On the eigencharacteristics of a centrifugally stiffened, visco-elastic beam

2009 ◽  
Vol 223 (8) ◽  
pp. 1767-1775 ◽  
Author(s):  
M Gürgöze ◽  
S Zeren
Keyword(s):  
Elastic Beam ◽  
Computer Time ◽  
Fe Modelling ◽  
Euler Beam ◽  
Fe Method ◽  
Cooling Fan ◽  
Out Of Plane ◽  
Method Of Solution ◽  
Set Up ◽  
Tip Mass

The present study is concerned with the out-of-plane vibrations of a rotating, internally damped (Kelvin—Voigt model) Bernoulli—Euler beam carrying a tip mass, which can be thought of as a simplified model of a helicopter rotor blade or a blade of an auto-cooling fan. The differential eigenvalue problem set up is solved by using the Frobenius method of solution in a power series. The developed characteristic equation is then solved numerically. The simulation results are tabulated for a variety of non-dimensional rotational speeds, tip mass, and internal damping parameters. These are compared with the results of conventional finite element (FE) modelling as well and excellent agreement is obtained. Furthermore, it is seen that the numerical calculations according to the proposed solution method need much less computer time as compared to the conventional FE method.

Nonlinear Dynamic Modeling of Elastic Beam Fixed on a Moving Cart and Carrying Lumped Tip Mass Subjected to External Periodic Force

2009 ◽  
Author(s):  
Fadi A. Ghaith
Keyword(s):  
Linear Model ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Open Loop ◽  
Beam Deflection ◽  
Mode Shapes ◽  
Euler Beam ◽  
Periodic Force ◽  
Assumed Mode Method ◽  
Tip Mass

In the present work, a Bernoulli – Euler beam fixed on a moving cart and carrying lumped tip mass subjected to external periodic force is considered. Such a model could describe the motion of structures like forklift vehicles or ladder cars that carry heavy loads and military airplane wings with storage loads on their span. The nonlinear equations of motion which describe the global motion as well as the vibration motion were derived using Lagrangian approach under the inextensibility condition. In order to investigate the influence of the axial movement of the cart on the response of the system, unconstrained modal analysis has been carried out, and accurate mode shapes of the beam deflection were obtained. The assumed mode method was utilized for approximating the beam elastic deformation based on the single unconstrained mode shapes. Numerical simulation has been carried out to estimate the open-loop response of the nonlinear beam-mass-cart model as well as for the simplified linear model under the influence of the periodic excitation force. Also a comparison study between the responses of the linear and nonlinear models was established. It was shown that the maximum values of the beam tip deflection estimated from the nonlinear model are lower than the corresponding values obtained via the linear model, which reveals the importance of considering nonlinear hardening term in formulating the equations of motion for such system in order to come with more accurate and reliable model.

Resistless Patterning of Magnetic Storage Media Using Ion Projection Structuring

2001 ◽  
Vol 705 ◽  
Author(s):  
A. Dietzel ◽  
R. Berger ◽  
H. Grimm ◽  
C. Schug ◽  
W. H. Bruenger ◽  
...  
Keyword(s):  
Process Development ◽  
Ion Beam ◽  
Silicon On Insulator ◽  
Magnetic Storage ◽  
Magnetic Islands ◽  
Superlattice Structure ◽  
Head Positioning ◽  
Out Of Plane ◽  
Set Up ◽  
The Impact

AbstractCo/Pt thin film multilayers with strong perpendicular anisotropy and out-of-plane coercivities of 5-11 kOe were magnetically altered in areas of local ion beam interaction. The ion irradiations were performed by ion projection through silicon stencil masks fabricated by silicon on insulator (SOI) membrane technology. The ion projector at the Fraunhofer Institute for Silicon Technology (ISiT) was operated at 73 keV ion energy and with a 8.7- fold demagnification. After exposure to 3 × 1014Ar+/ cm2 magnetic islands smaller than 100 nm in diameter were resolved in the Co/Pt multilayersby means of magnetic force microscopy. The impact of different ion species (He+, Ar+ and Xe+) and ion energies (10 – 200 keV) on the multilayer structure was evaluated using Monte Carlo simulations. The ballistic interface intermixing was used to predict magnetic coercivity changes for various irradiation conditions. The simulations revealed that with 73 keV Ar+ and Xe+ ions the irradiation dose could be reduced by a factor of 100 and 400 respectively in comparison to 73 keV He+which was verified in the experiments. X-ray reflectivity measurements confirmed that the Co/Pt superlattice structure is slightly weakened during the irradiation and that the surface smoothness of the media is preserved. Using the Ion Projection Process Development Tool (PDT) at IMS-Vienna concentric data tracks including head positioning servo informations were patterned onto a 1” IBM microdrive™ glass disk which was coated with Co/Pt multilayers. In a single exposure step several tracks within an exposure field of 17 mm in diameter were structured by 2 × 1015He+/ cm2 at 45 keV using a 4- fold demagnification set-up.

Computer Simulation of a Press Feed Mechanism and Experimental Confirmation

1994 ◽  
Vol 116 (1) ◽  
pp. 248-256 ◽  
Author(s):  
C. Chassapis ◽  
G. G. Lowen
Keyword(s):  
Computer Simulation ◽  
Data Acquisition System ◽  
Quantitative Agreement ◽  
Drive Shaft ◽  
Strain Gages ◽  
Motion Equations ◽  
Qualitative And Quantitative ◽  
Bending Strain ◽  
Out Of Plane ◽  
Set Up

An experimentally verified simulation of the elastic-dynamic behavior of a lever-type feed mechanism is presented. Based on a combination of experimental and analytical findings, simplified motion equations could be introduced. In the experimental set-up, the motion of the mechanism is monitored by three angular encoders, which are attached to the drive shaft, the rocker-link shaft, and the feed roller shaft, respectively. Their output, which is stored in a specially designed data acquisition system, allows the correlation of the instantaneous rotations of the feed roller and the rocker shafts to that of the drive shaft. Strain gages provide in and out-of-plane bending-strain histories of the bent coupler. Experiment and theory, for different loading conditions, are correlated by way of the coupler strain, the clutch windup angle and the total feed length. Good qualitative and quantitative agreement between computed and experimental results was found.

Static Instability of a Restrained Cantilever Column with a Tip Mass Subjected to a Subtangential Follower Force

2013 ◽  
Vol 345 ◽  
pp. 341-344
Author(s):  
Zhen Chao Su ◽  
Yan Xia Xue
Keyword(s):  
Differential Equation ◽  
Mass Parameter ◽  
Follower Force ◽  
Force Parameter ◽  
Euler Beam ◽  
Numerical Computations ◽  
Divergence Instability ◽  
Static Instability ◽  
Tip Mass

Based on the theory of Bernoulli-Euler beam, the differential equation of a restrained cantilever column with a tip mass subjected to a subtangential follower force is constructed, the solution of the differential equation is found, and the existence of regions of divergence instability of the system is discussed. The influence of the follower force parameter η, the tip mass parameter β and an end elastic end support on the divergence instability of the column is investigated. Several numerical computations of some cases have completed.

scholarly journals Energy Harvesting in a Nonlinear Cantilever Piezoelastic Beam System Excited by Random Vertical Vibrations

2014 ◽  
Vol 14 (08) ◽  
pp. 1440018 ◽  
Author(s):  
Marek Borowiec ◽  
Grzegorz Litak ◽  
Michael I. Friswell ◽  
Sondipon Adhikari
Keyword(s):  
Power Generation ◽  
Energy Harvester ◽  
Elastic Beam ◽  
Stochastic Force ◽  
Beam System ◽  
Voltage Output ◽  
Single Well ◽  
Vertical Vibrations ◽  
Ambient Excitation ◽  
Tip Mass

The vertical elastic beam with vertical ambient excitation is proposed as an energy harvester. The beam has a tip mass and piezoelectric patches which transduce the bending strains induced by the stochastic force caused by vertical kinematic forcing into electrical charge. We focus on the region with a fairly large amplitude of voltage output where the beam overcomes the potential barrier. Increasing the noise level allows the transition from single well oscillations to inter-well stochastic jumps with more power generation.

A Real-Time DSPI System for Measuring Surface Deformation in Clamped Bolted Joints

2008 ◽  
Author(s):  
Aidong Meng ◽  
Sayed A. Nassar
Keyword(s):  
Real Time ◽  
Vibration Isolation ◽  
Surface Deformation ◽  
Plane Surface ◽  
Speckle Pattern ◽  
The Real ◽  
Time Deformation ◽  
Out Of Plane ◽  
Phase Data ◽  
Set Up

A Digital Speckle Pattern Interferometry (DSPI) system is developed for the real-time measuring and monitoring the out-of-plane surface deformation around tightened threaded fasteners that are used to clamp bolted assemblies. Spatial phase shifting is employed to quantitatively determine the distribution of phase data by introducing a spatial carrier fringe pattern to the speckle interferogram. This is achieved by leading the object and reference beams to two separate apertures. The configuration is also suitable for collecting the real-time deformation during bolt tightening. The experimental DSPI system is set-up with optical components on a vibration-isolation table. A Matlab software is developed for the image acquisition and phase data calculation, which yields the out-of-plane surface deformation caused by the bolt preload. An aluminum joint is used with an M12 steel fastener. For miniature screw application, however, a plastic joint is used for collecting data.

ENERGY HARVESTING IN PIEZOELASTIC SYSTEMS DRIVEN BY RANDOM EXCITATIONS

2013 ◽  
Vol 13 (07) ◽  
pp. 1340006 ◽  
Author(s):  
M. BOROWIEC ◽  
G. LITAK ◽  
M. I. Friswell ◽  
S. F. Ali ◽  
S. Adhikari ◽  
...  
Keyword(s):  
Noise Level ◽  
Large Amplitude ◽  
Energy Harvester ◽  
Elastic Beam ◽  
Horizontal Displacement ◽  
Beam System ◽  
Piezoelectric Layers ◽  
Single Well ◽  
Beam Motion ◽  
Tip Mass

The inverted elastic beam is proposed as an energy harvester. The beam has a tip mass and piezoelectric layers which transduce the bending strains induced by the stochastic horizontal displacement into electrical charge. The efficiency of this nonlinear device is analyzed, focusing on the region of stochastic resonance where the beam motion has a large amplitude. Increasing the noise level allows the motion of the beam system to escape from single well oscillations and thus generate more power.

VISCO-ELASTIC BEAM TRANSVERSE VIBRATIONS GENERATED BY ENERATED BY CIRCULAR DISC (SOIL COMPRESSOR) MOTIN

2012 ◽  
Vol 2 (4) ◽  
pp. 101-104 ◽  
Author(s):  
G. V PAVLOV ◽  
M. A KAL'MOVA
Keyword(s):  
Averaging Method ◽  
Elastic Beam ◽  
Circular Disc ◽  
Transverse Vibrations ◽  
Set Up ◽  
Energy Type

A new problem for disk motion along Kelvin rheological beam is solved. Amplitude-phase equations are set up according to the energy type averaging method. Instability of the disc motion along the beam is shown.

Stress invariance in planar Cosserat elasticity

1995 ◽  
Vol 451 (1942) ◽  
pp. 453-470 ◽  
Keyword(s):  
Torsion Tensor ◽  
Plane Elasticity ◽  
Planar Problem ◽  
Effective Moduli ◽  
Classical Elasticity ◽  
Displacement Gradient ◽  
Additional Degree ◽  
Linear Elastic ◽  
Out Of Plane ◽  
Set Up

We extend the CLM theorem (Cherkaev, Lurie & Milton, Proc. R. Soc. Lond. A (1992) 438, 519-529) to planar linear elastic materials of Cosserat (micropolar) type, that is those having microrotation as an additional degree of freedom besides the two in-plane displacements. More specifically, it is shown that in the first planar problem of such media with smoothly varying material properties, a shift in three, out of four, compliances is possible without changing the stress field; the fourth coefficient represents a connection between the couple stress tensor and the torsion tensor, while the other three represent compliances relating traction-stress vector with the strains. Same shift holds for a locally anisotropic material, whereby the shift tensor is seen to be a multiple of a rotation by a right angle; a null-Lagrangian formulation is set up on this basis. These results are obtained for materials with smooth properties, with natural implications being drawn for their macroscopically effective moduli. Also, it is shown that no shift is possible in case of a pseudo-continuum – a material admitting couple stresses but restricted to have the same connection between rotation and displacement gradient as in classical elasticity. Finally, we establish that there is no shift in the second planar problem which represents a micropolar generalization of the classical out-of-plane elasticity.

Buckling Loads and Natural Frequencies of Drill Bits and Fluted Cutters

1984 ◽  
Vol 106 (3) ◽  
pp. 196-204 ◽  
Author(s):  
E. B. Magrab ◽  
D. E. Gilsinn
Keyword(s):  
Natural Frequencies ◽  
Twist Angle ◽  
Axial Loading ◽  
Basis Functions ◽  
Mode Shapes ◽  
Euler Beam ◽  
Buckling Loads ◽  
Drill Bits ◽  
Out Of Plane ◽  
Beam Type

The buckling loads, natural frequencies and mode shapes of twist-drill bits and certain fluted cutters under a variety of combinations of twist angle, cross-section geometry, and axial loading have been obtained. The drill bit is modelled as a twisted Euler beam under axial loading that is clamped at both ends. The governing system of differential equations is solved by the Galerkin procedure. Explicit forms for the basis functions used to generate the Galerkin coefficients are presented in general form in an appendix. They may be used for obtaining numerical results for that class of problems which use the Rayleigh-Ritz-Galerkin methods with beam-type functions as the basis functions. The representative set of modes obtained exhibit a complex out-of-plane twisting-type motion that suggests a possible explanation for the out-of-roundness of certain drilled holes.

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