Nonlinear study of the dynamic behavior of a string-beam coupled system under combined excitations

Hamed, Y. S.; Sayed, M.; Cao, Dongxing; Zhang, W.

doi:10.1007/s10409-011-0519-8

Cited by 21 publications

(7 citation statements)

References 30 publications

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“…Case 6. Figures 17,18,19,20,21,22,23,24,and 25 show that the frequency response curves for practical case stability, where 1 ̸ = 0, 2 ̸ = 0, and 3 ̸ = 0. Figure 17 shows that the effects of the detuning parameter 1 on the amplitudes of the three modes.…”

Section: Response Curve Of Casementioning

confidence: 99%

“…The stability of the system is investigated applying both frequency response equations and phaseplane method. Hamed et al [22] studied the nonlinear dynamic behavior of a string-beam coupled system subjected to external, parametric, and tuned excitations that are presented. The case of 1 : 1 internal resonance between the modes of the beam and string, and the primary and combined resonance for the beam is considered.…”

Section: Introductionmentioning

confidence: 99%

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Vibration, Stability, and Resonance of Angle-Ply Composite Laminated Rectangular Thin Plate under Multiexcitations

Sayed

Mousa

2013

Mathematical Problems in Engineering

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An analytical investigation of the nonlinear vibration of a symmetric cross-ply composite laminated piezoelectric rectangular plate under parametric and external excitations is presented. The method of multiple time scale perturbation is applied to solve the nonlinear differential equations describing the system up to and including the second-order approximation. All possible resonance cases are extracted at this approximation order. The case of 1 : 1 : 3 primary and internal resonance, whereΩ3≅ω1,ω2≅ω1, andω3≅3ω1, is considered. The stability of the system is investigated using both phase-plane method and frequency response curves. The influences of the cubic terms on nonlinear dynamic characteristics of the composite laminated piezoelectric rectangular plate are studied. The analytical results given by the method of multiple time scale is verified by comparison with results from numerical integration of the modal equations. Reliability of the obtained results is verified by comparison between the finite difference method (FDM) and Runge-Kutta method (RKM). It is quite clear that some of the simultaneous resonance cases are undesirable in the design of such system. Such cases should be avoided as working conditions for the system. Variation of the parametersμ1,μ2,α7,β8,ω1,ω2,f1,f2leads to multivalued amplitudes and hence to jump phenomena. Some recommendations regarding the different parameters of the system are reported. Comparison with the available published work is reported.

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Section: Response Curve Of Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibration, Stability, and Resonance of Angle-Ply Composite Laminated Rectangular Thin Plate under Multiexcitations

Sayed

Mousa

2013

Mathematical Problems in Engineering

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“…Kamel and Hamed [23] utilized the multiple scale technique to investigate the vibrations behavior of the inclined cable system with harmonic excitation at the simultaneous of primary and internal resonance cases. Hamed et al [24] investigated the behavior of vibrations for the nonlinear string beam system under external, parametric and tuned excitations forces. Sayed and Hamed [25] presented a mathematical study for the analytical, numerical solutions and stability of a coupled pitch roll system to harmonic and parametric excitation forces.…”

Section: Introductionmentioning

confidence: 99%

Active vibration suppression of a nonlinear electromechanical oscillator system with simultaneous resonance

Hamed¹,

Sayed²,

Alshehri³

2018

J. vibroeng.

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In this paper, we explored the nonlinear dynamics behavior and vibration suppression of a nonlinear electromechanical oscillator system under harmonic and parametric excitation. The model comprises of an electrical part coupled to mechanical part and displayed by a coupled nonlinear ordinary differential equations. The analytical up to second order approximate solutions are sought applying the method of multiple scales method. We utilized the time-series and method of averaging to analyze the response and stability of the solutions at the worst resonance cases. We checked the results of perturbation solution through numerical simulations and the effects of different system parameters have been reported. Comparison between analytical and numerical solutions is obtained. Also, the numerical results are obtained using MAPLE and MATLAB algorisms.

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“…Although the dynamic characteristics of a single beam can be obtained exactly by many ways, when a secondary beam is attached to the main beam by springs at several places, its solution becomes complicated. Previous studies mostly focus on beams with continuous elastica connection such as sandwich beam and composite beam [8,9], or beams with string connected at their ends [10]. Only a few researchers have performed dynamic analysis for the double-beam system connected by springs at several discrete locations.…”

Section: Introductionmentioning

confidence: 99%

Effects of Cable on the Dynamics of a Cantilever Beam with Tip Mass

Huang

Hao

Zhao

2016

Shock and Vibration

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The dynamic effects of cable attachment on a cantilever beam with tip mass are investigated by an improved Chebyshev spectral element method. The cabled beam is modeled as a double-beam system connected by springs at several discrete locations. By utilizing high order Chebyshev polynomials as basis functions and meshing the system at the locations of connections, precise numerical results of the natural frequencies and mode shapes can be obtained using only a few elements. The accuracy of this method is validated through comparing the results of finite element method and those of spectral element method in literature. The validated method is implemented to investigate the effects of parameters, including spring stiffness, number of connections, density, and Young’s modulus of cable. The results show that the mode shapes of the cabled beam system can be classified into two types: beam mode shapes and cable mode shapes, according to their main deformation. Their corresponding natural frequencies change in very different ways with the variation of system parameters. This work can be applied to optimize the dynamic characteristics of precise spacecraft structures with cable attachments.

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Nonlinear study of the dynamic behavior of a string-beam coupled system under combined excitations

Cited by 21 publications

References 30 publications

Vibration, Stability, and Resonance of Angle-Ply Composite Laminated Rectangular Thin Plate under Multiexcitations

Vibration, Stability, and Resonance of Angle-Ply Composite Laminated Rectangular Thin Plate under Multiexcitations

Active vibration suppression of a nonlinear electromechanical oscillator system with simultaneous resonance

Effects of Cable on the Dynamics of a Cantilever Beam with Tip Mass

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