Assignment of Geometrical and Physical Parameters for the Confinement of Vibrations in Flexible Structures

Gafsi, Wajih; Choura, Slim; Nayfeh, Ali H.

doi:10.1061/(asce)0893-1321(2009)22:4(403)

Cited by 2 publications

(6 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We now apply the strategy of vibration confinement for linear structures based on the orthogonality of linear mode shapes [4]. This strategy outputs a set of physical and geometrical parameters for the confinement of vibrations in desired regions of the structure to be controlled.…”

Section: Inverse Eigenvalue Problemmentioning

confidence: 99%

“…We now apply the inverse eigenvalue problem to each of the values of to determine the beam spatially varying geometry. To this end, 1 ( ) and 2 ( ) are written as linear combinations of simple polynomials [4]:…”

Section: Inverse Eigenvalue Problemmentioning

confidence: 99%

“…To obtain accurate results, the inverse eigenvalue problem is numerically solved using the first 5 assumed modes ( = 5) [4]. Figures 4 and 5 show the resulting nondimensional stiffness 1 ( ) and mass functions 2 ( ).…”

Section: Inverse Eigenvalue Problemmentioning

confidence: 99%

“…In certain cases, vibration excites unwanted resonances characterized by intolerable amplitudes. Because of the need for controlling structural vibrations and satisfying the increasing demand on security, accuracy, and long-life of these structures, researches focused on synthesizing control strategies, which are classified into three types: active [1,2], passive [3,4], and hybrid [5,6]. Allaei [7] showed that vibration confinement is a superior control issue over the conventional control in isolating the sensitive parts of a structure.…”

Section: Introductionmentioning

confidence: 99%

“…They established conditions for selecting the rod's material and geometrical properties by constructing positive Lyapunov functions whose derivative with respect to the space variable is required to be negative. Baccouch et al [3] and Gafsi et al [4] used the orthogonality conditions of mode shapes, for approximating the physical and geometrical parameters of an inhomogeneous beam for the purpose of confining the vibratory motion in prespecified parts of its spatial domain.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam

Gafsi

Najar

Choura³

et al. 2014

Shock and Vibration

Self Cite

View full text Add to dashboard Cite

In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.

show abstract

Section: Inverse Eigenvalue Problemmentioning

confidence: 99%

Section: Inverse Eigenvalue Problemmentioning

confidence: 99%

Section: Inverse Eigenvalue Problemmentioning

confidence: 99%