scholarly journals Shooting/continuation based bifurcation analysis of large order nonlinear rotordynamic systems

2018 ◽  
Vol 211 ◽  
pp. 18003 ◽  
Author(s):  
Sitae Kim ◽  
Alan Palazzolo
Keyword(s):  
Continuation Method ◽  
Numerical Procedure ◽  
Beam Theory ◽  
Computational Techniques ◽  
Euler Beam ◽  
Compressor Rotor ◽  
Large Order ◽  
Complex Models ◽  
Reaction Forces ◽  
Triangular Type

This study introduces an improved numerical algorithm that is capable of analyzing nonlinear vibrations and bifurcations of general, finite, large-order rotordynamic systems supported on nonlinear bearings. An industrial rotor generally consists of several sections and stages, but numerical shooting/continuation method has been applied to a simple Jeffcott type rotor instead of complex models due to the computational burden of the numerical procedure; it becomes significant when the rotor combined with nonlinear finite bearing models. Here, some mathematical/computational techniques such as a deflation algorithm and the parallel computing are suggested for acceleration along with the conventional treatment of model reduction scheme. An eight-stage compressor rotor supported by two identical five-pad tilting pad journal bearings (TPJB) is selected as a mechanical model to test the numerical incorporation of the algorithms. The rotor beam is modelled with 35 nodes, 140 DOF based on Euler beam theory, and the fluid reaction forces from the two TPJB are calculated using simplex, triangular type finite meshes on the pads. In the numerical procedure, the shooting/continuation combined with the acceleration schemes identifies the solution curves of periodic responses and determines their stability. The orbital motions of coexistent responses are obtained from the solution manifolds.

scholarly journals Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 923
Author(s):  
Kun Huang ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Beam Theory ◽  
Bending Stiffness ◽  
Single Wall Carbon Nanotubes ◽  
Beam Model ◽  
Euler Beam ◽  
New Model ◽  
Mechanical Coupling ◽  
Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

Aeroelastic Optimization of an Industrial Compressor Rotor Blade Geometry

2018 ◽  
Author(s):  
Federico Vanti ◽  
Lorenzo Pinelli ◽  
Andrea Arnone ◽  
Andrea Schneider ◽  
Pio Astrua ◽  
...  
Keyword(s):  
Numerical Procedure ◽  
Optimization Procedure ◽  
Multidisciplinary Optimization ◽  
Optimization Process ◽  
Geometrical Parameters ◽  
Aerodynamic Optimization ◽  
Compressor Rotor ◽  
Wide Range ◽  
Automatic Optimization ◽  
Blade Geometry

This paper describes a multidisciplinary optimization procedure applied to a compressor blade-row. The numerical procedure takes into account both aerodynamic (efficiency) and aeromechanic (flutter-free design) goals nowadays required by turbo-machinery industries and is applied to a low pressure compressor rotor geometry provided by Ansaldo Energia S.p.A.. Some typical geometrical parameters have been selected and modified during the automatic optimization process in order to generate an optimum geometry with an improved efficiency and, at the same time, a safety flutter margin. This new automatic optimization procedure, which now includes a flutter stability assessment, is an extension of an existing aerodynamic optimization process, which randomly perturbs a starting 3D blade geometry inside a constrained range of values, build the fluid mesh and run the CFD steady analysis. The new implementation provides the self-building of the solid mesh, the FEM analysis and finally the unsteady uncoupled aeroelastic analysis to assess the flutter occurrence. After simulating a wide range of geometries, a database with all the constraint parameters and objective functions is obtained and then used to train a neural network algorithm. Once the ANN validation error is converged, an optimization strategy is used to build the Pareto front and to provide a set of optimum geometries redesigning the original compressor rotor. The aim of this paper is to show the opportunity to also take into account the aeroelastic issues in optimization processes.

Vibration Analysis of a Partially Covered Double Sandwich Cantilever Beam With Concentrated Mass at the Free End

1993 ◽  
Author(s):  
C. Levy ◽  
Q. Chen
Keyword(s):  
Loss Factor ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Physical Parameters ◽  
Mass Ratio ◽  
Euler Beam ◽  
Concentrated Mass ◽  
Sandwich Type ◽  
Euler Beam Theory ◽  
Two Parameters

Abstract The partially covered, sandwich-type cantilever with concentrated mass at the free end is studied. The equations of motion for the system modeled via Euler beam theory are derived and the resonant frequency and loss factor of the system are analyzed. The variations of resonance frequency and system loss factor for different geometrical and physical parameters are also discussed. Variation of these two parameters are found to strongly depend on the geometrical and physical properties of the constraining layers and the mass ratio.

Active Damping of Vibrations of a Cantilever Beam by Axial Force Control

2007 ◽  
Author(s):  
Thomas Pumho¨ssel ◽  
Horst Ecker
Keyword(s):  
Cantilever Beam ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Open Loop ◽  
Active Damping ◽  
Nonlinear Feedback ◽  
Euler Beam ◽  
Bending Vibrations ◽  
Loop Control ◽  
Damping Of Vibrations

In several fields, e.g. aerospace applications, robotics or the bladings of turbomachinery, the active damping of vibrations of slender beams which are subject to free bending vibrations becomes more and more important. In this contribution a slender cantilever beam loaded with a controlled force at its tip, which always points to the clamping point of the beam, is treated. The equations of motion are obtained using the Bernoulli-Euler beam theory and d’Alemberts principle. To introduce artificial damping to the lateral vibrations of the beam, the force at the tip of the beam has to be controlled in a proper way. Two different methods are compared. One concept is the closed-loop control of the force. In this case a nonlinear feedback control law is used, based on axial velocity feedback of the tip of the beam and a state-dependent amplification. By contrast, the concept of open-loop parametric control works without any feedback of the actual vibrations of the mechanical structure. This approach applies the force as harmonic function of time with constant amplitude and frequency. Numerical results are carried out to compare and to demonstrate the effectiveness of both methods.

scholarly journals Load transfer of nanocomposite film on aluminum substrate

2018 ◽  
Vol 16 (1_suppl) ◽  
pp. 10-16
Author(s):  
Shiuh-Chuan Her ◽  
Pao-Chu Chien
Keyword(s):  
Young’S Modulus ◽  
Nanocomposite Film ◽  
Load Transfer ◽  
Young's Modulus ◽  
Tensile Load ◽  
Beam Theory ◽  
Aluminum Substrate ◽  
Nanocomposite Films ◽  
Euler Beam ◽  
Load Carrying

Introduction: Nanocomposite films have attracted much attention in recent years. Depending on the composition of the film and fabrication method, a large range of applications has been employed for nanocomposite films. Method: In this study, nanocomposite films reinforced with multi-walled carbon nanotubes (MWCNTs) were deposited on the aluminum substrate through hot press processing. A shear lag model and Euler beam theory were employed to evaluate the stress distribution and load carrying capability of the nanocomposite film subjected to tensile load and bending moment. Results: The influence of MWCNT on the Young’s modulus and load carrying capability of the nanocomposite film was investigated through a parametric study. The theoretical predictions were verified by comparison with experimental tests. A close agreement with difference less than 6% was achieved between the theoretical prediction and experimental measurements. Conclusions: The Young’s modulus and load transfer of the nanocomposite film reinforced with MWCNTs increases with the increase of the MWCNT loading. Compared to the neat epoxy film, nanocomposite film with 1 wt % of MWCNT exhibits an increase of 20% in both the Young’s modulus and load carrying capability.

Dynamic Formulations and Energy Analysis of Rotating Flexible-Shaft/Multi-Flexible-Disk System With Eddy-Current Brake

2000 ◽  
Vol 122 (4) ◽  
pp. 365-375 ◽  
Author(s):  
Rong-Fong Fung ◽  
Shih-Ming Hsu
Keyword(s):  
Eddy Current ◽  
Energy Analysis ◽  
Virtual Work ◽  
Beam Theory ◽  
Brake System ◽  
Euler Beam ◽  
Disk System ◽  
Coupling System ◽  
Flexible Disk ◽  
Work Done

In this paper, the rotating flexible-Timoshenko-shaft/flexible-disk coupling system is formulated by introducing the kinetic and strain energies, and the virtual work done by the eddy-current brake system into Hamilton’s principle. The attachment of disk to shaft becomes flexible for Timoshenko-beam theory and rigid for Euler-beam theory. It is found that the eddy-current brake system can be used to decrease speed and suppress flexible and shear vibrations simultaneously. From the dynamic formulations and energy analysis, some important discussions are made. Numerical results are provided to validate the theoretical analysis. [S0739-3717(00)01504-X]

Resonance Responses of Geometrically Imperfect Functionally Graded Extensible Microbeams

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Hamed Farokhi ◽  
Alireza Gholipour ◽  
Shahid Hussain ◽  
Maziar Arjomandi
Keyword(s):  
Couple Stress Theory ◽  
Continuation Method ◽  
Dynamical Behavior ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Dynamical Response ◽  
Weighted Residual Method ◽  
Size Dependent ◽  
Rotational Motions

This paper aims at analyzing the size-dependent nonlinear dynamical behavior of a geometrically imperfect microbeam made of a functionally graded (FG) material, taking into account the longitudinal, transverse, and rotational motions. The size-dependent property is modeled by means of the modified couple stress theory, the shear deformation and rotary inertia are modeled using the Timoshenko beam theory, and the graded material property in the beam thickness direction is modeled via the Mori–Tanaka homogenization technique. The kinetic and size-dependent potential energies of the system are developed as functions of the longitudinal, transverse, and rotational motions. On the basis of an energy method, the continuous models of the system motion are obtained. Upon application of a weighted-residual method, the reduced-order model is obtained. A continuation method along with an eigenvalue extraction technique is utilized for the nonlinear and linear analyses, respectively. A special attention is paid on the effects of the material gradient index, the imperfection amplitude, and the length-scale parameter on the system dynamical response.

Dynamic Total Head Loss Characteristic for an Axial Compressor Rotor

1980 ◽  
Vol 22 (6) ◽  
pp. 269-276 ◽  
Author(s):  
P. B. Sharma ◽  
J. W. Railly
Keyword(s):  
Time Delay ◽  
Time Lag ◽  
Axial Compressor ◽  
Numerical Procedure ◽  
Head Loss ◽  
Rotating Stall ◽  
Phase Lock ◽  
Compressor Rotor ◽  
Total Head ◽  
Loss Characteristic

Detailed flow field and pressure measurements during rotating stall operation have been carried out at inlet to and exit from an axial compressor rotor using hot wire anemometers and probes incorporating fast response pressure transducers. An on-line data-acquisition system which employs a phase-lock sampling and averaging technique has been used to obtain ‘phase-lock averaged’ values of flow quantities and pressures. The dynamic total head loss/incidence characteristic for the rotor section at mean diameter has been computed from the above data. The dynamic characteristic exhibits a loop in the stalled region. A simple numerical procedure has been used to obtain the steady-state loss characteristic and the time-lag of this loss. It has been found that the loss time-lag of boundary layer time delay corresponds to a value equal to 1.8 times the time delay due to inertia of fluid in a blade passage. A simple theory for the prediction of this loss time-lag is also presented which shows reasonable agreement with the value determined from measurements.

Elastic Analysis of Beam-Support Impact

1985 ◽  
Vol 107 (1) ◽  
pp. 64-67 ◽  
Author(s):  
M. A. Salmon ◽  
V. K. Verma ◽  
T. G. Youtsos
Keyword(s):  
Analytical Solutions ◽  
Beam Theory ◽  
Bending Moment ◽  
General Purpose ◽  
Euler Beam ◽  
Piping Systems ◽  
Euler Beam Theory ◽  
Impact Problems ◽  
Fixed End ◽  
Spring Support

The effect of gaps present in the seismic supports of nuclear piping systems has been studied with the use of such large general-purpose analysis codes as ANSYS. Exact analytical solutions to two simple beam-impact problems are obtained to serve as benchmarks for the evaluation of the ability of such codes to model impact between beam elements and their supports. Bernoulli-Euler beam theory and modal analysis are used to obtain analytical solutions for the motion of simply supported and fixed-end beams after impact with a spring support at midspan. The solutions are valid up to the time the beam loses contact with the spring support. Numerical results are obtained which show that convergence for both contact force and bending moment at the point of impact is slower as spring stiffness is increased. Finite element solutions obtained with ANSYS are compared to analytical results and good agreement is obtained.

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