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.

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.

Transient Vibrations of Two-Dimensional Beam Frames at Mid- and High-Frequencies

2019 ◽  
Author(s):  
Yichi Zhang ◽  
Bingen Yang
Keyword(s):  
Frequency Analysis ◽  
High Frequency ◽  
Transfer Functions ◽  
Flexible Structures ◽  
Frame Structure ◽  
Inverse Laplace Transform ◽  
Two Dimensional ◽  
Beam Structure ◽  
Element Analysis ◽  
High Frequencies

Abstract Transient vibrations of flexible structures at mid- and high-frequencies have important applications in aerospace, civil, auto and ship engineering. In this paper, a new method is developed for the determination of the transient vibration solutions of two-dimensional beam frames in mid- and high-frequency regions. In the development, the governing equations of a beam frame structure are formulated by an augmented Distributed Transfer Function Method (DTFM), without the need for discretization and approximation. The augmented DTFM differs from the traditional DTFM in that it does not contain the singularities of subsystem transfer functions, which is crucially important in a mid- or high-frequency analysis. The proposed method delivers exact eigensolutions of a beam structure from low- to high-frequencies without numerical instability. With the platform provided by the augmented DTFM, the transient response of a beam structure can be conveniently estimated by either modal expansion or the residue formula for inverse Laplace transform. A highlight of the augmented DTFM lies in that detailed information at mid- and high-frequencies, such as local displacement, slope, bending moment and shear force at any point, can be obtained, which otherwise may be difficult with conventional methods for mid- and high-frequency analysis. The proposed method is illustrated on several examples and is computationally efficient and stable from low- to high-frequency regions. In the numerical simulation, the augmented DTFM is shown to produce more accurate results than traditional finite element analysis (FEA). The proposed method is extensible to three-dimensional beam structures.

scholarly journals Damage localization for beam structure by moving load

2017 ◽  
Vol 9 (3) ◽  
pp. 168781401769595 ◽  
Author(s):  
Qiuwei Yang ◽  
JK Liu ◽  
BX Sun ◽  
CF Liang
Keyword(s):  
Moving Load ◽  
Damage Localization ◽  
Beam Structure

Dynamic Analysis and Parametric Excitation of a Multi-Span Beam Structure Coupled With a Sequence of Moving Rigid Bodies

2018 ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Rigid Bodies ◽  
Time Varying ◽  
Beam Structure ◽  
Assumed Mode Method ◽  
Mode Method

Dynamic analysis of a multi-span beam structure carrying moving rigid bodies is essentially important in various engineering applications. With many rigid bodies having different speeds and varying inter-distances, number of degrees of freedom of the coupled beam-moving rigid body system is time-varying and the beam-rigid body interaction is thus complicated. Developed in this paper is a method of extended solution domain (ESD) that resolves the issue of time-varying number of degrees and delivers a consistent mathematical model for the coupled system. The governing equation of the coupled system is derived with generalized assumed mode method through use of exact eigenfunctions and solved via numerical integration. Numerical simulation shows the accuracy and efficiency of the proposed method. Moreover, a preliminary study on parametric resonance on a beam structure with 10 rigid bodies provides guidance for future development of conditions on parametric resonance induced by moving rigid bodies, which can be useful for operation of certain coupled structure systems.

Vibration Control of Smart Structures Using Piezofilm Actuators

2006 ◽  
Vol 306-308 ◽  
pp. 1205-1210
Author(s):  
Seung Bok Choi ◽  
Jung Woo Sohn
Keyword(s):  
Vibration Control ◽  
Time Domain ◽  
Sliding Mode ◽  
Flexible Structures ◽  
Space Representation ◽  
Sliding Mode Controller ◽  
Separation Principle ◽  
Beam Structure ◽  
Experimental Realization ◽  
Smart Beam

This paper presents vibration control of a flexible smart beam structure using a new discrete-time sliding mode controller. After formulating the dynamic model in the space representation, so called the separation principle for equivalent controller is established so that the sliding mode conditions are satisfied. By doing this, undesirable chattering of the flexible structures can be attenuated in the settled phase. In order to demonstrate some benefits of the proposed methodology, an experimental realization is undertaken. Both transient and forced vibration control responses are evaluated in time domain and compared between with and without the separation principle.

scholarly journals Model Reduction Technique Tailored to the Dynamic Analysis of a Beam Structure under a Moving Load

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Yuanchang Chen ◽  
Bangji Zhang ◽  
Shengzhao Chen
Keyword(s):  
Dynamic Analysis ◽  
Model Reduction ◽  
Moving Load ◽  
Single Point ◽  
Point Load ◽  
Computational Time ◽  
Small Scale ◽  
Response Analysis ◽  
Computational Accuracy ◽  
Beam Structure

This study presents a technique that uses a model reduction method for the dynamic response analysis of a beam structure to a moving load, which can be modeled either as a moving point force or as a moving body. The nature of the dedicated condensation method tailored to address the moving load case is that the master degrees of freedom are reselected, and the coefficient matrices of the condensed model are recalculated as the load travels from one element to another. Although this process increases computational burden, the overall computational time is still greatly reduced because of the small scale of motion equations. To illustrate and validate the methodology, the technique is initially applied to a simply supported beam subjected to a single-point load moving along the beam. Subsequently, the technique is applied to a practical model for wheel-rail interaction dynamic analysis in railway engineering. Numerical examples show that the condensation model can solve the moving load problem faster than an analytical model or its full finite element model. The proposed model also exhibits high computational accuracy.

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