APPLICATION OF GLOBAL METHODS FOR ANALYZING DYNAMICAL SYSTEMS TO SHIP ROLLING MOTION AND CAPSIZING

1992 ◽  
Vol 02 (01) ◽  
pp. 101-115 ◽  
Author(s):  
JEFFREY M. FALZARANO ◽  
STEVEN W. SHAW ◽  
ARMIN W. TROESCH
Keyword(s):  
Nonlinear Dynamic ◽  
Invariant Manifolds ◽  
Initial Conditions ◽  
Global Analysis ◽  
Relative Size ◽  
Nonlinear Dynamic Analysis ◽  
Periodic Wave ◽  
Industry Standards ◽  
Highly Nonlinear ◽  
Lobe Dynamics

Ship capsizing is a highly nonlinear dynamic phenomenon where global system behavior is dominant. However the industry standards for analysis are limited to linear dynamics or nonlinear statics. Until recently, most nonlinear dynamic analysis relied upon perturbation methods which are severely restricted both with respect to the relative size of the nonlinearity and the region of consideration in the phase space (i.e., they are usually restricted to a small local region about a single equilibrium), or on numerical studies of idealized system models. In this work, recently developed global analysis techniques (e.g., those found in Guckenheimer and Holmes [1986], and Wiggins [1988, 1990]) are used to study transient rolling motions of a small ship which is subjected to a periodic wave excitation. This analysis is based on determining criteria which can predict the qualitative nature of the invariant manifolds which represent the boundary between safe and unsafe initial conditions, and how these depend on system parameters for a specific ship model. Of particular interest is the transition which this boundary makes from regular to fractal, implying a loss in predictability of the ship’s eventual state. In this paper, actual ship data is used in the development of the model and the effects of various ship and wave parameters on this transition are investigated. Finally, lobe dynamics are used to demonstrate how unpredictable capsizing can occur.

Nonlinear Rolling Motion of a Statically Biased Ship Under the Effect of External and Parametric Excitation

1993 ◽  
Author(s):  
Isaac Esparza ◽  
Jeffrey Falzarano
Keyword(s):  
Steady State ◽  
Parametric Excitation ◽  
Poincaré Map ◽  
Initial Conditions ◽  
Global Analysis ◽  
Wave Train ◽  
Periodic Wave ◽  
Rolling Motion ◽  
Poincare Map ◽  
Safe Basin

Abstract In this work, global analysis of ship rolling motion as effected by parametric excitation is studied. The parametric excitation results from the roll restoring moment variation as a wave train passes. In addition to the parametric excitation, an external periodic wave excitation and steady wind bias are also included in the analysis. The roll motion is the most critical motion for a ship because of the possibility of capsizing. The boundaries in the Poincaré map which separate initial conditions which eventually evolve to bounded steady state solutions and those which lead to unbounded capsizing motion are studied. The changes in these boundaries or manifolds as effected by changes in the ship and environmental conditions are analyzed. The region in the Poincaré map which lead to bounded steady state motions is called the safe basin. The size of this safe basin is a measure of the vessel’s resistance to capsizing.

scholarly journals Nonlinear Dynamic Analysis of Axially Moving Laminated Shape Memory Alloy Beam with 1:3 Internal Resonance

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4022
Author(s):  
Ying Hao ◽  
Ming Gao ◽  
Yuda Hu ◽  
Yuehua Li
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Axial Velocity ◽  
Nonlinear Dynamic ◽  
Internal Resonance ◽  
Initial Conditions ◽  
Nonlinear Dynamic Analysis ◽  
Time History ◽  
Resonance Amplitude ◽  
Axially Moving

The remarkable properties of shape memory alloys (SMA) are attracting significant technological interest in many fields of science and engineering. In this paper, a nonlinear dynamic analytical model is developed for a laminated beam with a shape memory alloy layer. The model is derived based on Falk’s polynomial model for SMAs combined with Timoshenko beam theory. In addition, axial velocity, axial pressure, temperature, and complex boundary conditions are also parameters that have been taken into account in the creation of the SMA dynamical equation. The nonlinear vibration characteristics of SMA laminated beams under 1:3 internal resonance are studied. The multi-scale method is used to solve the discretized modal equation system, the characteristic equation of vibration modes coupled to each other in the case of internal resonance, as well as the time-history and phase diagrams of the common resonance amplitude in the system are obtained. The effects of axial velocity and initial conditions on the nonlinear internal resonance characteristics of the system were also studied.

Analysis On the In-Plane 2:2:1 Internal Resonance of a Complex Cable-Stayed Bridge System Under External Harmonic Excitation

2021 ◽  
Author(s):  
Houjun Kang ◽  
Tieding Guo ◽  
Weidong Zhu
Keyword(s):  
Nonlinear Dynamic ◽  
Internal Resonance ◽  
Multiple Scales ◽  
Initial Conditions ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Phenomena ◽  
Arch Model ◽  
Shallow Arch ◽  
Cable Stayed Bridge ◽  
Bridge System

Abstract Nonlinear dynamic analysis of a cable-stayed bridge has been a hot topic due to its structural flexibility. Based on integro-partial differential equations of a double-cable-stayed shallow-arch model, in-plane 2:2:1 internal resonance among three first in-plane modes of two cables and a shallow arch under external primary or subharmonic resonance is considered. Galerkin's method and the method of multiple scales are used to derive averaged equations of the cable-stayed bridge system. Nonlinear dynamic behaviours of the system are investigated via the numerical simulation. Results show rich nonlinear phenomena of the cable-stayed bridge system and some new phenomena are observed. Two identical cables that are symmetrically located above the shallow arch can have different dynamic behaviours even when initial conditions of the system are symmetrically given. Two cables with some differences between their parameters can exhibit either softening or hardening characteristics.

Nonlinear dynamic analysis of the bridge bearing and genetic algorithm–based optimization for seismic mitigation

2020 ◽  
Vol 23 (12) ◽  
pp. 2539-2556
Author(s):  
Xuan Liang ◽  
Lin Cheng ◽  
TianQiao Liu ◽  
JianBin Du
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Dynamic ◽  
Parametric Optimization ◽  
Nonlinear Dynamic Analysis ◽  
Bridge Pier ◽  
Hysteresis Curve ◽  
Mechanical Responses ◽  
Highly Nonlinear ◽  
Bridge Bearing ◽  
Seismic Mitigation

Seismic mitigation for bridges by the specific bearing with highly elastoplastic dissipaters is very important to ensure safety of superstructures exposed to earthquakes. To study the lateral vibration of the bridge bearing, a nonlinear dynamic model is developed while thoroughly considering highly nonlinear mechanical properties of the bearing in this article. The generalized- α method is specifically adapted to solve the nonlinear equations. Moreover, nonlinear behavior of the bearing is fully incorporated through direct path-following of the practical experimental hysteresis curve. The proposed method is validated through careful comparison between the dynamic simulation and the quasi-static experimental results. Mechanical responses of the bridge-pier system under earthquake excitations can be calculated in a more reliable manner. On this basis, a parametric optimization model involving several key parameters of the bearing-pier system is developed. The optimization problem is solved by the genetic algorithm as the searching tool. Numerical examples show that mechanical responses of the bridge-pier system subjected to the earthquake excitations can be effectively mitigated after parametric optimization. The extensive applicability of the proposed method is validated through finding the optimized parameters for the bearing when multiple different earthquakes are considered. Moreover, the accumulative energy absorption of the bearing is also considered to enhance the seismic performance of the bearing. This work provides a reliable way of dynamic performance prediction and seismic mitigation study of nonlinear bridge bearing under earthquake excitations given any complex experimental hysteresis curve.

Nonlinear Dynamic Response of a Simple Ice-Structure Interaction Model

1993 ◽  
Vol 115 (4) ◽  
pp. 246-252 ◽  
Author(s):  
D. G. Karr ◽  
A. W. Troesch ◽  
W. C. Wingate
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Initial Conditions ◽  
Ice Sheet ◽  
Interaction Model ◽  
Offshore Structure ◽  
Analogue Model ◽  
Nonlinear Dynamic Response ◽  
Structure Interaction ◽  
Highly Nonlinear

The problem addressed is the continuous indentation of a ship or offshore structure into an ice sheet. The impacting ship or offshore structure is represented by a mass-spring-dashpot system having a constant velocity relative to the ice sheet. The dynamic response of this simple analogue model of ice-structure interaction is studied in considerable detail. The complicated, highly nonlinear dynamic response is due to intermittent ice breakage and intermittent contact of the structure with the ice. Periodic motions are found and the periodicity for a particular system is dependent upon initial conditions. For a representative system, a Poincare´ map is presented showing the fixed points. A description of some of the effects of random variations in system parameters is also presented. Some implications of these findings regarding structural design for ice interaction are discussed.

An Efficient and Robust Nonlinear Dynamic Analysis Method for Framed Structures Using the Rigid Body Rule

2021 ◽  
Author(s):  
Zhaohui Chen ◽  
Min He ◽  
Yuchen Tao ◽  
Y. B. Yang
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Integration Method ◽  
Nonlinear Dynamic Analysis ◽  
Direct Integration ◽  
Analysis Method ◽  
Framed Structures ◽  
Geometric Stiffness ◽  
Highly Nonlinear

In this paper, by implanting the rigid body rule (RBR)-based strategy for static nonlinear problems into the implicit direct integration procedure, an efficient and robustness nonlinear dynamic analysis method for the response of framed structures with large deflections and rotations is proposed. The implicit integration method proposed by Newmark is improved by inserting an intermediate time into the time step and by adding the 3-point backward difference in the second substep so as to preserve the momentum conservation and to maintain the stability of the direct integration method. To solve the equivalent incremental equations of motion, the RBR is built in to deal with the rigid rotations and the resulting additional nodal forces of element. During the increment-iterative procedure, the use of RBR-qualified geometric stiffness in the predictor reduces the numbers of iterations, while the elastic stiffness alone in the corrector to update the element nodal forces makes the computation efficiency and convergence with no virtual forces caused by the ill geometric stiffness. The proposed algorithm is advanced in the applications of several framed structures with highly nonlinear behavior in the dynamic response by its simplicity, efficient and robustness.

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