Periodic behavior of a nonlinear dynamical system

Esmailzadeh, Ebrahim; Ghorashi, Mehrdaad; Mehri, B.

doi:10.1007/bf00046307

Cited by 17 publications

(13 citation statements)

References 5 publications

(8 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Variation of the internal force components along the beam at t = 3s. the method has been discussed in detail in, for example, [Esmailzadeh et al 1995] and [Zwillinger 1998]. In this section this method is briefly reviewed and in the next section it will be used to provide solutions for the case of perturbed steady state.…”

Section: Steady State Solution Using the Shooting Methodsmentioning

confidence: 99%

Nonlinear dynamic response of an accelerating composite rotor blade using perturbations

Ghorashi

Nitzsche

2009

J. Mech. Mater. Struct.

View full text Add to dashboard Cite

The general nonlinear intrinsic differential equations of a composite beam are solved in order to obtain the elastodynamic response of an accelerating rotating hingeless composite beam. The solution utilizes the results of the linear variational asymptotic method applied to cross-sectional analysis. The integration algorithm implements the finite difference method in order to solve the transient form of the nonlinear intrinsic differential equations. The motion is analyzed since the beam starts rotating from rest, until it reaches the steady state condition. It is shown that the transient solution of the nonlinear dynamic formulation of the accelerating rotating beam converges to the steady state solution obtained by an alternative integration algorithm based on the shooting method. The effects of imposing perturbations on the steady state solution have also been analyzed and the results are shown to be compatible with those of the accelerating beam. Finally, the response of a nonlinear composite beam with embedded anisotropic piezocomposite actuators is illustrated. The effect of activating actuators at various directions on the steady state forces and moments generated in a rotating beam has been analyzed. These results can be used in controlling the nonlinear elastodynamic response of adaptive rotating beams.A list of symbols can be found starting on page 713.

show abstract

Section: Steady State Solution Using the Shooting Methodsmentioning

confidence: 99%

Nonlinear dynamic response of an accelerating composite rotor blade using perturbations

Ghorashi

Nitzsche

2009

J. Mech. Mater. Struct.

View full text Add to dashboard Cite

show abstract

“…In [Ghorashi and Nitzsche 2008] and [Ghorashi 2009] a method for obtaining the steady state response of rotating hingeless beams using the shooting method has been presented. The mathematical basis for Figure 7.…”

Section: Steady State Solution Using the Shooting Methodsmentioning

confidence: 99%

“…They were used in [Ghorashi 1994] and [Esmailzadeh and Ghorashi 1997] to solve a moving load problem. In what follows, Equations (12)- (14) will be used in order to convert the system of nonlinear partial differential equations (1) and (4) …”

Section: Derivation Of the Generic Nonlinear Termmentioning

confidence: 99%

See 1 more Smart Citation

Untitled

2009

J. Mech. Mater. Struct.

View full text Add to dashboard Cite

See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $600 a year (print and electronic); $460 a year (electronic only).Subscriptions, requests for back issues, and changes of address should be sent to contact@mathscipub.org or to Mathematical Sciences Publishers, 798 Evans Hall, Department of Mathematics, University of California, Berkeley, CA 94720-3840. His research interests were broad, and touched on many of the major themes in mechanics over the last 60 years: plate and shell theory, stability theory, vibrations of elastic bodies, wave propagation, and fracture mechanics. He remained active in research following his retirement from Stanford, and, in later years, developed an interest in the mechanics of solids as viewed from an Eshelbean standpoint. This he pursued vigorously with longtime collaborator Reinhold Kienzler up to his death in 2007. His work brought him wide recognition and a number of awards from various professional societies. Among these were election to the National Academy of Engineering, the Centennial Medal of the American Society of Mechanical Engineers, the von Karman medal of the American Society of Civil Engineers, and the Eringen medal of the Society of Engineering Science.His service to the mechanics community was equally important. He served on innumerable boards and committees, and was quite influential in the Applied Mechanics Division of the American Society of Mechanical Engineers. In an era in which important Soviet work in mechanics was largely unknown in the West, he began the English translation of Prikladnaya Matematika i Mekhanika, the premier Russian language mechanics journal and served for many years as its translation editor. Perhaps most significantly, he founded the International Journal of Solids and Structures in 1965 and served as its Editor until his retirement from Stanford, building it into one of the most reputable journals in the field.On a personal level, George Herrmann was a man of great warmth and charm. Those of us who were his students will recall his kindness and consideration, even on those occasions on which we tried his patience. Particularly impressive was his uncanny ability to find the best line of attack on a given research problem, where he was often able to obtain significant results with only a minimum of tools. His lectures were clear, focused, and well-organized, and his courses were always popular with the students. He was an accomplished linguist, and constantly amazed those of us around him by his ability to converse 629 630 TERRY J. DELPH AND DEWEY H. HODGES with the seminar speaker of the day in the speaker's native language. While at Stanford, he organized frequent outings, excursions, and dinners for the students and faculty that did much to build a strong sense of camaraderie within the Department, and later the Division, of Applied Mechanics.We think that we can speak for the contributors to this issue, and certainly for ourselves, in saying that it was a privilege to have known him.

show abstract

“…Schauder's theorem states that if a completely continuous operator A maps the closed convex set H of a Banach space X into itself, then there exists a fixed point of this mapping, being Ax0 = x0 [16,17].…”

Section: Second Order Autonomous Nonlinear System 309mentioning

confidence: 99%

Periodic solution of a second order, autonomous, nonlinear system

1996

Self Cite

View full text Add to dashboard Cite

There exist a sufficient condition for the existence of at least one periodic solution for a type of second order autonomous ordinary differential equations. The correctness of the condition has been pointed out by Schauder's fixed point theorem. In order to indicate the validity of the assumptions made, two illustrative examples, showing its application in the nonlinear vibration and relaxation oscillation are presented.

show abstract

Periodic behavior of a nonlinear dynamical system

Cited by 17 publications

References 5 publications

Nonlinear dynamic response of an accelerating composite rotor blade using perturbations

Nonlinear dynamic response of an accelerating composite rotor blade using perturbations

Untitled

Periodic solution of a second order, autonomous, nonlinear system

Contact Info

Product

Resources

About