Parametric Vibration of a Flexible Structure Excited by Periodic Passage of Moving Oscillators

2020 ◽  
Vol 87 (7) ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Dynamic Stability ◽  
Parametric Resonance ◽  
Flexible Structures ◽  
Coupled System ◽  
Analytical Form ◽  
Stability Criteria ◽  
Analysis Method ◽  
State Equations ◽  
Supporting Structure ◽  
Moving Oscillator

Abstract Flexible structures carrying moving subsystems are found in various engineering applications. Periodic passage of subsystems over a supporting structure can induce parametric resonance, causing vibration with ever-increasing amplitude in the structure. Instead of its engineering implications, parametric excitation of a structure with sequentially passing oscillators has not been well addressed. The dynamic stability in such a moving-oscillator problem, due to viscoelastic coupling between the supporting structure and moving oscillators, is different from that in a moving-mass problem. In this paper, parametric resonance of coupled structure-moving oscillator systems is thoroughly examined, and a new stability analysis method is proposed. In the development, a set of sequential state equations is first derived, leading to a model for structures carrying a sequence of moving oscillators. Through the introduction of a mapping matrix, a set of stability criteria on parametric resonance is then established. Being of analytical form, these criteria can accurately and efficiently predict the dynamic stability of a coupled structure-moving oscillator system. In addition, by the spectral radius of the mapping matrix, the global stability of a coupled system can be conveniently investigated in a parameter space. The system model and stability criteria are illustrated and validated in numerical examples.

A Computational Investigation of Dynamic Stabilization of Rayleigh-Bénard Convection Under System Acceleration

2020 ◽  
Author(s):  
Ilker Topcuoglu ◽  
Robert F. Kunz ◽  
Robert W. Smith
Keyword(s):  
Dynamic Stability ◽  
Compressible Flows ◽  
Coupled System ◽  
Boussinesq Approximation ◽  
State Equations ◽  
Bénard Convection ◽  
Flow Stabilization ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract The static and dynamic stability of Rayleigh-Bénard convection in a rectangular flow domain is computationally investigated. Sinusoidal vertical oscillations are applied to the system to provide dynamic flow stabilization. Stability maps are produced for a range of flow and heating conditions, and are compared to experimental measurements and linear stability analysis predictions from existing literature. Density variation is introduced through: 1) the Boussinesq approximation, 2) a linearly varying temperature dependent equation of state (EOS) and 3) the perfect gas EOS. Significant effects of choice of EOS on dynamic stability are observed. These weakly compressible flows are solved efficiently using an implicit numerical method that has been developed to solve the momentum, continuity, enthalpy and state equations simultaneously in fully coupled fashion. This block coupled system of equations is linearized with Newton’s method, and quadratic convergence is achieved. The details of these numerics are presented.

Parametric Resonance of a Beam Structure Induced by Groups of Oscillators in Periodic Movement

2020 ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Parametric Resonance ◽  
Moving Load ◽  
Flexible Structures ◽  
Beam Structure ◽  
State Equations ◽  
Transit Systems ◽  
Weapon Systems ◽  
Periodic Movement ◽  
Domain Mapping ◽  
External Loads

Abstract Flexible structures carrying moving subsystems have various engineering applications, including cable transport, fast transit systems, and weapon systems. In some applications, the vibration of the supporting structure induced by successively moving subsystems can become significant and develop into parametric resonance. In study of the parametric resonance caused by moving subsystems, a conventional approach is to model subsystems as moving concentrated external loads, which leads to traditional resonance due to periodic excitation. In this paper, with consideration of the inertia effect and flexible coupling of subsystems, parametric resonance of a beam structure induced by groups of oscillators moving over it is investigated. Through a special formulation of sequential state equations, dynamic stability of the beam structure is predicted by eigenvalues of a time-domain mapping matrix. From numerical simulation, it shows that apart from the speed of oscillators that directly determines the characteristic period, the inertia and stiffness of the oscillators can also alter the parametric resonance conditions. This phenomenon cannot be captured with the conventional moving load assumption.

Aeroservoelasticity Analysis Method Based on an Error Analytical Form Applied on a Business Aircraft

2008 ◽  
Vol 14 (8) ◽  
pp. 1217-1230 ◽  
Author(s):  
D.E. Biskri ◽  
R.M. Botez ◽  
N. Stathopoulos ◽  
S. Thérien ◽  
M. Dickinson ◽  
...  
Keyword(s):  
Analytical Form ◽  
Analysis Method

scholarly journals Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Tao Liao ◽  
Hao-Chih Lee ◽  
Ge Yang ◽  
Yongjie Jessica Zhang
Keyword(s):  
Correspondence Analysis ◽  
Flexible Structures ◽  
Spectral Shape ◽  
The Other ◽  
Shape Deformation ◽  
Second Step ◽  
Analysis Method ◽  
Shape Correspondence ◽  
Dense Point ◽  
Different Shapes

AbstractThe functionality of biomolecules depends on their flexible structures, which can be characterized by their surface shapes. Tracking the deformation and comparing biomolecular shapes are essential in understanding their mechanisms. In this paper, a new spectral shape correspondence analysis method is introduced for biomolecules based on volumetric eigenfunctions. The eigenfunctions are computed from the joint graph of two given shapes, avoiding the sign flipping and confusion in the order of modes. An initial correspondence is built based on the distribution of a shape diameter, which matches similar surface features in different shapes and guides the eigenfunction computation. A two-step scheme is developed to determine the final correspondence. The first step utilizes volumetric eigenfunctions to correct the assignment of boundary nodes that disobeys the main structures. The second step minimizes the distortion induced by deforming one shape to the other. As a result, a dense point correspondence is constructed between the two given shapes, based on which we approximate and predict the shape deformation, as well as quantitatively measure the detailed shape differences.

Stochastic Earthquake Analysis of Underwater Storage Tanks

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
H. Karadeniz
Keyword(s):  
Finite Element ◽  
Water Pressure ◽  
Water Structure ◽  
Coupled System ◽  
Earthquake Loading ◽  
Storage Tanks ◽  
Analysis Method ◽  
Eulerian Formulation ◽  
Analysis Technique ◽  
Flexible Wall

In this paper, the problem and analysis method of underwater storage tanks resting on a horizontal seabed is presented under stochastic earthquake loading. The tank is axisymmetrical and has a flexible wall/roof. The finite element method is used for the response solution. A solid axisymmetrical finite element has been formulated to idealize the tank whereas an axisymmetrical fluid element is used for the idealization of the fluid domain. The Eulerian formulation of the fluid system is used to calculate the interactive water pressure acting on the tank during the free motion of the tank and earthquake motion. For the response calculation, the modal analysis technique is used with a special algorithm to obtain natural frequencies of the water-structure coupled system. For the stochastic description of the earthquake loading, the modified Kanai–Tajimi earthquake spectrum is used. Finally, the analysis method presented in the paper is demonstrated by an example.

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