Nonlinear Responses and Stability of an Elastic Suspended Cable System Subjected to Parametrical External Excitations

2017 ◽  
Vol 6 (1) ◽  
pp. 1-13
Author(s):  
Liming Dai ◽  
Dandan Xia ◽  
Changping Chen
Keyword(s):  
Nonlinear Vibrations ◽  
Nonlinear Behavior ◽  
Single Frequency ◽  
External Excitation ◽  
Cable System ◽  
Suspended Cable ◽  
Nonlinear Responses ◽  
Out Of Plane ◽  
The Stability ◽  
Parametric And External Excitations

AbstractThis research investigates the nonlinear behavior and stability of an elastic suspended cable system under combined parametric and external excitations, with an approach of higher accuracy and reliability. Geometric nonlinearity of the cable and its in-plane and out-of-plane vibrations are considered. Multiple solutions of the system are found existing, corresponding to a single frequency of external excitation. The nonlinear stability of the cable system is investigated with focus on the influence of different system parameters. With the newly developed Periodicity-Ratio (P-R) method, the influences of different external excitations on the nonlinear vibrations of the cable system are examined, and a periodic-nonperiodic-chaotic region diagram is created for quantitatively and graphically identifying the stability and nonlinear behavior of the system.

The Periodic Solution and Numerical Simulations for Iced Cable System

2013 ◽  
Vol 394 ◽  
pp. 144-149
Author(s):  
Jing Li ◽  
Yan Ping Ran ◽  
Xiao Na Yin ◽  
Li Hua Chen
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Parametric Resonance ◽  
Blow Up ◽  
Melnikov Function ◽  
Principal Resonance ◽  
Internal Resonances ◽  
Cable System ◽  
Out Of Plane ◽  
The Stability

In this paper, the periodic behavior of iced cable in the case of the in-plane fundamental parametric resonance-principal resonance, out-of-plane principal parametric resonance-principal resonance, and in 1:2 internal resonances is investigated. The sufficient condition for the existence of the periodic solutions about the system is obtained through using Melnikov function and Poincare mapping, then the stability of periodic solution is investigated by using blow-up transformations and the average method. Numerical simulations are performed to verify the analytical predictions and get three groups of diagrams.

scholarly journals Out-of-plane local mechanism analysis with finite element method

2021 ◽  
Vol 8 (1) ◽  
pp. 130-136
Author(s):  
Roberto Spagnuolo
Keyword(s):  
Finite Element ◽  
Masonry Walls ◽  
Finite Element Models ◽  
Mechanism Analysis ◽  
Fem Method ◽  
Local Mechanism ◽  
Out Of Plane ◽  
Smeared Crack ◽  
The Stability ◽  
No Tension Material

Abstract The stability check of masonry structures is a debated problem in Italy that poses serious problems for its extensive use. Indeed, the danger of out of plane collapse of masonry walls, which is one of the more challenging to evaluate, is traditionally addressed not using finite element models (FEM). The power of FEM is not properly used and some simplified method are preferred. In this paper the use of the thrust surface is suggested. This concept allows to to evaluate the eccentricity of the membrane stresses using the FEM method. For this purpose a sophisticated, layered, finite element with a no-tension material is used. To model a no-tension material we used the smeared crack method as it is not mesh-dependent and it is well known since the early ’80 in an ASCE Report [1]. The described element has been implemented by the author in the program Nòlian by Softing.

scholarly journals Parametric Instability of a Traveling Plate Partially Supported by a Laterally Moving Elastic Foundation

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
V. Kartik ◽  
J. A. Wickert
Keyword(s):  
Data Storage ◽  
Parametric Instability ◽  
Primary Resonance ◽  
Free Edge ◽  
Moving Plate ◽  
Torsional Mode ◽  
Plane Vibration ◽  
Out Of Plane ◽  
Axially Moving ◽  
The Stability

The parametric excitation of an axially moving plate is examined in an application where a partial foundation moves in the plane of the plate and in a direction orthogonal to the plate’s transport. The stability of the plate’s out-of-plane vibration is of interest in a magnetic tape data storage application where the read/write head is substantially narrower than the tape’s width and is repositioned during track-following maneuvers. In this case, the model’s equation of motion has time-dependent coefficients, and vibration is excited both parametrically and by direct forcing. The parametric instability of out-of-plane vibration is analyzed by using the Floquet theory for finite values of the foundation’s range of motion. For a relatively soft foundation, vibration is excited preferentially at the primary resonance of the plate’s fundamental torsional mode. As the foundation’s stiffness increases, multiple primary and combination resonances occur, and they dominate the plate’s stability; small islands, however, do exist within unstable zones of the frequency-amplitude parameter space for which vibration is marginally stable. The plate’s and foundation’s geometry, the foundation’s stiffness, and the excitation’s amplitude and frequency can be selected in order to reduce undesirable vibration that occurs along the plate’s free edge.

Retuning the actuator proportional–integral–derivative controller of spinning missiles

2016 ◽  
Vol 231 (14) ◽  
pp. 2594-2602 ◽  
Author(s):  
Wei Zhou ◽  
Shuxing Yang ◽  
Liangyu Zhao
Keyword(s):  
Angular Motion ◽  
Proportional Integral Derivative ◽  
Proportional Integral Derivative Controller ◽  
Proportional Integral ◽  
Out Of Plane ◽  
Integral Element ◽  
The Stability ◽  
Proportional Derivative Controller

The hinge moment acting on the actuator will cause an out-of-plane moment, which is a destabilizing factor to the angular motion of spinning missiles. A new tuning criterion for the actuator controller is proposed to decrease the out-of-plane moment. It is noted that the integral element does not decrease the out-of-plane moment. A carefully designed proportional–derivative controller with some compromises can ensure the stability of the missile and provide good performance for the actuator.

Nonlinear Vibration of Sheet Metal Plates Under Interacting Parametric and External Excitation During Manufacturing

2005 ◽  
Vol 127 (1) ◽  
pp. 36-43 ◽  
Author(s):  
Chung Hwan Kim ◽  
Chong-Won Lee ◽  
N. C. Perkins
Keyword(s):  
Sheet Metal ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Synergistic Effects ◽  
Broad Band ◽  
Metal Plate ◽  
Time Dependent ◽  
Single Frequency ◽  
Cubic Nonlinearity ◽  
External Excitation

This study is motivated by the vibrations that plague coating processes used in the manufacturing of coated sheet metal. These vibrations arise from time-dependent tension fluctuations within the sheet metal plate as well as from the eccentricity of the rollers used to transport the plate. The time-dependent tension is observed to be rather broad-band and creates multi-frequency parametric excitation. By contrast, the roller eccentricity is largely single-frequency (synchronized with the roller speed) and creates single-frequency external excitation. The plate and excitation sources are studied herein using a single-degree-of-freedom model with a cubic nonlinearity, subject to combined parametric and external excitation. In our study, we investigate the resonances that arise from the synergistic effects of multi-frequency parametric excitation and single-frequency external excitation. For the simpler case of single-frequency parametric excitation, we observe both sum and difference combination resonances in addition to principal parametric resonance. For the case of multi-frequency parametric excitation, we observe a frequency shift for the parametric resonance that derives from the cubic nonlinearity and external excitation. Moreover, the phase relationships of the external and each parametric excitation source have a significant effect on the resulting response amplitude. We use these analyses to explain the resonance mechanisms observed in experiments conducted on an example sheet metal coating process.

scholarly journals Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

2006 ◽  
Author(s):  
M. Amabili ◽  
C. Touze´ ◽  
O. Thomas
Keyword(s):  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Nonlinear Responses ◽  
Nonlinear Normal ◽  
The Galerkin Method ◽  
Proper Orthogonal

The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.

A Multi-Mode Approach for the Nonlinear Vibrations of Circular Cylindrical Shells

2001 ◽  
Author(s):  
Francesco Pellicano ◽  
Marco Amabili ◽  
Michael P. Païdoussis
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Symbolic Manipulation ◽  
Comparison Functions ◽  
Circular Cylindrical Shells ◽  
Multi Mode

Abstract The nonlinear vibrations of simply supported, circular cylindrical shells, having geometric nonlinearities is analyzed. Donnell’s nonlinear shallow-shell theory is used, and the partial differential equations are spatially discretized by means of the Galerkin procedure, using a large number of degrees of freedom. A symbolic manipulation code is developed for the discretization, allowing an unlimited number of modes. In the displacement expansion particular care is given to the comparison functions in order to reduce as much as possible the dimension of the dynamical system, without losing accuracy. Both driven and companion modes are included, allowing for traveling-wave response of the shell. The fundamental role of the axisymmetric modes, which are included in the expansion, is confirmed and a convergence analysis is performed. The effect of the geometric shell characteristics, radius, length and thickness, on the nonlinear behavior is analyzed.

Stability Coefficient of Interlocking Compressed Earth Block Masonry under Axial Compression

2020 ◽  
Author(s):  
Tianya Wang ◽  
Yihong Wang ◽  
Guiyuan Zeng ◽  
Jianxiong Zhang ◽  
Dan Shi
Keyword(s):  
Compressive Strength ◽  
Axial Compression ◽  
Design Guidelines ◽  
Stability Coefficient ◽  
Strength Failure ◽  
Compressed Earth Block ◽  
Out Of Plane ◽  
The Stability ◽  
Earth Block ◽  
Plane Deformations

To investigate the effects of the height-thickness ratio (β) on the mechanical properties and stability coefficients (φs) of interlocking compressed earth block (ICEB) masonry members under axial compression, four groups of specimens with different β of 3.75, 6.75, 11.25, and 14.25 were tested, thereby assessing their stress process, failure mode, compressive strength, and in- and out-of-plane deformations. All the specimens underwent brittle failure under axial compression: the compressive strength was found to decrease in a range from 5.6% to 43% with increasing β, whereas the initial stacking defects and the in- and out-of-plane deformations increased. The specimens became less stable, and we noticed that the overall damage was caused by strength failure and not instability failures. Because the stability coefficient of ICEB-based masonry components cannot be calculated as those of more conventional brickwork, we combined our results with well-established masonry design guidelines and derived an interlocking improvement coefficient.

scholarly journals Nonlinear dynamical behaviors of a moving membrane under external excitation

2018 ◽  
Vol 37 (4) ◽  
pp. 774-788
Author(s):  
Mingyue Shao ◽  
Jimei Wu ◽  
Yan Wang ◽  
Shudi Ying
Keyword(s):  
Nonlinear Vibration ◽  
Plate Theory ◽  
State Equation ◽  
Vibration Characteristics ◽  
The State ◽  
External Excitation ◽  
Nonlinear Dynamical ◽  
Runge Kutta Method ◽  
Time Histories ◽  
The Stability

In this paper, the nonlinear vibration characteristics of a moving printing membrane under external excitation are studied. Based on the Von Karman nonlinear plate theory, the nonlinear vibration equation of the axial motion membrane under the external excitation is deduced. The Galerkin’s method is used to discretize the vibration differential equations of the membrane, and then the state equation of the system is obtained. The state equation of the system is numerically solved by the fourth-order Runge–Kutta method. The relationship between the nonlinear vibration characteristics and the amplitude of external excitation, damping coefficient, and aspect ratio of the printing membrane is analyzed by using the time histories, phase-plane portraits, Poincare maps, and bifurcation diagrams. Chaotic intervals and the stable working range of the moving membrane are obtained. This study provides a theoretical basis for predicting and controlling the stability of the membrane.

Bursting Oscillations as well as the Mechanism in a Filippov System with Parametric and External Excitations

2020 ◽  
Vol 30 (12) ◽  
pp. 2050168
Author(s):  
Hongfang Han ◽  
Qinsheng Bi
Keyword(s):  
Autonomous System ◽  
Type System ◽  
External Excitation ◽  
Nonsmooth Boundary ◽  
Bursting Oscillations ◽  
Fold Bifurcation ◽  
Different Types ◽  
Boundary Equilibrium ◽  
Parametric And External Excitations ◽  
Filippov Type

The main purpose of this paper is to explore the bursting oscillations as well as the mechanism of a parametric and external excitation Filippov type system (PEEFS), in which different types of bursting oscillations such as fold/nonsmooth fold (NSF)/fold/NSF, fold/NSF/fold and fold/fold bursting oscillations can be observed. By employing the overlap of the transformed phase portrait and the equilibrium branches of the generalized autonomous system, the mechanisms of the bursting oscillations are investigated. Our results show that the fold bifurcation and the boundary equilibrium bifurcation (BEB) can cause the transitions between the quiescent states and repetitive spiking states. The oscillating frequencies of the spiking states can be approximated theoretically by their occurring mechanisms, which agree well with the numerical simulations. Furthermore, some nonsmooth evolutions are investigated by employing differential inclusions theory, which reveals that the positional relationship between the points of the trajectory interacting with the nonsmooth boundary and the related sliding boundary of the nonsmooth system may affect the nonsmooth evolutions.

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