A Combined Steady-State/Transient Approach to Study Very Large Amplitude Ship Rolling

1995 ◽  
Author(s):  
J. Falzarano ◽  
R. Kota ◽  
I. Esparza
Keyword(s):  
Steady State ◽  
Large Amplitude ◽  
Wave Amplitude ◽  
Practical Importance ◽  
Rolling Motion ◽  
Frequency Range ◽  
Response Curves ◽  
Type Of Behavior ◽  
Steady State Solutions ◽  
Ship Rolling

Abstract For ships, rolling motion is the most critical due to the possibility of capsizing. In a regular (periodic) sea, if no bounded steady state solutions exist, then capsizing may be imminent. Determining for exactly which wave amplitude and frequency the steady-state solutions disappear or become unstable is of great practical importance. In previous works (Falzarano, Esparza, and Taz Ul Mulk, 1994) and abstracted presentations (Falzarano, 1993), the global transient dynamics of large amplitude ship rolling motion was studied. The effect on the steady-state solutions of changing wave frequency for a fixed wave amplitudes was studied. It was shown how the in-phase and out-of-phase solutions evolve as the frequency passes through the linear natural frequency. For small wave amplitudes (external forcing) there exists a single steady-state throughout the frequency range, for moderate wave amplitudes there exists a frequency range where multiple steady state harmonic solutions exists. As the wave amplitude was increased further there existed a frequency range where no steady-state harmonic solution existed. In the present work, the very large amplitude ship rolling motion in the region where no steady-state solutions exist will be studied in more detail. Moreover, the mechanisms (bifurcations) that cause this type of behavior to evolve from more simple behavior will be studied using a combination of both frequency response curves and Poincaré maps. It is expected that global chaotic bifurcations such as those previously described (e.g., Thompson and Stewart, 1989) will be identified.

Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation

2014 ◽  
Vol 14 (04) ◽  
pp. 1450009 ◽  
Author(s):  
Andrew Yee Tak Leung ◽  
Hong Xiang Yang ◽  
Ping Zhu
Keyword(s):  
Steady State ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Homotopy Continuation ◽  
Response Curves ◽  
System A ◽  
Structural Responses ◽  
Voigt Model ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

This paper is concerned with the steady state bifurcations of a harmonically excited two-member plane truss system. A two-degree-of-freedom Duffing system having nonlinear fractional derivatives is derived to govern the dynamic behaviors of the truss system. Viscoelastic properties are described by the fractional Kelvin–Voigt model based on the Caputo definition. The combined method of harmonic balance and polynomial homotopy continuation is adopted to obtain steady state solutions analytically. A parametric study is conducted with the help of amplitude-response curves. Despite its seeming simplicity, the mechanical system exhibits a wide variety of structural responses. The primary and sub-harmonic resonances and chaos are found in specific regions of system parameters. The dynamic snap-through phenomena are observed when the forcing amplitude exceeds some critical values. Moreover, it has been shown that, suppression of undesirable responses can be achieved via changing of viscosity of the system.

Combined Steady State and Transient Analysis of a Patrol Vessel as Affected by Varying Amounts of Damping and Periodic and Random Wave Excitation

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Jeffrey M. Falzarano ◽  
Srinivas Vishnubhotla ◽  
Sarah E. Juckett
Keyword(s):  
Dynamical System ◽  
Steady State ◽  
Critical Behavior ◽  
Large Amplitude ◽  
Transient Analysis ◽  
System Analysis ◽  
Random Wave ◽  
Rolling Motion ◽  
Wave Excitation ◽  
Random Forcing

In this paper various techniques of dynamical system analysis are used to analyze the effect of damping on large amplitude nonlinear ship-rolling motion of a patrol vessel. In particular steady state magnification curves, Poincare maps are for harmonic forcing and project phase planes are for random forcing. It has been found that varying amounts of damping substantially affect the vessel’s critical behavior. This is important since most stability regulations ignore damping and solely concentrate on the vessel’s righting ram curve. Moreover roll damping is difficult to predict accurately and small changes in damping may have a significant effect.

Modal Analysis to Interpret Localization Phenomena in Two Nonlinear Tuned Mass Dampers

2021 ◽  
Author(s):  
Yuji Harata ◽  
Takashi Ikeda
Keyword(s):  
Steady State ◽  
Modal Analysis ◽  
Equations Of Motion ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Response Curves ◽  
Tuned Mass Dampers ◽  
Second Mode ◽  
Steady State Solutions ◽  
Modal Coordinates

Abstract This study investigates localization phenomena in two identical nonlinear tuned mass dampers (TMDs) installed on an elastic structure, which is subjected to external, harmonic excitation. In the theoretical analysis, the mode shapes of the system are determined, and the modal equations of motion are derived using modal analysis. These equations are demonstrated as forming an autoparametric system in which external excitation directly acts on the first and third vibration modes, whereas the second vibration mode is indirectly excited due to the nonlinear coupling with the other modes. Van der Pol’s method is employed to obtain the frequency response curves for both physical and modal coordinates. The two TMDs vibrate in phase for the first and third modes, but vibrate out of phase for the second mode. Consequently, when all modes appear, the two TMDs may vibrate at different amplitudes, i.e., localization phenomena may occur because the TMD motions are expressed by the summation of motions for all modes. The numerical calculations clarify that the localization phenomena may occur in the two TMDs when all three modes appear simultaneously. Moreover, there are two steady-state solutions of the harmonic oscillations for the second mode with identical amplitudes; however, their phases differ by π. Hence, which TMD vibrates at higher amplitudes depends on which of these two steady-state solutions for the phase.

Large-amplitude compression waves in an adiabatic two-fluid model of a collision-free plasma

1962 ◽  
Vol 14 (3) ◽  
pp. 369-384 ◽  
Author(s):  
K. W. Morton
Keyword(s):  
Steady State ◽  
Large Amplitude ◽  
Numerical Solutions ◽  
Discontinuous Solution ◽  
Compression Waves ◽  
Amplitude Compression ◽  
Mach Numbers ◽  
Steady State Solutions ◽  
Free Plasma ◽  
Two Fluid

The development of large amplitude compression waves in a collision-free plasma is studied by considering the motion of a plane piston into a uniform stationary plasma containing a magnetic field parallel to the plane of the piston. The adiabatic two-fluid equations are solved by finite-difference methods and the form of the waves after a long time is compared with the possible steady-state solutions.A generalized discontinuous solution of the steady-state equations is found for sufficiently high Mach numbers. At the highest Mach numbers this leads to a constant state at the piston; while at lower speeds a wave train results whose amplitude increases as the speed decreases. In each of these cases the numerical solutions of the time-dependent equations converge rapidly to the steady-state solutions. At still lower speeds, where the solitary-wave solution exists, the situation is less clear.

Bifurcation Phenomena Caused by Multiple Nonlinear Vibration Absorbers

2010 ◽  
Vol 5 (2) ◽  
Author(s):  
Takashi Ikeda
Keyword(s):  
Steady State ◽  
Nonlinear Vibration ◽  
Excitation Frequency ◽  
Pitchfork Bifurcation ◽  
Harmonic Excitation ◽  
Vibration Absorbers ◽  
Response Curves ◽  
System Parameters ◽  
Chaotic Vibrations ◽  
Steady State Solutions

The characteristics of two, three, and four nonlinear vibration absorbers or nonlinear tuned mass dampers (NTMDs) attached to a structure under harmonic excitation are investigated. The frequency response curves are theoretically determined using van der Pol’s method. When the parameters of the absorbers are equal, it is found from the theoretical analysis that pitchfork bifurcations may occur on the part of the response curves, which are unstable in the multi-absorber systems, but are stable in a system with one NTMD. Multivalued steady-state solutions, such as three steady-state solutions for a dual-absorber system with different amplitudes, five steady-state solutions for a triple-absorber system, and seven steady-state solutions for a quadruple-absorber system, appear near bifurcation points. The NTMDs behave in that one of them vibrates at high amplitudes while the others vibrate at low amplitudes, even if the dimensions of the NTMDs are identical. Namely, “localization phenomenon” or “mode localization” occurs. After the pitchfork bifurcation, Hopf bifurcations may occur depending on the values of the system parameters, and amplitude- and phase-modulated motions, including chaotic vibrations, appear after the Hopf bifurcation when the excitation frequency decreases. Lyapunov exponents are numerically calculated to prove the occurrence of chaotic vibrations. Bifurcation sets are also calculated to investigate the influence of the system parameters on the response of the systems.

Large Amplitude Rolling Motion of an Ocean Survey Vessel

1994 ◽  
Vol 31 (04) ◽  
pp. 278-285
Author(s):  
Jeffrey Falzarano ◽  
Mohammad Taz Ul Mulk
Keyword(s):  
New Orleans ◽  
Large Amplitude ◽  
Roll Motion ◽  
Rolling Motion ◽  
Additional Work ◽  
Large Amplitude Motions ◽  
The Subject ◽  
The University ◽  
Insight Into ◽  
Ship Rolling

This paper describes some recently completed research at the University of New Orleans into the nonlinear and coupled aspects of large amplitude ship rolling motion, including capsizing, at all heading angles. The study analyzes the roll motion of a vessel which experienced large amplitude motions. By studying the nonlinear and coupled aspects of the critical roll motion, insight into the important parameters affecting the roll was obtained. The roll was found to be multivalued and highly coupled to the sway and the yaw motion. Additional work has been completed and more work is in progress to investigate additional aspects of the subject vessel's motion.

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