Nonlinear Vibration of Rotating Corotational Two-Dimensional Beams With Large Displacement

2018 ◽  
Vol 141 (5) ◽  
Author(s):  
Zihan Shen ◽  
Benjamin Chouvion ◽  
Fabrice Thouverez ◽  
Aline Beley ◽  
Jean-Daniel Beley
Keyword(s):  
Transient Analysis ◽  
Nonlinear Vibrations ◽  
Local Coordinate System ◽  
Body Part ◽  
Mechanical Analysis ◽  
Large Displacements ◽  
Governing Equations ◽  
Rotating Reference Frame ◽  
Gyroscopic Effects ◽  
Stiffening Effect

In this paper, the nonlinear vibrations of rotating beams with large displacements are investigated by the use of the co-rotational (C-R) finite element method. In the C-R approach, the full motion is decomposed into a rigid body part and a pure deformational part by introducing a local coordinate system attached to the element. The originality we propose in this study is to derive its formulation in a rotating reference frame and include both centrifugal and gyroscopic effects. The nonlinear governing equations are obtained from Lagrange's equations using a consistent expression for the kinetic energy. With this formulation, the spin-stiffening effect from geometrical nonlinearities due to large displacements is accurately handled. The proposed approach is then applied to several types of mechanical analysis (static large deformation, modal analysis at different spin speeds, and transient analysis after an impulsive force) to verify its accuracy and demonstrate its efficiency.

Non-Linear Vibration of Rotating Co-Rotational Two-Dimensional Beams With Large Displacement

2018 ◽  
Author(s):  
Zihan Shen ◽  
Benjamin Chouvion ◽  
Fabrice Thouverez ◽  
Aline Beley ◽  
Jean-Daniel Beley
Keyword(s):  
Rigid Body ◽  
Large Deformation ◽  
Local Coordinate System ◽  
Geometrical Nonlinearity ◽  
Body Part ◽  
Mechanical Analysis ◽  
Body Motion ◽  
Large Displacements ◽  
Geometrical Nonlinearities ◽  
Gyroscopic Effects

In order to achieve better performances and reduce fuel consumption, the new generation of turbomachines uses larger and lighter design, for instance the “open-rotor” concept, and is conceived to rotate at higher speeds. Parts of the structure become then even more likely to undergo large amplitude vibrations. Consequently, the conception of future aero-engine requires a sound and robust technique to predict the rotating machine vibrations considering geometrical nonlinearities (large displacements and large deformation). In this paper, the nonlinear vibrations of rotating beams with large displacements is investigated by the use of the Co-Rotational (C-R) finite element method. In the C-R approach, the full motion of each element is decomposed into a rigid body part and a pure deformational part by introducing a local coordinate system attached to the element. The utilization of the C-R method offers the possibility to treat geometrical nonlinearity directly with pre-extracted rigid body motion displacements. The originality we propose in this study is to derive its formulation in a rotating reference frame and include both centrifugal and gyroscopic effects. The nonlinear governing equations are obtained from Lagrange’s equations using a consistent expression for the kinetic energy. With this formulation, the spin-stiffening effect from geometrical nonlinearities due to large displacements is accurately handled. The proposed approach is then applied to several types of mechanical analysis (static large deformation, modal analysis at different spin speeds, and transient analysis after an impulsive force) to verify its accuracy and demonstrate its efficiency.

Nonlinear vibrations of a thin isotropic circular plate subjected to moving point loads

2020 ◽  
pp. 095440622097615
Author(s):  
Amit K Rai ◽  
Shakti S Gupta
Keyword(s):  
Boundary Conditions ◽  
Frequency Response ◽  
Circular Plate ◽  
Nonlinear Vibrations ◽  
Moving Load ◽  
Harmonic Balance Method ◽  
Angular Speed ◽  
Transverse Displacement ◽  
Governing Equations ◽  
Rotating Load

Here, we have studied the linear and nonlinear vibrations of a thin circular plate subjected to circularly, radially, and spirally moving transverse point loads. We follow Kirchoff’s theory and then incorporate von Kármán nonlinearity and employ Hamilton’s principle to obtain the governing equations and the associated boundary conditions. We solve the governing equations for the simply-supported and clamped boundary conditions using the mode summation method. Using the harmonic balance method for frequency response and Runge-Kutta method for time response, we solve the resulting coupled and cubic nonlinear ordinary differential equations. We show that the resonance instability due to a circularly moving load can be avoided by splitting it into multiple loads rotating at the same radius and angular speed. With the increasing magnitude of the rotating load, the frequency response of the transverse displacement shows jumps and modal interaction. The transverse response collected at the centre of the plate shows subharmonics of the axisymmetric frequencies only. The spectrum of the linear response due to spirally moving load contains axisymmetric frequencies, the angular speed of the load, their combination, and superharmonics of axisymmetric frequencies.

scholarly journals Autotomy in plants: organ sacrifice in Oxalis leaves

2019 ◽  
Vol 16 (151) ◽  
pp. 20180737 ◽  
Author(s):  
Ilana Shtein ◽  
Alex Koyfman ◽  
Amram Eshel ◽  
Benny Bar-On
Keyword(s):  
South African ◽  
Invasive Plant ◽  
Body Part ◽  
Mechanical Analysis ◽  
Small Cells ◽  
African Origin ◽  
Whole Plant ◽  
Defence Strategy ◽  
Far Field Stress ◽  
The Sacrifice

Autotomy is a self-defence strategy of sacrificing a body part for survival. This phenomenon is widespread in the animal kingdom (e.g. gecko's tail) but was never reported in plants. In this study, we characterize the autotomy mechanism in the leaves of an invasive plant of South African origin, Oxalis pes-caprae. When the leaves and flowers of this plant are pulled, they break easily at their base, leaving the rest of the plant intact. Microscopic observations of the leaves reveal an area of small cells and a marked notch at this designated breaking point. Mechanical analysis showed that the strength statistics of the petioles follow Weibull's function. A comparison of the function parameters confirmed that strength of the tissue at that point is significantly smaller than at other points along the petiole, while the toughness of the tissue at the notch and at mid-petiole are approximately the same. We conclude that leaf fracture in Oxalis is facilitated by an amplification of the far-field stress in the vicinity of local, but abrupt, geometrical modification in the form of a notch. This presents an autotomy-like defence mechanism which involves the sacrifice of vital organs in order to prevent the uprooting of the whole plant.

scholarly journals Nonlinear multimodal electromagnetic device for vibration energy harvesting

2019 ◽  
Vol 286 ◽  
pp. 01003
Author(s):  
K. Aouali ◽  
Z. Zergoune ◽  
N. Kacem ◽  
E. Mrabet ◽  
N. Bouhaddi ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Periodic System ◽  
Vibration Energy ◽  
Large Displacements ◽  
Multimodal Approach ◽  
Arc Length ◽  
Energy Localization ◽  
Governing Equations ◽  
Vibration Energy Harvesting ◽  
Weakly Coupled

A multimodal vibration energy harvesting in a periodic system is proposed. The multimodal approach and the nonlinearity are implemented in order to improve the performances of the studied device. The periodic system, based on electromagnetic transduction, consists of two weakly coupled magnets mechanically guided by two elastic beams. The quasi-periodic system is obtained by varying the mass of one of the moving magnets which leads to the vibration energy localization in regions close to the imperfections. This phenomenon is exploited to maximize the harvested energy. The mechanical nonlinearity is introduced by considering large displacements of the beams. The system is modeled by two coupled forced Duffing equations. The governing equations are solved using finite difference method combined with arc-length method. It is shown that the introduction of the nonlinearity leads to the enlargement of the bandwidth and the increase of the amplitude of the vibration.

ON REGULAR AND IRREGULAR NONLINEAR VIBRATIONS IN TORSIONAL DISCRETE-CONTINUOUS SYSTEMS

2011 ◽  
Vol 21 (10) ◽  
pp. 3073-3082 ◽  
Author(s):  
AMALIA PIELORZ ◽  
DANUTA SADO
Keyword(s):  
Arbitrary Number ◽  
Nonlinear Vibrations ◽  
Rigid Bodies ◽  
Continuous Systems ◽  
Bifurcation Diagrams ◽  
Governing Equations ◽  
Mass System ◽  
The Third ◽  
Multimass System ◽  
Local Nonlinearity

The paper deals with regular and irregular nonlinear vibrations of discrete-continuous systems torsionally deformed. The systems consist of an arbitrary number of shafts connected by rigid bodies. In the systems, a local nonlinearity having a soft type characteristic is introduced. This nonlinearity is described by the polynomial of the third degree. General governing equations using the wave approach are derived for a multimass system. Detailed numerical considerations are presented for a two-mass system and a three-mass system. The possibility of occurrence of irregular vibrations is discussed on the basis of the Poincaré maps and bifurcation diagrams.

scholarly journals Terminal Falling Characteristics of a Sand Grain with Dufour and Soret Effects

2012 ◽  
Vol 5 (1) ◽  
pp. 91-103
Author(s):  
R. Nasrin ◽  
M. A. Alim
Keyword(s):  
Transient Analysis ◽  
Vertical Wall ◽  
Soret Coefficient ◽  
Governing Equations ◽  
Transient Effect ◽  
Fixed Temperature ◽  
Average Form ◽  
The Right ◽  
Penalty Finite Element Method ◽  
Inlet Opening

The transient effect of double diffusive natural convection of flow in a differentially heated sand grain with Soret and Dufour coefficients is studied numerically. The right vertical wall has constant temperature Tc. The lower inlet opening is heated uniformly with fixed temperature Th and the velocity at the inlet of the fluid domain is set to the falling velocity Vi. The condition Th > Tc is maintained all over the domain. The concentration in right wall is maintained higher than inlet opening (Cc < Ch). The governing equations are solved numerically subject to appropriate boundary conditions by a penalty finite-element method. Solutions are obtained for fixed Prandtl number (Pr = 1.73), Rayleigh number (Ra = 104), Dufour coefficient (Df = 0.5) and Soret coefficient (Sr = 0.5). Transient analysis of the streamlines, isotherms, iso-concentration, falling velocity and forces on sand grain, the local and average Nusselt number and Sherwood number, temperature and concentration at subdomain centre as well as average form, subdomain horizontal and vertical velocities are presented graphically. It is found that the rate of heat transfer and mass transfer in the sand grain enhances and reduces respectively for shorter time periods and then they become almost steady.© 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v5i1.10003        J. Sci. Res. 5 (1), 91-103 (2013) 

scholarly journals Dynamic Behavior of the Full-Car Model in the J-Turn Maneuver by Considering the Engine Gyroscopic Effects

2021 ◽  
Vol 23 (3) ◽  
pp. B237-B249
Author(s):  
Ali Shahabi ◽  
Amir Hossein Kazemian ◽  
Said Farahat ◽  
Faramarz Sarhaddi
Keyword(s):  
Numerical Simulation ◽  
Coordinate System ◽  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Simulation Method ◽  
Governing Equations ◽  
Car Model ◽  
Roll Rate ◽  
Gyroscopic Effects ◽  
Engine Crankshaft

This study presents a new dynamic modeling of a vehicle by considering the engine dynamics. By selecting the vehicle coordinate system as the reference frame, all the force-torque equations of the sprung mass and unsprung masses are derived in this coordinate system by using the Newton’s equations of motion. Unlike the previous researches, in this work the sprung mass of the vehicle is not considered as a rigid body. The dynamics of the sprung mass components, such as gyroscopic effects of the engine crankshaft, is considered. In order to study the vehicle's dynamic behavior, in the J-turn maneuver, the governing equations of the full-car model are evaluated and validated by the numerical simulation method and ADAMS/Car software. Based on the results, the maximum roll angle and roll rate of a vehicle reach about 8 degrees and 40 degrees per second, respectively.

Thermo-Mechanical Transient Analysis and Conceptual Optimization of a First Stage Bucket

2008 ◽  
Author(s):  
A. Campos-Amezcua ◽  
Z. Mazur ◽  
A. Gallegos-Mun˜oz
Keyword(s):  
Transient Analysis ◽  
Computational Models ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Mechanical Analysis ◽  
Element Analysis ◽  
Simulation Techniques ◽  
Start Up ◽  
Three Dimensional Models ◽  
Almost All

This paper presents a thermo-mechanical analysis of a first stage bucket during a gas turbine start-up. This analysis uses two simulation techniques, Computational Fluid Dynamics (CFD) for the conjugate heat transfer and flow analysis, and Finite Element Analysis (FEA) for the thermo-structural analysis. Computational three dimensional models were developed using two commercial codes, including all elements of the real bucket, to avoid geometric simplifications. An interface was developed to transfer the three-dimensional behavior of bucket temperatures during turbine start-up from CFD analysis to subsequent FEA analysis, imposing them as a thermal load. This interface virtually integrates the computational models, although they have different grids. The results of this analysis include temperature evolution and related stresses, as well as the thermo-mechanical stresses and zones where they are present. These stresses are dominated by thermal mechanisms, so a new temperature start-up curve is proposed where the maximum calculated stress decline around 100 MPa, and almost all stresses are lower throughout the transient analysis. The results are compared to experimental data reported in the literature obtaining acceptable approximation.

SASSYS/SAS4A-FPIN2 Liquid-Metal Reactor Transient Analysis Code System for Mechanical Analysis of Metallic Fuel Elements

1996 ◽  
Vol 113 (3) ◽  
pp. 268-279 ◽  
Author(s):  
Tanju Sofu ◽  
John M. Kramer ◽  
James E. Cahalan
Keyword(s):  
Liquid Metal ◽  
Transient Analysis ◽  
Mechanical Analysis ◽  
Code System ◽  
Metallic Fuel ◽  
Liquid Metal Reactor ◽  
Fuel Elements

Thermohydrodynamic Seizure: Experimental and Theoretical Analysis

1998 ◽  
Vol 120 (1) ◽  
pp. 8-15 ◽  
Author(s):  
J. Y. Jang ◽  
M. M. Khonsari ◽  
M. D. Pascovici
Keyword(s):  
Theoretical Analysis ◽  
Transient Analysis ◽  
Journal Bearing ◽  
Governing Equations ◽  
Flow Rates ◽  
Thermally Induced ◽  
Experimental Apparatus ◽  
Parametric Studies ◽  
Current Limiter ◽  
A Current

An experimental apparatus was designed and tested to study the thermally induced seizure in bearing. The setup consists of a simple, unloaded journal bearing configuration which lends itself to useful physical interpretation without the complexities that are present in the control of flow rates and eccentricity in a loaded journal bearing in which the clearance would vary with time. The motor was fitted with a current limiter which stopped the motor when the torque exceeded a certain limit. Experiments revealed that with this particular system, the journal speed undergoes a significant reduction with time until the operation is halted by the current limiter, which signifies the occurrence of a seizure. The time of seizure is appreciably influenced by this behavior. A parallel theoretical analysis, which takes into account the speed variation with time, was developed. The analysis includes the derivation of the appropriate governing equations which involve the transient analysis of flow velocity, heat transfer, and thermomechanical expansion of the surfaces, together with the numerical solution. The results of the simulations compare favorably to those obtained experimentally both in trend and magnitude. Finally, general behavior of the system in terms of its time-to-seizure characteristic is illustrated through a series of parametric studies.

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