Dynamic Analysis of Several Kinds of Structures with Nonlinear Effects

考慮非線性效應下幾類結構的動力學研究

Student thesis: Doctoral Thesis

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Award date15 Jan 2019

Abstract

Beams, plates, and shells are typical structures widely used as components in the fields of aerospace and aeronautical engineering, civil engineering and mechanical engineering fields. The nonlinearities in such structures cannot be neglected because large deformation may have significant influence on structural stability and dynamics. A well-established understanding of the dynamic characteristics of these structures subjected to various excitations would be useful and necessary for improvement in design and optimal distribution of material as well as oscillation control.

The research works contained in this thesis include three main parts. The first part focuses on two typical flow-induced vibrations of cylinders: galloping and vortex-induced vibrations. The second investigates the flutter and nonlinear dynamics of composite laminated plates and shells under supersonic airflow. The third part concerns the vibration characteristics of complicated structures, such as a rotating pre-twisted blade and a foldable multibeam structure.

Galloping, which arises from aerodynamic forces induced by structural vibration in wind flows, mainly occurs in across-wind direction and can lead to catastrophic structural failures. Evaluations of coupled two-degree-of-freedom (2DOF) galloping oscillations of slender structures with nonlinear effects are presented. Influences of various parameters, such as structural damping ratio, angle of wind attack, structural height, width and aspect ratio, on the onset wind velocity for the occurrence of coupled galloping are analyzed numerically and analytically.

Vortex-induced vibration occurs due to excitation caused by periodic alternating vortex shedding from two sides of a bluff body. When the vortex-shedding frequency is close to one of the natural frequencies of a bluff body, a large-amplitude resonant response occurs, termed as lock-in. A fluid-structure coupling model is established to investigate the vortex-induced vibration of a cylinder subjected to a uniform cross-flow. The transient responses of vortex-induced vibration of the fluid-structure coupled model are numerically analyzed in time domain and frequency domain. The resonant response of the model in the lock-in region is studied by the multiple scales method.

Flutter is a self-excited oscillation occurring at a critical Mach number above which the structural motion becomes unstable and grows exponentially with time. In the second part, the aeroelasticity and nonlinear dynamics of composite laminated plates and shells subjected to aerodynamic pressures and external excitations are investigated. The first-order piston theory is employed to model the air pressures. Nonlinear governing equations of motion for the plates and shells are derived by applying Hamilton’s principle, and then they are discretized to a set of nonlinear ordinary differential equations by adopting the Galerkin method. Numerical simulations are conducted to study the influences of the external excitations and aerodynamic pressures on the structural dynamic behaviors.

The vibration or modal characteristics of rotating structures change significantly when the structures undergo overall motions. A suitable formulation for a rotating blade can enable the use of analytical or semi-analytical methods to understand and identify the dynamic properties of the blade with good accuracy and fast calculation speed. In the third part, a dynamic model based on the shell theory is developed to investigate the vibration characteristics of a rotating composite laminated blade. The phenomena of frequency loci veering and crossing are observed and discussed in detail.

Foldable multibeam structures are widely used in aeronautical engineering. They could be modeled as folding wings of aircrafts that allow the aircrafts to optimize flight performance in different portions of flight missions. Modal analysis is conducted to find the specific folding angle at which one to two internal resonances will occur between the first two modes. Two cases of excitation frequencies are considered to investigate the nonlinear oscillation of the foldable multibeam structures. The saturation and jumping phenomena are identified and discussed by analyzing the frequency-response curves and force-response curves.

In this study, the vibration problems aforementioned are analyzed by theoretical methods and numerical simulations. The primary objective is to further investigate and explain many complicated nonlinear phenomena for these structures, such as multiple solutions, jumps, hysteresis, modal interactions, chaos, and transfer of energy from high-frequency to low-frequency modes. The validity of mathematical modeling and numerical simulations of this study are verified by comparing with results in literatures.