• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.21 no.10
• /
• pp.1580-1588
• /
• 1997

A modeling method for the flapwise bending vibration of a rotating cantilever beam which has small slenderness ratio is presented in this paper. It is shown that as the slenderness ratio decreases the shear and rotary inertia effects increase. Such effects become critical for the accurate estimation of the natural frequencies and modeshapes, especially higher frequencies and modes, as the angular speed increases. It is also shown that the flapwise bending natural frequencies are higher than the chordwise bending natural frequencies. The discrepancy between first natural frequencies are especially significant when the hub radius ratio is small.

• Structural Engineering and Mechanics
• /
• v.72 no.2
• /
• pp.229-244
• /
• 2019

Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

• Proceedings of the KSME Conference
• /
• 2000.04a
• /
• pp.613-618
• /
• 2000

It is well known that the rotating motion of a blade-like structure induces centrifugal inertia force that causes the variation of the natural frequencies of the structure. Even though most of blade-like structures can be successfully Idealized as beams, some behave like plates rather than beams. This paper presents a modeling method for the flapwise bending vibration analysis of rotating cantilever plates. The dependence of natural frequencies and free vibration modes on the angular speed as well as the aspect ratio of a rotating plate is investigated. Particularly. the natural frequency loci crossing is observed and discussed In the present study.

• Smart Structures and Systems
• /
• v.21 no.3
• /
• pp.257-262
• /
• 2018

Vibrational problems in the domestic Small Horizontal Axis Wind Turbines (SHAWT) are due to flap wise vibrations caused by varying wind velocities acting perpendicular to its blade surface. It has been reported that monitoring the structural health of the turbine blades requires special attention as they are key elements of a wind power generation, and account for 15-20% of the total turbine cost. If this vibration problem is taken care, the SHAWT can be made as commercial success. In this work, Shape Memory Alloy (SMA) wires made of Nitinol (Ni-Ti) alloys are embedded into the Glass Fibre Reinforced Polymer (GFRP) wind turbine blade in order to reduce the flapwise vibrations. Experimental study of Nitinol (Ni-Ti) wire characteristics has been done and relationship between different parameters like current, displacement, time and temperature has been established. When the wind turbine blades are subjected to varying wind velocity, flapwise vibration occurs which has to be controlled continuously, otherwise the blade will be damaged due to the resonance. Therefore, in order to control these flapwise vibrations actively, a non-linear current controller unit was developed and fabricated, which provides actuation force required for active vibration control in smart blade. Experimental analysis was performed on conventional GFRP and smart blade, depicted a 20% increase in natural frequency and 20% reduction in amplitude of vibration. With addition of active vibration control unit, the smart blade showed 61% reduction in amplitude of vibration.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.2
• /
• pp.348-353
• /
• 1995

When cantilever beams rotate, their bending stiffnesses change due to the stretching caused by centrifugal inertia forces. Such phenomena result in variations of natural frequencies and mode shapes associated with constant speed rotational motions of the beams. These variations are important in many practical applications such as helicopter blades, turbomachines, and space structures. This paper presents the formulation of a set of linear equations governing the flapwise bending vibration of rotating cantilever beams. These equations can be used to provide accurate predictions of the variations of natural frequencies and mode shapes due to rotation.

• Journal of KSNVE
• /
• v.8 no.2
• /
• pp.353-360
• /
• 1998

In this paper, a modeling method for the bending vibration analysis of rotating Timoshenko beams with concentrated mass and mass moment of inertia is presented. The shear and rotary inertia effects become critical for the accurate estimation of the natural frequencies and mode shapes as the slenderness ratio decreases. The natural frequencies obtained by using the Timoshenko beam theory are lower than those by using the Euler beam theory. The critical angular speed, which does not exist only with the concentrated mass, exists with the concentrated mass moment of inertia.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2003.11a
• /
• pp.994-999
• /
• 2003

A modeling method for the modal analysis of a rotating cross-ply composite beam based on Timoshenko beam theory is presented. To analyze the composite beam exactly, the effects of shear deformation and rotary inertia are included. Linear differential equations of motion are derived using the assumed mode method. For the modeling, hybrid deformation variables are employed and approximated to derive the equations of motion. The effects of the dimensionless angular velocity and the slenderness ratio parameter on the variations of modal characteristics are investigated

• Proceedings of the KSME Conference
• /
• 2003.04a
• /
• pp.887-892
• /
• 2003

A modeling method for the modal analysis of a rotating composite beam is presented in this paper. Linear differential equations of motion are derived by using the assumed mode method. For the modeling, hybrid deformation variables are employed and approximated to derive the equations of motion Symmetrical laminated layers are considered for the composite beam. The effects of the dimensionless angular velocity, the hub radius and the fiber orientation angle parameter on the variations of modal characteristics are investigated.

• Journal of Mechanical Science and Technology
• /
• v.18 no.2
• /
• pp.240-245
• /
• 2004

A modeling method for the modal analysis of a rotating composite cantilever beam is presented in this paper. Linear differential equations of motion are derived using the assumed mode method. For the modeling, hybrid deformation variables are employed and approximated to derive the equations of motion. Symmetrical laminated composite beams are considered to obtain the numerical results. The effects of the dimensionless angular velocity, the hub radius and the fiber orientation angle on the variations of modal characteristics are investigated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2012.04a
• /
• pp.144-149
• /
• 2012

The transfer matrix method is used to determine the dynamic characteristics(natural frequencies and mode shapes) by rotational speed of wind turbine blade. The problems treated on this study is coupled flapwise bending and chordwise bending of pre-twisted nonuniform wind turbine blade. The orthogonality relations that exist between the vibrational modes is derived and the algorithm for determination of the natural vibrational characteristics is suggested.