On 2D Forcespinning™ Modeling

2011 ◽  
Author(s):  
Simon Padron ◽  
Dumitru I. Caruntu ◽  
Karen Lozano
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Fiber Diameter ◽  
Production Method ◽  
Fiber Formation ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Novel Method ◽  
Jet Theory ◽  
High Yields

Forcespinning™ is a novel method that makes used of centrifugal forces to produce nanofibers rapidly and at high yields. To improve and enhance this new nanofiber production method a model of the system is begun. The process is started by deriving the governing equations of the forcespinning™ sytem and the constraints associated it. A simple 2D model is then obtained using the derived governing equations for the inviscid case to determine the trends of fiber diameter and trajectories. Then, focus is given to the time-dependency of these equations, and the effects of parametric excitation of the system on fiber formation are analyzed. The equations are solved using a combination of the method of multiple scales and the finite difference method with slender-jet theory assumptions.

Influence of Viscosity on Forcespinning™ Dynamics

2012 ◽  
Author(s):  
Simon Padron ◽  
Dumitru I. Caruntu ◽  
Karen Lozano
Keyword(s):  
Fluid Dynamics ◽  
Multiple Scales ◽  
Tangential Velocity ◽  
Centrifugal Forces ◽  
Dynamics Model ◽  
Novel Method ◽  
The Finite Difference Method ◽  
Jet Theory ◽  
High Yields ◽  
Fluid Dynamics Equations

Forcespinning™ is a novel method that makes use of centrifugal forces to produce nanofibers rapidly and at high yields. A 2D computational Forcespinning™ viscous fluid dynamics model is developed, that improves on previous models. The fluid dynamics equations are solved using themethod of multiple scales along with the finite difference method, and including slender-jet theory assumptions. The effects that the Reynolds (Re) number has on the resulting fiber trajectory, radius, and tangential velocity are presented.

Parametric Stability of Axially Accelerating Viscoelastic Beams With the Recognition of Longitudinally Varying Tensions

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Li-Qun Chen ◽  
You-Qi Tang
Keyword(s):  
Governing Equation ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Finite Support ◽  
Governing Equations ◽  
Parametric Stability ◽  
Stability Boundaries ◽  
Axial Acceleration ◽  
The Stability ◽  
Longitudinally Varying Tension

In this paper, the parametric stability of axially accelerating viscoelastic beams is revisited. The effects of the longitudinally varying tension due to the axial acceleration are highlighted, while the tension was approximately assumed to be longitudinally uniform in previous studies. The dependence of the tension on the finite support rigidity is also considered. The generalized Hamilton principle and the Kelvin viscoelastic constitutive relation are applied to establish the governing equations and the associated boundary conditions for coupled planar motion of the beam. The governing equations are linearized into the governing equation in the transverse direction and the expression of the longitudinally varying tension. The method of multiple scales is employed to analyze the parametric stability of transverse motion. The stability boundaries are derived from the solvability conditions and the Routh-Hurwitz criterion for principal and sum resonances. In terms of stability boundaries, the governing equations with or without the longitudinal variance of tension are compared and the effects of the finite support rigidity are also examined. Some numerical examples are presented to demonstrate the effects of the stiffness, the viscosity, and the mean axial speed on the stability boundaries. The differential quadrature scheme is developed to numerically solve the governing equation, and the computational results confirm the outcomes of the method of multiple scales.

Response variations of a cantilever beam–tip mass system with nonlinear and linearized boundary conditions

2018 ◽  
Vol 25 (3) ◽  
pp. 485-496 ◽  
Author(s):  
Vamsi C. Meesala ◽  
Muhammad R. Hajj
Keyword(s):  
Boundary Conditions ◽  
Cantilever Beam ◽  
Nonlinear Boundary ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Boundary Conditions ◽  
Distributed Parameter ◽  
Governing Equations ◽  
Mass System ◽  
Tip Mass

The distributed parameter governing equations of a cantilever beam with a tip mass subjected to principal parametric excitation are developed using a generalized Hamilton's principle. Using a Galerkin's discretization scheme, the discretized equation for the first mode is developed for simpler representation assuming linear and nonlinear boundary conditions. The discretized governing equation considering the nonlinear boundary conditions assumes a simpler form. We solve the distributed parameter and discretized equations separately using the method of multiple scales. Through comparison with the direct approach, we show that accounting for the nonlinear boundary conditions boundary conditions is important for accurate prediction in terms of type of bifurcation and response amplitude.

scholarly journals Principal Parametric Resonance of Axially Accelerating Viscoelastic Beams: Multi-Scale Analysis and Differential Quadrature Verification

2012 ◽  
Vol 19 (4) ◽  
pp. 527-543 ◽  
Author(s):  
Li-Qun Chen ◽  
Hu Ding ◽  
C.W. Lim
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Steady State ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Steady State Response ◽  
Governing Equations ◽  
State Response ◽  
Non Linear ◽  
Axial Speed

Transverse non-linear vibration is investigated in principal parametric resonance of an axially accelerating viscoelastic beam. The axial speed is characterized as a simple harmonic variation about a constant mean speed. The material time derivative is used in the viscoelastic constitutive relation. The transverse motion can be governed by a non-linear partial-differential equation or a non-linear integro-partial-differential equation. The method of multiple scales is applied to the governing equations to determine steady-state responses. It is confirmed that the mode uninvolved in the resonance has no effect on the steady-state response. The differential quadrature schemes are developed to verify results via the method of multiple scales. It is demonstrated that the straight equilibrium configuration becomes unstable and a stable steady-state emerges when the axial speed variation frequency is close to twice any linear natural frequency. The results derived for two governing equations are qualitatively the same, but quantitatively different. Numerical simulations are presented to examine the effects of the mean speed and the variation of the amplitude of the axial speed, the dynamic viscosity, the non-linear coefficients, and the boundary constraint stiffness on the instability interval and the steady-state response amplitude.

Dynamics of a Cubic Nonlinear Vibration Absorber

1999 ◽  
Author(s):  
Shafic S. Oueini ◽  
Char-Ming Chin ◽  
Ali H. Nayfeh
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Primary Resonance ◽  
Response Amplitude ◽  
Vibration Absorber ◽  
Governing Equations ◽  
Excited Mode ◽  
Saturation Phenomenon ◽  
Plant Remains ◽  
Active Vibration

Abstract We study the dynamics of a nonlinear active vibration absorber. We consider a plant model possessing curvature and inertia nonlinearities and introduce a second-order absorber that is coupled with the plant through user-defined cubic nonlinearities. When the plant is excited at primary resonance and the absorber frequency is approximately equal to the plant natural frequency, we show the existence of a saturation phenomenon. As the forcing amplitude is increased beyond a certain threshold, the response amplitude of the directly excited mode (plant) remains constant, while the response amplitude of the indirectly excited mode (absorber) increases. We obtain an approximate solution to the governing equations using the method of multiple scales and show that the system possesses two possible saturation values. Using numerical techniques, we perform stability analyses and demonstrate that the system exhibits complicated dynamics, such as Hopf bifurcations, intermittency, and chaotic responses.

Nonlinear Vibration of Parametrically Excited, Viscoelastic, Axially Moving Strings

2005 ◽  
Vol 72 (3) ◽  
pp. 374-380 ◽  
Author(s):  
Eric M. Mockensturm ◽  
Jianping Guo
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Time Derivative ◽  
Excitation Frequency ◽  
Viscoelastic Behavior ◽  
Solution Procedure ◽  
Governing Equations ◽  
Translation Speed ◽  
Parametrically Excited ◽  
Axially Moving

The dynamic response of parametrically excited, axially moving viscoelastic belts is investigated in this paper. Results are compared to previous work in which the partial, not material, time derivative was used in the viscoelastic constitutive relation. It is found that this added “steady state” dissipation greatly affects both the existence and amplitudes of nontrivial limit cycles. The discrepancy increases with increasing translation speed. To limit the comparison to the additional physics included in the model, the solution procedure of Zhang and Zu [1,2], who applied the method of multiple scales to the governing equations prior to discretization, is retained. The excitation here is provided by physically stretching the belt. In this case, viscoelastic behavior and excitation frequency also affects the amplitude of the tension fluctuations.

A Novel Method for the Rapid Purification of Human and Rat Fibrin(OGEN) Degradation Products in High Yields

1979 ◽  
Author(s):  
W. Nieuwenhuizen ◽  
I. A. M. van Ruijven-Vermeer ◽  
F. Haverkate ◽  
G. Timan
Keyword(s):  
Degradation Products ◽  
Complete Separation ◽  
Purification Method ◽  
Amino Terminal ◽  
Novel Method ◽  
Rapid Purification ◽  
The One ◽  
High Yields ◽  
Size Heterogeneity ◽  
D Dimer

A novel method will be described for the preparation and purification of fibrin(ogen) degradation products in high yields. The high yields are due to two factors. on the one hand an improved preparation method in which the size heterogeneity of the degradation products D is strongly reduced by plasmin digestion at well-controlled calcium concentrations. At calcium concentrations of 2mM exclusively D fragments, M.W.= 93-000 (Dcate) were formed; in the presence of 1OmM EGTA only fragments M.W.= 80.000 (D EGTA) were formed as described. on the other hand a new purification method, which includes Sephadex G-200 filtration to purify the D:E complexes and separation of the D and E fragments by a 16 hrs. preparative isoelectric focussing. The latter step gives a complete separation of D (fragments) (pH = 6.5) and E fragments (at pH = 4.5) without any overlap, thus allowing a nearly 100% recovery in this step. The overall recoveries are around 75% of the theoretical values. These recoveries are superior to those of existing procedures. Moreover the conditions of this purification procedure are very mild and probably do not affect the native configuration of the products. Amino-terminal amino acids of human Dcate, D EGTA and D-dimer are identical i.e. val, asx and ser. in the ratgly, asx and ser were found. E 1% for rat Dcate=17-8 for rat D EGTA=16.2 and for rat D- dimer=l8.3. for the corresponding human fragments, these values were all 20.0 ± 0.2.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

scholarly journals Dynamic analysis of a parametrically excited golden Muga silk embedded pneumatic artificial muscle

2018 ◽  
Vol 211 ◽  
pp. 02008 ◽  
Author(s):  
Bhaben Kalita ◽  
S. K. Dwivedy
Keyword(s):  
Dynamic Analysis ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Quadratic Function ◽  
Artificial Muscle ◽  
Equation Of Motion ◽  
Time Response ◽  
Phase Portraits ◽  
Pneumatic Artificial Muscle ◽  
Pneumatic Muscle

In this work a novel pneumatic artificial muscle is fabricated using golden muga silk and silicon rubber. It is assumed that the muscle force is a quadratic function of pressure. Here a single degree of freedom system is considered where a mass is supported by a spring-damper-and pneumatically actuated muscle. While the spring-mass damper is a passive system, the addition of pneumatic muscle makes the system active. The dynamic analysis of this system is carried out by developing the equation of motion which contains multi-frequency excitations with both forced and parametric excitations. Using method of multiple scales the reduced equations are developed for simple and principal parametric resonance conditions. The time response obtained using method of multiple scales have been compared with those obtained by solving the original equation of motion numerically. Using both time response and phase portraits, variation of few systems parameters have been carried out. This work may find application in developing wearable device and robotic device for rehabilitation purpose.

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