Equation Chapter 1 Section 1 Dynamic stability in parametric resonance of vibrating beam micro-gyroscopes

Author(s):  
Hong-Yan Chen ◽  
Wei Li ◽  
Hong Yang
2020 ◽  
Vol 87 (7) ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang

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.


2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Hooi-Siang Kang ◽  
Moo Hyun Kim ◽  
Shankar S. Bhat Aramanadka

Abstract The development of a dry-tree semisubmersible (DTS), a new type offshore hydrocarbon production system, is facing unconventional challenges in the issues of dynamic stability, structural integrity, and parametric resonance. The Mathieu equation is used to assess the dynamic stability of a top-tensioned riser (TTR) in order to prevent the parametric resonance which leads to detrimental effects on structural integrity. The objectives of this paper are to (i) study a Mathieu stability diagram and its coefficients for an assessment of the stability of a TTR, (ii) identify the effects of the dynamic tension variations in the Mathieu stability assessment, and (iii) analyze the stability of the TTR on a DTS, which is equipped with a long-stroke tensioner, by using numerical simulation. The dynamic tension variation in the DTS was identified to induce instability in the TTR. Hence, the Mathieu stability assessment is recommended to be included in an analysis of TTR behaviors in a dry-tree interface of semisubmersibles.


Meccanica ◽  
2016 ◽  
Vol 51 (10) ◽  
pp. 2459-2472 ◽  
Author(s):  
Hamed Farokhi ◽  
Mergen H. Ghayesh ◽  
Shahid Hussain

2011 ◽  
Vol 308-310 ◽  
pp. 1389-1394 ◽  
Author(s):  
Nian Li Lu ◽  
Shi Ming Liu

In this paper, the dynamic stability of stepped columns under the axial resonant force is investigated, and the dynamic stability, which is also known as parametric resonance, of stepped columns with two ends simply supported and clamped ones are studied, respectively. The dynamic stability of multi-stepped columns is obtained by using Mathieu Equation deduced by Hamiliton Principle. The formula of the dynamic stability region is given and the effect of stiffness of stepped columns on the dynamic stability is analyzed. Results show that the area of dynamic instability decreases with the increase of the ratio of each section’s stiffness, and that the dynamic stability would be better when each section is of similar size.


2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668565 ◽  
Author(s):  
Hai An ◽  
Ling Zhou ◽  
Xing Wei ◽  
Weiguang An

The dynamic stability of supercavitating vehicles under periodic axial loading is investigated in this article. The supercavitating vehicle is simulated as a long and thin cylindrical shell subjected to periodic axial loading and simply supported boundary conditions. The nonlinear transverse vibration differential equation is obtained in terms of nonlinear geometric equations, physical equations, and balance equations of cylindrical shells. Mathieu equation with periodic coefficients and nonlinear term is derived by employing Galerkin variational method and Bolotin method. The analytical expressions of the steady-state amplitudes of vibrations in the first- and second-order instable regions are obtained by solving nonlinear Mathieu equation derived in this article. Numerical results are presented to analyze the influence of the sailing speed, ratio of loads, the frequency of axial loads, and the mode of vibration on parametric resonance curves and to show the nonlinear parametric resonance curves incline toward the side where it is greater than the excitation frequency, which significantly extends the range of the exciting region. The presented results indicate the enlargement of the exciting region will cause shrinkage of the safe frequency range of external loads and decrease in dynamic stability of supercavitating vehicle.


2021 ◽  
Vol 23 (1) ◽  
pp. 219-228
Author(s):  
Nabanita Saikia ◽  
Mohamed Taha ◽  
Ravindra Pandey

The rational design of self-assembled nanobio-molecular hybrids of peptide nucleic acids with single-wall nanotubes rely on understanding how biomolecules recognize and mediate intermolecular interactions with the nanomaterial's surface.


2000 ◽  
Vol 5 (5) ◽  
pp. 4-5

Abstract Spinal cord (dorsal column) stimulation (SCS) and intraspinal opioids (ISO) are treatments for patients in whom abnormal illness behavior is absent but who have an objective basis for severe, persistent pain that has not been adequately relieved by other interventions. Usually, physicians prescribe these treatments in cancer pain or noncancer-related neuropathic pain settings. A survey of academic centers showed that 87% of responding centers use SCS and 84% use ISO. These treatments are performed frequently in nonacademic settings, so evaluators likely will encounter patients who were treated with SCS and ISO. Does SCS or ISO change the impairment associated with the underlying conditions for which these treatments are performed? Although the AMA Guides to the Evaluation of Permanent Impairment (AMA Guides) does not specifically address this question, the answer follows directly from the principles on which the AMA Guides impairment rating methodology is based. Specifically, “the impairment percents shown in the chapters that consider the various organ systems make allowance for the pain that may accompany the impairing condition.” Thus, impairment is neither increased due to persistent pain nor is it decreased in the absence of pain. In summary, in the absence of complications, the evaluator should rate the underlying pathology or injury without making an adjustment in the impairment for SCS or ISO.


2000 ◽  
Vol 5 (6) ◽  
pp. 1-7
Author(s):  
Christopher R. Brigham ◽  
James B. Talmage ◽  
Leon H. Ensalada

Abstract The AMA Guides to the Evaluation of Permanent Impairment (AMA Guides), Fifth Edition, is available and includes numerous changes that will affect both evaluators who and systems that use the AMA Guides. The Fifth Edition is nearly twice the size of its predecessor (613 pages vs 339 pages) and contains three additional chapters (the musculoskeletal system now is split into three chapters and the cardiovascular system into two). Table 1 shows how chapters in the Fifth Edition were reorganized from the Fourth Edition. In addition, each of the chapters is presented in a consistent format, as shown in Table 2. This article and subsequent issues of The Guides Newsletter will examine these changes, and the present discussion focuses on major revisions, particularly those in the first two chapters. (See Table 3 for a summary of the revisions to the musculoskeletal and pain chapters.) Chapter 1, Philosophy, Purpose, and Appropriate Use of the AMA Guides, emphasizes objective assessment necessitating a medical evaluation. Most impairment percentages in the Fifth Edition are unchanged from the Fourth because the majority of ratings currently are accepted, there is limited scientific data to support changes, and ratings should not be changed arbitrarily. Chapter 2, Practical Application of the AMA Guides, describes how to use the AMA Guides for consistent and reliable acquisition, analysis, communication, and utilization of medical information through a single set of standards.


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