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.

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.

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.

scholarly journals Analysis of Nonlinear Vibrations and Dynamic Responses in a Trapezoidal Cantilever Plate Using the Rayleigh-Ritz Approach Combined with the Affine Transformation

2019 ◽  
Vol 2019 ◽  
pp. 1-23 ◽  
Author(s):  
Wei Tian ◽  
Zhichun Yang ◽  
Tian Zhao
Keyword(s):  
Nonlinear Dynamic ◽  
Affine Transformation ◽  
Internal Resonance ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Dynamic Responses ◽  
Geometrical Parameters ◽  
Cantilever Plate ◽  
Chaotic Motions ◽  
Trapezoidal Plate

Nonlinear vibrations of a trapezoidal cantilever plate subjected to transverse external excitation are investigated. Based on von Karman large deformation theory, the Rayleigh-Ritz approach combined with the affine transformation is developed to obtain the nonlinear ordinary differential equation of a trapezoidal plate with irregular geometries. With the variation of geometrical parameters, there exists the 1:3 internal resonance for the trapezoidal plate. The amplitude-frequency formulations of the system in three different coupled conditions are derived by using multiple scales method for 1:3 internal resonance analysis. It is found that the strong coupling of two modes can change nonlinear stiffness behaviors of modes from hardening-spring to soft-spring characteristics. The detuning parameter and excitation amplitude have significant influence on nonlinear dynamic responses of the system. The bifurcation diagrams show that there exist the periodic, quasi-periodic, and chaotic motions for the trapezoidal cantilever plate in the 1:3 internal resonance cases and the nonlinear dynamic responses are dependent on the amplitude of excitation. The possible adverse dynamic behaviors and undesired resonance can be avoided by designing appropriate excitation and system parameters.

Nonlinear dynamic analysis for coupled vehicle-bridge system with harmonic excitation

Meccanica ◽  
2016 ◽  
Vol 52 (9) ◽  
pp. 2219-2243
Author(s):  
Shihua Zhou ◽  
Guiqiu Song ◽  
Zhaohui Ren ◽  
Bangchun Wen
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Harmonic Excitation ◽  
Bridge System
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