled Bending-Bending Vibration of a Rotating Pre-Twisted Beam With Aerofoil Cross-Section and Flexible Root by Finite Element Method
(Hindawi Publishing Corporation, 2004) Yardımoğlu, Bülent; Yardımoğlu, Bülent; Inman, Daniel J.; 03.10. Department of Mechanical Engineering; 03. Faculty of Engineering; 01. Izmir Institute of Technology
The purpose of this paper is to extend a previously published beam model of a turbine blade including the centrifugal force field and root flexibility effects on a finite element model and to demonstrate the performance, accuracy and efficiency of the extended model for computing the natural frequencies. Therefore, only the modifications due to rotation and elastic root are presented in great detail. Considering the shear center effect on the transverse displacements, the geometric stiffness matrix due to the centrifugal force is developed from the geometric strain energy expression based on the large deflections and the increase of torsional stiffness because of the axial stress. In this work, the root flexibility of the blade is idealized by a continuum model unlike the discrete model approach of a combination of translational and rotational elastic springs, as used by other researchers. The cross-section properties of the fir-tree root of the blade considered as an example are expressed by assigning proper order polynomial functions similar to cross-sectional properties of a tapered blade. The correctness of the present extended finite element model is confirmed by the experimental and calculated results available in the literature. Comparisons of the present model results with those in the literature indicate excellent agreement.
Citation - Scopus: 6
Coupled Out of Plane Vibrations of Spiral Beams
(American Institute of Aeronautics and Astronautics Inc. (AIAA), 2009) Karami, M. A.; Yardımoğlu, Bülent; Yardımoğlu, Bülent; Inman, Daniel J.; 03.10. Department of Mechanical Engineering; 03. Faculty of Engineering; 01. Izmir Institute of Technology
An analytical method is proposed to calculate the natural frequencies and corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equation and the boundary conditions are derived using Hamilton's principle. The vibration problem of a constant radius curved beam is solved using a general exponential solution with complex coefficients. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the R′ terms have negligible effect on the structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joint together to consider the slow change of radius along the spiral. The natural frequencies and mode shapes of two spiral structures have been calculated for illustration.
Citation - WoS: 30
Citation - Scopus: 33
Coupled Out of Plane Vibrations of Spiral Beams for Micro-Scale Applications
(Academic Press Inc., 2010-12) Karami, M. A.; Yardımoğlu, Bülent; Yardımoğlu, Bülent; Inman, Daniel J.; 03.10. Department of Mechanical Engineering; 03. Faculty of Engineering; 01. Izmir Institute of Technology
An analytical method is proposed to calculate the natural frequencies and the corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equations and the boundary conditions are derived using Hamilton's principle. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the derivative of the radius terms have negligible effect on structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joined together to approximate the slow change of radius along the spiral. The equations of motion are formulated in non-dimensional form and the effect of all the key parameters on natural frequencies is presented. Non-dimensional curves are used to summarize the results for clarity. We also solve the governing equations using Rayleigh's approximate method. The fundamental frequency results of the exact and Rayleigh's method are in close agreement. This to some extent verifies the exact solutions. The results show that the vibration of spirals is mostly torsional which complicates using the spiral beam as a host for a sensor or energy harvesting device.