Additional Investigations Into the Natural Frequencies and Critical Speeds of a Rotating, Flexible Shaft-Disk System

2007 ◽  
Author(s):  
Lyn M. Greenhill ◽  
Valerie J. Lease
Keyword(s):  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Rotor Dynamics ◽  
Axial Position ◽  
Disk System ◽  
Apparent Contradiction ◽  
Critical Speeds ◽  
Shaft Flexibility ◽  
Gyroscopic Effects ◽  
Lumped Masses

Traditional rotor dynamics analysis programs make the assumption that disk components are rigid and can be treated as lumped masses. Several researchers have studied this assumption with specific analytical treatments designed to simulate disk flexibility. The general conclusions reached by these studies indicated disk flexibility has little effect on critical speeds but significantly influences natural frequencies. This apparent contradiction has been reexamined by using axisymmetric harmonic finite elements to directly represent both disk and shaft flexibility along with gyroscopic effects. Results from this improved analysis show that depending on the thickness-to-diameter (slenderness) ratio of the disk and the axial position of the disk on the shaft, there are significant differences in all natural frequencies, for both forward and backward modes, including synchronous crossings at critical speeds.

scholarly journals A Simulation Model for Computing the Loads Generated at Landing Site During Helicopter Take-Off or Landing Operation

2019 ◽  
Vol 2019 (2) ◽  
pp. 59-75
Author(s):  
Jarosław Stanisławski
Keyword(s):  
Equations Of Motion ◽  
Landing Site ◽  
Simulation Method ◽  
Rigid Bodies ◽  
Landing Gear ◽  
Rotor Blades ◽  
Wind Gust ◽  
The Galerkin Method ◽  
Lumped Masses ◽  
And Control

Summary The paper presents simulation method and results of calculations determining behavior of helicopter and landing site loads which are generated during phase of the helicopter take-off and landing. For helicopter with whirling rotor standing on ground or touching it, the loads of landing gear depend on the parameters of helicopter movement, occurrence of wind gusts and control of pitch angle of the rotor blades. The considered model of helicopter consists of the fuselage and main transmission treated as rigid bodies connected with elastic elements. The fuselage is supported by landing gear modeled by units of spring and damping elements. The rotor blades are modeled as elastic axes with sets of lumped masses of blade segments distributed along them. The Runge-Kutta method was used to solve the equations of motion of the helicopter model. According to the Galerkin method, it was assumed that the parameters of the elastic blade motion can be treated as a combination of its bending and torsion eigen modes. For calculations, data of a hypothetical light helicopter were applied. Simulation results were presented for the cases of landing helicopter touching ground with different vertical speed and for phase of take-off including influence of rotor speed changes, wind gust and control of blade pitch. The simulation method may help to define the limits of helicopter safe operation on the landing surfaces.

A new simplified method for anti-symmetric mode in-plane vibrations of frame structures with column cracks

2016 ◽  
Vol 24 (24) ◽  
pp. 5794-5810 ◽  
Author(s):  
Kemal Mazanoglu ◽  
Elif C Kandemir-Mazanoglu
Keyword(s):  
Beam Theory ◽  
Equivalent Model ◽  
Frame Structures ◽  
Symmetric Mode ◽  
Lumped Mass ◽  
Beam Elements ◽  
Local Flexibility ◽  
Mode Vibration ◽  
Frame Systems ◽  
Lumped Masses

This paper is on the natural frequency and mode shape computation of frame structures with column cracks. First, a model of intact frame structures is built to perform vibration analysis. Beam elements are considered as lumped masses and rotational springs at the storey levels of frames. Equivalent model of columns and lumped mass-stiffness effects of beams have been combined to carry out continuous solution for the anti-symmetric mode in-plane vibrations of frames. In addition, frame systems with multiple column cracks are analyzed in terms of anti-symmetric mode vibration characteristics. Cracks are considered as massless rotational springs in compliance with the local flexibility model. Compatibility and continuity conditions are satisfied at crack and storey locations of the equivalent column, modeled using the Euler–Bernoulli beam theory. The proposed method is tested for single-storey single- and multi-bay, H-type and double-storey single-bay frame systems with intact and cracked columns. Results are validated by those given in the current literature and/or obtained by the finite element analyses.

scholarly journals Experimental feedback linearisation of a non-smooth nonlinear system by the method of receptances

2018 ◽  
Vol 24 (2) ◽  
pp. 465-482 ◽  
Author(s):  
Domenico Lisitano ◽  
Shakir Jiffri ◽  
Elvio Bonisoli ◽  
John E Mottershead
Keyword(s):  
Nonlinear System ◽  
Dynamic Behaviour ◽  
Complete System ◽  
Degree Of Freedom ◽  
System Matrix ◽  
The Third ◽  
Partial Feedback ◽  
Lumped Masses ◽  
First Time ◽  
Experimental Rig

Input–output partial feedback linearisation is experimentally implemented on a non-smooth nonlinear system without the necessity of a conventional system matrix model for the first time. The experimental rig consists of three lumped masses connected and supported by springs with low damping. The input and output are at the first degree of freedom with a non-smooth clearance-type nonlinearity at the third degree of freedom. Feedback linearisation has the effect of separating the system into two parts: one linear and controllable and the other nonlinear and uncontrollable. When control is applied to the former, the latter must be shown to be stable if the complete system is to be stable with the desired dynamic behaviour.

Near-Optimal Trajectory Generation of a Two-Legged Robot with Soft Sole on Staircase using PSO and ABC

2015 ◽  
Vol 3 (2) ◽  
pp. 1-19
Author(s):  
Naga Sudha Rani B ◽  
Vundavilli Pandu Ranga
Keyword(s):  
Dynamic Balance ◽  
Reaction Force ◽  
Biped Robot ◽  
Legged Robot ◽  
Walking Machine ◽  
Bee Colony ◽  
Zero Moment ◽  
Lumped Masses ◽  
Least Energy ◽  
Generation Problem

During biped locomotion the foot ground interaction plays an important role, as it takes the reaction force acting on the foot and allows stable walking of the biped robot. Generally, the foot is considered to be hard to solve the gait generation problem and dynamic balance aspects of the two-legged robot. However, a layer of rubber is placed on the sole of the robot to act as a shock absorber for all practical purposes. It is important to note that the soft sole gets deformed during walking of the robot and allows the limbs of the robot to bend that influences the dynamic balance of the walking machine. The aim of this study is to use two different non-traditional optimization algorithms, such as particle swarm optimization (PSO) and artificial bee colony (ABC) algorithms to obtain the optimal hip trajectory, damping coefficient and position of the lumped masses for a 7-DOF biped robot ascending the staircase. The dynamic balance of the gaits generated with soft sole is verified using the concept of zero moment point (ZMP). Further, the energy consumed in ascending the staircase with and without soft sole has been computed. The results of this study proved that, least energy is consumed with soft sole having correction for the deformation.

scholarly journals Impact of Damping Models in Damage Identification

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Michael Souza ◽  
Daniel Castello ◽  
Ney Roitman ◽  
Thiago Ritto
Keyword(s):  
Computational Models ◽  
Damage Identification ◽  
Model Parameters ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Key Issues ◽  
Delayed Rejection ◽  
Lumped Masses ◽  
Aluminum Beam ◽  
The Impact

Several damage identification approaches are based on computational models, and their diagnostics depend on the set of modelling hypotheses adopted when building the model itself. Among these hypotheses, the choice of appropriate damping models seems to be one of the key issues. The goal of this paper is to analyze the impact of a set of damping models on the damage identification diagnostics. The damage identification is built on a Bayesian framework, and the measured data are the modal data associated with the first modes of the structure. The exploration of the posterior density of unknown model parameters is performed by means of the Markov chain Monte Carlo method (MCMC) with Delayed Rejection Adaptive Metropolis (DRAM) algorithm. The analyses are based on experimental dynamic response obtained from an aluminum beam instrumented with a set of accelerometers. The presence of damage/anomaly within the system is physically simulated by placing lumped masses over the beam, considering three different masses and two different placing positions. For the set of cases analyzed, it is shown that the proposed approach was able to identify both the position and magnitude of the lumped masses and that the damping models may not provide an increase of knowledge of some unknown parameters when damping rates are lower than 1%.

A simulation investigation of helicopter ground resonance phenomenon

2019 ◽  
Vol 91 (3) ◽  
pp. 484-497
Author(s):  
Jaroslaw Stanislawski
Keyword(s):  
Simulation Method ◽  
Landing Gear ◽  
Rotor Blades ◽  
Resonance Phenomenon ◽  
Content Type ◽  
Damping Characteristics ◽  
Runge Kutta Method ◽  
Ground Resonance ◽  
Lumped Masses ◽  
Stiffness And Damping

Purpose The purpose of this paper is to present a simulation method applied for investigation of helicopter ground resonance phenomenon. Design/methodology/approach The considered physical model of helicopter standing on ground with rotating rotor consists of fuselage and main transmission gear treated as stiff bodies connected by elastic elements. The fuselage is supported on landing gear modeled by spring-damper units. The main rotor blades are treated as set of elastic axes with lumped masses distributed along blade radius. Due to Galerkin method, parameters of blades motion are assumed as a combination of bending and torsion eigen modes. A Runge–Kutta method is applied to solve equations of motions of rotor blades and helicopter fuselage. Findings The presented simulation method may be applied in preliminary stage of helicopter design to avoid ground resonance by proper selection of landing gear units and blade damper characteristics. Practical implications Ground resonance may occur in form of violently increasing mutual oscillations of helicopter fuselage and lead-lag motion of rotor blades. According to changes of stiffness and damping characteristics, simulations show stable behavior or arising oscillations of helicopter. The effects of different blade balance or defect of blade damper are predicted. Originality/value The simulation method may help to determine the envelope of safe operation of helicopter in phase of take-off or landing. The effects of additional disturbances as results of blades pitch control as swashplate deflection are introduced.

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