ALBERT — All Library Books, journals and Electronic Records Telegrafenberg

1

Electronic Resource

The nonlinear vibration analysis of a clamped-clamped beam by a reduced multibody method (1996)

Kovacs, A. P. ; Ibrahim, R. A.

Springer

Nonlinear dynamics 11 (1996), S. 121-141

add to mindlist on the mindlist

Details

ISSN: 1573-269X

Keywords: d'Alembert principle ; reduced multibody method ; constrained flexibility ; nonlinear vibration ; Galerkin's method ; checking function ; differential and algebraic equations (DAE) ; bifurcation

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The nonlinear response characteristics for a dynamic system with a geometric nonlinearity is examined using a multibody dynamics method. The planar system is an initially straight clamped-clamped beam subject to high frequency excitation in the vicinity of its third natural mode. The model includes a pre-applied static axial load, linear bending stiffness and a cubic in-plane stretching force. Constrained flexibility is applied to a multibody method that lumps the beam into N elements for three substructures subjected to the nonlinear partial differential equation of motion and N-1 linear modal constraints. This procedure is verified by d'Alembert's principle and leads to a discrete form of Galerkin's method. A finite difference scheme models the elastic forces. The beam is tuned by the axial force to obtain fourth order internal resonance that demonstrates bimodal and trimodal responses in agreement with low and moderate excitation test results. The continuous Galerkin method is shown to generate results conflicting with the test and multibody method. A new checking function based on Gauss' principle of least constraint is applied to the beam to minimize modal constraint error.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00044998

Permalink

	Location	Call Number	Expected	Availability

Others were also interested in ...

Paper (German National Licenses)

Fulltext

2

Electronic Resource

Parametric random excitation of nonlinear coupled oscillators (1995)

Yoon, Y. J. ; Ibrahim, R. A.

Springer

Nonlinear dynamics 8 (1995), S. 385-413

add to mindlist on the mindlist

Details

ISSN: 1573-269X

Keywords: Parametric excitation ; nonlinear random vibration ; bifurcation and stochastic stability ; experimental testing ; on-off intermittency ; moment closures ; Monte Carlo simulation

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The stochastic bifurcation and response statistics of nonlinear modal interaction under parametric random excitation are studied analytically, numerically and experimentally. Two basic definitions of stochastic bifurcation are first introduced. These are bifurcation in distribution and bifurcation in moments. bifurcation in moments is examined for the case of a coupled oscillator subjected to parametric filtered white noise. The center frequency of the excitation is selected to be close to either twice the first mode or second mode natural frequencies or the sum of the two. The stochastic bifurcation in moments is predicted using the Fokker-Planck equation together with gaussian and non-Gaussian closures and numerically using the Monte Carlo simulation. When one mode is parametrically excited it transfers energy to the other mode due to nonlinear modal interaction. The Gaussian closure solution gives close results to those predicted numerically only in regions well remote from bifurcation points. However, bifurcation points predicted by the non-Gaussian closure are in good agreement with those estimated by numerical simulation. Depending on the excitation level, the probability density of the excited mode is strongly non-Gaussian and exhibits multi-maxima as predicted by Monte Carlo simulation. Experimental tests are carried out at relatively low excitation levels. In the neighborhood of stochastic bifurcation in mean square the measured results exhibit different regimes of response characteristics including zero motion and occasional small random motion regimes. These two regimes are characterized by the phenomenon of on-off intermittency. Both regimes overlap and thus it is difficult to locate experimentally the bifurcation point.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00045623

Permalink

	Location	Call Number	Expected	Availability

Others were also interested in ...

Paper (German National Licenses)

Fulltext

3

Electronic Resource

Nonlinear Random Response of Ocean Structures Using First- and Second-Order Stochastic Averaging (1997)

Hijawi, M. ; Ibrahim, R. A. ; Moshchuk, N.

Springer

Nonlinear dynamics 12 (1997), S. 155-197

add to mindlist on the mindlist

Details

ISSN: 1573-269X

Keywords: Nonlinear modeling ; structure-fluid interaction ; parametric excitation ; first- and second-order stochastic averaging ; closure schemes ; noise-induced transition ; on-off-intermittency

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract This paper deals with the dynamic response of nonlinear elastic structure subjected to random hydrodynamic forces and parametric excitation using a first- and second-order stochastic averaging method. The governing equation of motion is derived by using Hamilton's principle, taking into account inertia and curvature nonlinearities and work done due to hydrodynamic forces. Within the framework of first-order stochastic averaging, the system response statistics and stability boundaries are obtained. Unfortunately, the effects of nonlinear inertia and curvature are not reflected in the final results, since the contribution of these nonlinearities is lost during the averaging process. In the absence of hydrodynamic forces, the method fails to give bounded response statistics, and the analysis yields stability conditions. It is the second-order stochastic averaging which can capture the influence of stiffness and inertia nonlinearities that were lost in the first-order averaging process. The results of the second-order averaging are compared with those predicted by Gaussian and non-Gaussian closures and by Monte Carlo simulation. In the absence of parametric excitation, the non-Gaussian closure solutions are in good agreement with Monte Carlo simulation. On the other hand, in the absence of hydrodynamic forces, second-order averaging gives more reliable results in the neighborhood of stochastic bifurcation. However, under pure parametric random excitation, the stochastic averaging and Monte Carlo simulation predict the on-off intermittency phenomenon near bifurcation point, in addition to stochastic bifurcation in probability.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1008299615084

Permalink

	Location	Call Number	Expected	Availability

Others were also interested in ...

Paper (German National Licenses)

Fulltext

4

Electronic Resource

Multiple Internal Resonance in Suspended Cables under Random In-Plane Loading (1997)

Chang, W. K. ; Ibrahim, R. A.

Springer

Nonlinear dynamics 12 (1997), S. 275-303

add to mindlist on the mindlist

Details

ISSN: 1573-269X

Keywords: Suspended cables ; internal resonances ; intermittency ; random excitation ; closure schemes ; Monte Carlo simulation

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The random excitation of a suspended cable with simultaneous internal resonances is considered. The internal resonances can take place among the first in-plane and the first two out-of-plane modes. The external loading is represented by a wide-band random process. The response statistics are estimated using the Fokker-Planck-Kolmogorov (FPK) equation, together with Gaussian and non-Gaussian closures. Monte Carlo simulation is also used for numerical verification. The unimodal in-plane motion exists in regions away from the internal resonance condition. The mixed mode interaction is manifested within a limited range of internal detuning parameters, depending on the excitation power spectrum density and damping ratios. The Gaussian closure scheme failed to predict bounded solutions of mixed mode interaction. The non-Gaussian closure results are in good agreement with the Monte Carlo simulation. The on-off intermittency of the autoparametrically excited modes is observed in the Monte Carlo simulation over a small range of excitation levels. The influence of the cable parameters, such as damping ratios, sag-to-span ratio, internal detuning parameters, and excitation level on the autoparametric interaction, is studied. It is found that the internal detuning and excitation level are the two main parameters which affect the autoparametric interaction among the three modes. Due to the system's nonlinearity, the response of the three modes is strongly non-Gaussian and the coupled modes experience irregular modulation.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1008232209273

Permalink

	Location	Call Number	Expected	Availability

Others were also interested in ...

Paper (German National Licenses)

Fulltext

5

Electronic Resource

Fluid Flow-Induced Nonlinear Vibration of Suspended Cables (1997)

Chang, W. K. ; Pilipchuk, V. ; Ibrahim, R. A.

Springer

Nonlinear dynamics 14 (1997), S. 377-406

add to mindlist on the mindlist

Details

ISSN: 1573-269X

Keywords: Cable nonlinear dynamics ; co-ordinate transformation ; fluid-structure interaction ; divergence and flutter stability ; two-time-scale asymptotic analysis

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The nonlinear interaction of the first two in-plane modes of a suspended cable with a moving fluid along the plane of the cable is studied. The governing equations of motion for two-mode interaction are derived on the basis of a general continuum model. The interaction causes the modal differential equations of the cable to be non-self-adjoint. As the flow speed increases above a certain critical value, the cable experiences oscillatory motion similar to the flutter of aeroelastic structures. A co-ordinate transformation in terms of the transverse and stretching motions of the cable is introduced to reduce the two nonlinearly coupled differential equations into a linear ordinary differential equation governing the stretching motion, and a strongly nonlinear differential equation for the transverse motion. For small values of the gravity-to-stiffness ratio the dynamics of the cable is examined using a two-time-scale approach. Numerical integration of the modal equations shows that the cable experiences stretching oscillations only when the flow speed exceeds a certain level. Above this level both stretching and transverse motions take place. The influences of system parameters such as gravity-to-stiffness ratio and density ratio on the response characteristics are also reported.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1008223909270

Permalink

	Location	Call Number	Expected	Availability

Others were also interested in ...

Paper (German National Licenses)

Fulltext

6

Electronic Resource

Deterministic and Stochastic Response of Nonlinear Coupled Bending-Torsion Modes in a Cantilever Beam (1998)

Ibrahim, R. A. ; Hijawi, M.

Springer

Nonlinear dynamics 16 (1998), S. 259-292

add to mindlist on the mindlist

Details

ISSN: 1573-269X

Keywords: Beams ; nonlinear bending-torsion dynamics ; parametric excitation ; stochastic stability ; Monte Carlo simulation

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The purpose of this study is to understand the main differences between the deterministic and random response characteristics of an inextensible cantilever beam (with a tip mass) in the neighborhood of combination parametric resonance. The excitation is applied in the plane of largest rigidity such that the bending and torsion modes are cross-coupled through the excitation. In the absence of excitation, the two modes are also coupled due to inertia nonlinearities. For sinusoidal parametric excitation, the beam experiences instability in the neighborhood of the combination parametric resonance of the summed type, i.e., when the excitation frequency is in the neighborhood of the sum of the first bending and torsion natural frequencies. The dependence of the response amplitude on the excitation level reveals three distinct regions: nearly linear behavior, jump phenomena, and energy transfer. In the absence of nonlinear coupling, the stochastic stability boundaries are obtained in terms of sample Lyapunov exponent. The response statistics are estimated using Monte Carlo simulation, and measured experimentally. The excitation center frequency is selected to be close to the sum of the bending and torsion mode frequencies. The beam is found to experience a single response, two possible responses, or non-stationary responses, depending on excitation level. Experimentally, it is possible to obtain two different responses for the same excitation level by providing a small perturbation to the beam during the test.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1008096810969

Permalink

	Location	Call Number	Expected	Availability

Others were also interested in ...

Paper (German National Licenses)

Fulltext

7

Electronic Resource

Parametric Excitation of Nonlinear Elastic Systems Involving Hydrodynamic Sloshing Impact (1999)

El-Sayad, M. A. ; Hanna, S. N. ; Ibrahim, R. A.

Springer

Nonlinear dynamics 18 (1999), S. 25-50

add to mindlist on the mindlist

Details

ISSN: 1573-269X

Keywords: liquid sloshing modeling ; impact ; parametric resonance

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The parametric excitation of an elevated water tower experiencing sloshing hydro-dynamic impact is studied using the multiple scales method. The liquid sloshing mass is replaced by a mechanical model in the form of a simple pendulum experiencing impacts with the tank walls. The impact loads are modeled based on a phenomenological representation in the form of a power function with a higher exponent. In this case the system equations of motion include impact nonlinearities (selected to be of fifth power) and cubic structural geometric nonlinearities. When the first mode is parametrically excited the system exhibits hard nonlinear behavior and the impact loading reduced the response amplitude. On the other hand, when the second mode is parametrically excited, the impact loading results in complex response behavior characterized by multiple steady state solutions, where the response switches from soft to hard nonlinear characteristics. Under combined parametric resonance, the system possesses a single steady-state response in the absence and in the presence of impact. However, the system behaves like a soft system in the absence of impact and like a hard system in the presence of impact.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1008384709906

Permalink

	Location	Call Number	Expected	Availability

Others were also interested in ...

Paper (German National Licenses)

Fulltext

8

Electronic Resource

Random excitation of coupled oscillators with single and simultaneous internal resonances (1996)

Afaneh, A. A. ; Ibrahim, R. A.

Springer

Nonlinear dynamics 11 (1996), S. 347-400

add to mindlist on the mindlist

Details

ISSN: 1573-269X

Keywords: Random excitation ; nonlinear inertia ; internal resonance ; Monte Carlo testing

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The primary objective of this paper is to examine the random response characteristics of coupled nonlinear oscillators in the presence of single and simultaneous internal resonances. A model of two coupled beams with nonlinear inertia interaction is considered. The primary beam is directly excited by a random support motion, while the coupled beam is indirectly excited through autoparametric coupling and parametric excitation. For a single one-to-two internal resonance, we used Gaussian and non-Gaussian closures, Monte Carlo simulation, and experimental testing to predict and measure response statistics and stochastic bifurcation in the mean square. The mean square stability boundaries of the coupled beam equilibrium position are obtained by a Gaussian closure scheme. The stochastic bifurcation of the coupled beam is predicted theoretically and experimentally. The stochastic bifurcation predicted by non-Gaussian closure is found to take place at a lower excitation level than the one predicted by Gaussian closure and Monte Carlo simulation. It is also found that above a certain excitation level, the solution obtained by non-Gaussian closure reveals numerical instability at much lower excitation levels than those obtained by Gaussian and Monte Carlo approaches. The experimental observations reveal that the coupled beam does not reach a stationary state, as reflected by the time evolution of the mean square response. For the case of simultaneous internal resonances, both Gaussian and non-Gaussian closures fail to predict useful results, and attention is focused on Monte Carlo simulation and experimental testing. The effects of nonlinear coupling parameters, internal detuning ratios, and excitation spectral density level are considered in both investigations. It is found that both studies reveal common nonlinear features such as bifurcations in the mean square responses of the coupled beam and modal interaction in the neighborhood of internal resonances. Furthermore, there is an upper limit for the excitation level above which the system experiences unbounded response in the neighborhood of simultaneous internal resonances.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00045332

Permalink

	Location	Call Number	Expected	Availability

Others were also interested in ...

Paper (German National Licenses)

Fulltext

9

Electronic Resource

On the interaction of single-charged counterions with a macroion in arbitrary media (1997)

Brenerman, Mikhail L. ; Manyurov, Ibrahim R. ; Tukhvatullin, Rashid G. ; [et al.]

Bognor Regis [u.a.] : Wiley-Blackwell

Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 33-46

add to mindlist on the mindlist

Details

ISSN: 0887-6266

Keywords: polyelectrolyte ; counterion association ; site binding ; solvation ; coil-globule transition ; Physics ; Polymer and Materials Science

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology , Physics

Notes: This article represents an attempt to develop a generalized approach to the creation of a model of ionic interactions in polyelectrolyte solutions. Particular attention is given to the problems of considering nonelectrostatic interactions. A theoretical description is made of solvophobic effects arising in nonaqueous media between undissociated salt units. The influence of such phenomena on the counterion association is illustrated with experimental data. The model is based on the consideration of the configurational integral of a macromolecule. The solvent is assumed to have different solvation properties with respect to different groups within the polymer, resulting in an attractive component in the interaction potential between the undissociated units. It is shown that with a certain critical fraction of undissociated units the “phase separation” of a macromolecule into coil and globular parts may occur. This is accompanied by drastic enhancement of counterion association and suppression of the growth of the electrostatic potential of a macroion. With a further increase in the number of such units the complete globulization of a macromolecule takes place. The theoretical pH and conductivity dependences on the neutralization degree are calculated and correlated with experimental results. © 1997 John Wiley & Sons, Inc.

Additional Material: 14 Ill.

Type of Medium: Electronic Resource

Permalink