Metin O. Kaya

Free vibration analysis of a rotating Timoshenko beam by differential transform method

Purpose – To perform the flapwise bending vibration analysis of a rotating cantilever Timoshenko beam.Design/methodology/approach – Kinetic and potential energy expressions are derived step by step. Hamiltonian approach is used to obtain the governing equations of motion. Differential transform method (DTM) is applied to solve these equations.Findings – It is observed that the ρIΩ2θ term which is ignored by many researchers and which becomes more important as the rotational speed parameter increases must be included in the formulation.Originality/value – Kinetic and potential energy expressions for rotating Timoshenko beams are derived clearly step by step. It is the first time, for the best of authors knowledge, that DTM has been applied to the blade type rotating Timoshenko beams.

Application of Parameter Expanding Methods to Nonlinear Oscillators with Discontinuities

In this paper Hes modified Lindstedt-Poincare method and bookkeeping parameter method known as Parameter Expanding Methods are applied to nonlinear oscillators with discontinuities. We obtained sufficiently accurate solutions with first-order approximations which are valid for whole domain. Comparison of the obtained solutions with the exact ones show the proposed methods are very effective and convenient.

High-Order Energy Balance Method to Nonlinear Oscillators

Energy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator.

Energy Expressions and Free Vibration Analysis of a Rotating Uniform Timoshenko Beam Featuring Bending—torsion Coupling

In this study; free vibration analysis of a uniform, rotating, cantilever Timoshenko beam featuring coupling between flapwise bending and torsional vibrations is performed. At the beginning of the study, kinetic and potential energy expressions of a rotating Timoshenko beam having single cross-sectional symmetry are derived by using several explanatory tables and figures. In the following section, Hamilton’s principle is applied to the derived energy expressions to obtain the governing differential equations of motion. The parameters for the hub radius, rotational speed, rotary inertia, shear deformation, slenderness ratio and bending—torsion coupling are incorporated into the equations of motion. In the solution part, an efficient mathematical technique, called the differential transform method, is used to solve the governing differential equations of motion. Using the computer package Mathematica, the mode shapes are plotted and the effects of the incorporated parameters on the natural frequencies are investigated. The calculated results are tabulated in several tables and plotted in several graphs. In order to validate the calculated results, the beam is also modeled in the finite-element program ABAQUS. Moreover, two illustrative examples, chosen from open literature, are solved for further validation. Consequently, it is observed that there is a good agreement between the results.

High Order Hamiltonian Approach to Nonlinear Oscillators

This paper suggests a high order Hamiltonian approach to nonlinear oscillators. Two examples are given to illustrate the effectiveness of the method. The maximum relative error of Duffing oscillator obtained by Hes Hamiltonian approach is 2.22% ; while the present approach leads to 0.19% and 0.009% accuracy, respectively, for the second and third approximations.

Approximate solutions for nonlinear oscillation of a mass attached to a stretched elastic wire

In this paper, the approximate solutions of the mathematical model of a mass attached to a stretched elastic wire are presented. At the beginning of the study, the equation of motion is derived in a detailed way. Hes max-min approach, Hes frequency-amplitude method and the parameter-expansion method are implemented to solve the established model. The numerical results are further compared with the approximate analytical solutions for both a small and large amplitude of oscillations, and a very good agreement is observed. The relative errors are computed to illustrate the strength of agreement between the numerical and approximate analytical results.

Formulation for flutter and vibration analysis of a hingeless helicopter blade in hover: part II. Results of flutter stability and vibration analysis of a hingeless helicopter blade in hover

Purpose – This study aims to carry out flutter stability and vibration analysis of a uniform hingeless rotor blade in hovering flight conditions.Design/methodology/approach – The perturbation equations are obtained using the governing differential equations of motion derived in Part I (Aircraft Engineering and Aerospace Technology, Vol. 79 No. 2, 2007). The differential transform method (DTM) is applied to the perturbation equations of motion and the transformed equations are coded in the computer package Mathematica.Findings – The effects of the built‐in pretwist angle and the rotational speed ratio on the natural frequencies are investigated and the results are compared with the results in literature.Originality/value – This study, in carrying out an analysis of flutter stability and vibration of a uniform hingless rotor blade, is in good agreement with previous studies in the literature.

A low cost prototyping approach for design analysis and flight testing of the TURAC VTOL UAV

Over the last decade, the market share of civilian UAVs within the general UAV market has consistently increased. As such, these systems are increasingly being used for applications ranging from the monitoring of crops to the tracking of air emissions around high-pollution areas. Most of the civilian applications of UAVs require these vehicles to be of low-cost and for the portability and packaging to be easy while also having vertical take-off and landing capability. TURAC - a VTOL Tilt Rotor UAV with these capabilities - is designed. Although mathematical and CFD analyses were performed iteratively in order to optimize the design, testing in real life conditions were needed to see the real performance of the TURAC UAV. However, as with such an iterative design process, the manufacturing process costs, including different molds for each design, can be exorbitant. In addition, once an imperfection in the design is encountered, making radical design modifications on the UAV in real life is difficult and expensive. Therefore, a cheap, rapid, and easily reproducible prototyping methodology is essential. In this study, the end result of an iterative design process of TURAC is presented. In addition, a low-cost prototyping methodology is developed and its application is demonstrated in detail by explaining all of its phases. The ground and flight tests are applied on a fully functional prototype and the results are given.

Energy Derivation and Extension-Flapwise Bending Vibration Analysis of a Rotating Piezolaminated Composite Timoshenko Beam

In this study, extension and flapwise bending vibrations of a rotating piezolaminated composite Timoshenko beam are analyzed. Energy expressions are derived using several explanatory tables and figures. Parameters for the hub radius, rotational speed, rotary inertia, shear deformation, slenderness ratio, and ply orientation are incorporated into the equations of motion. The differential transform method is used to transform the differential equations of motion and the boundary conditions into simple analytical expressions. Numerical results are obtained to investigate the effects of the applied voltage, ply orientation, rotational speed, and hub radius on the natural frequencies and tip deflection.

Formulation for flutter and vibration analysis of a hingeless helicopter blade in hover: Part I

Purpose – This study aims to derive the kinetic and the potential energy expressions of a rotating uniform hingeless rotor blade and the aerodynamic loads that act on the blade element in hovering flight conditions.Design/methodology/approach – The blade is modeled as an Euler‐Bernoulli beam. The governing partial differential equations of motion and the associated boundary conditions are derived using the Hamiltons principle.Findings – The derivations of the energy expressions and the aerodynamic loads are made in a detailed way by including several explanatory tables. The resultant equations of motion are in good agreement with the literature. Additionally, in this work the hub radius effect is included in the equations of motion.Originality/value – Arguably this study achieves a breakthrough in deriving the kinetic and the potential energy expressions of a rotating uniform hingeless rotor blade and the aerodynamic loads that act on the blade element in hovering flight conditions.