Vibrational Power Transmission in Curved Beams

Based on the Flügge curved beam theory and total inextensible assumption, the dynamic equations of curved pipe’s in-plane vibration are established using the Newton method. The wave propagation method is proposed for calculating the natural frequency of curved pipes with clamped-clamped supported at both ends. Then, the performance function of the resonance reliability of curved pipe conveying fluid is established. Main and total effect indices of global sensitivity analysis (GSA) are introduced. The truncated importance sampling (TIS) method is used for calculating these indices. In the example, the natural frequency and critical velocity of a semicircular pipe are calculated. The importance ranking of input variables is obtained at different working conditions. The method proposed in this paper is valuable and leads to reliability estimation and antiresonance design of curved pipe conveying fluid.

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“…In this paper, the Flügge beam model is used to approximate the curved pipe. The axial force and the shear force are [21,22]…”

Section: Dynamic Equations Ofmentioning

confidence: 99%

“…Solution of the Dynamic Equation. When the motion is simple harmonic vibration, tangential displacement and radial displacement can be written as [21,22] ( , ) = exp ( + ) ,…”

Section: Dynamic Equations Ofmentioning

confidence: 99%

The Resonance Reliability and Global Sensitivity Analysis of Curved Pipe Conveying Fluid Based on TIS Method

Zhao

Liu

Guo

et al. 2018

Mathematical Problems in Engineering

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“…Furthermore, Heron (1997) presented a paper on predictive sea using line wave impedances. Walsh & White (2000) investigated the vibrational power transmission in curved beams, and Bosmans & Nightingale (2001) focused on the vibrational energy transmission at bolted junctions between a plate and a stiffening rib. More importance, Wester & Mace (2005abc) contributed three papers for wave component analysis of energy flow in complex structures, which focuses on a deterministic model, ensemble statistics and two coupled plates, respectively.…”

Section: Travelling Wave Approachesmentioning

confidence: 99%

Energy Flow Theory of Nonlinear Dynamical Systems with Applications

Xing

2015

Emergence, Complexity and Computation

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com/mycopyOrder online at springer.com ▶ or for the Americas call (toll free) 1-800-SPRINGER ▶ or email us at: customerservice@springer.com. ▶ For outside the Americas call +49 (0) 6221-345-4301 ▶ or email us at: customerservice@springer.com.The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria. Prices indicated with ** include VAT for electronic products; 19% for Germany, 20% for Austria. All prices exclusive of carriage charges. Prices and other details are subject to change without notice. All errors and omissions excepted. This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing's oscillator, Van der Pol's equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as an undergraduate or graduate textbook or a comprehensive source for scientists, researchers and engineers, providing the statement of the art on energy flow or power flow theory and methods. J.T. Xing Energy Flow Theory of Nonlinear Dynamical Systems with Applications

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“…This is also the formulation adopted in this paper. Concerning the scattering properties of joints, wave approaches have been also used for the calculation of the reflection and transmission coefficients of plate/beam junctions [15], bolted joints [16] and curved beams [17]. The case of a junction with an elastic interlayer has been studied in [18], for a junction between semi-infinite plates [19,20] and for junctions in heavyweight buildings.…”

Section: Introductionmentioning

confidence: 99%

Wave transmission through two-dimensional structures by the hybrid FE/WFE approach

Mitrou

Ferguson

Renno

2017

Journal of Sound and Vibration

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The knowledge of the wave transmission and reflection characteristics in connected two-dimensional structures provides the necessary background for many engineering prediction methodologies. Extensive efforts have previously been exerted to investigate the propagation of waves in two-dimensional periodic structures. This work focuses on the analysis of the wave propagation and the scattering properties of joined structures comprising of two or more plates. The joint is modelled using the finite element (FE) method whereas each (of the joined) plate(s) is modelled using the wave and finite element (WFE) method. This latter approach is based on post-processing a standard FE model of a small segment of the plate using periodic structure theory; the FE model of the segment can be obtained using any commercial/in-house FE package. Stating the equilibrium and continuity conditions at the interfaces and expressing the motion in the plates in terms of the waves in each plate yield the reflection and transmission matrices of the joint. These can then be used to obtain the response of the whole structure, as well as investigating the frequency and incidence dependence for the flow of power in the system.

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Vibrational Power Transmission in Curved Beams

Cited by 42 publications

References 9 publications

The Resonance Reliability and Global Sensitivity Analysis of Curved Pipe Conveying Fluid Based on TIS Method

The Resonance Reliability and Global Sensitivity Analysis of Curved Pipe Conveying Fluid Based on TIS Method

Energy Flow Theory of Nonlinear Dynamical Systems with Applications

Wave transmission through two-dimensional structures by the hybrid FE/WFE approach

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