Stochastic Dynamic Analysis of U-OWC Wave Energy Converters

2017 ◽  
Author(s):  
Pol D. Spanos ◽  
Federica M. Strati ◽  
Giovanni Malara ◽  
Felice Arena
Keyword(s):  
Monte Carlo ◽  
Wave Energy ◽  
Random Vibration ◽  
Equations Of Motion ◽  
Statistical Linearization ◽  
Stochastic Dynamic ◽  
Sea Waves ◽  
Monte Carlo Data ◽  
Linear Differential ◽  
Stochastic Dynamic Analysis

The paper presents a random vibration analysis of a U-Oscillating Water Column wave energy harvester (U-OWC). The U-OWC comprises a vertical duct on the wave beaten side, in addition to the elements of conventional OWCs. From a mathematical perspective, the U-OWC dynamic response is governed by a set of coupled non-linear differential equations with asymmetric matrices of mass, damping, and stiffness. In this work, an approximate analytical solution of the U-OWC equations of motion is sought by using the technique of statistical linearization. This technique allows pursuing rapid random vibration analyses via classical linear input-output relationships. The analysis is conducted by considering the case of the full-scale prototype in the port of Civitavecchia (Rome, Italy). The reliability of the proposed approach is assessed versus relevant Monte Carlo data. For this, realizations of sea states compatible with typical power spectral density functions of sea waves are employed. The performed analyses prove that the statistical linearization technique based approach is an efficient and reliable tool which may both circumvent the use of time-consuming Monte Carlo simulations, and be used for a variety of design optimization related parameter studies.

A Method for Fatigue Analysis of Pipelines on Topsides of FPSO Systems

2005 ◽  
Author(s):  
Pol Spanos ◽  
Alba Sofi ◽  
Juan Wang ◽  
Berry Peng
Keyword(s):  
Fatigue Life ◽  
Random Vibration ◽  
Equations Of Motion ◽  
Plug Flow ◽  
Fatigue Curve ◽  
Sea Waves ◽  
Random Loading ◽  
Euler Beam ◽  
Stress Spectrum ◽  
The Galerkin Method

Pipelines located on the decks of FPSO systems are exposed to damage due to sea waves induced random loading. In this context, a methodology for estimating the fatigue life of conveying-fluid pipelines is presented. The pipeline is subjected to a random support motion which simulates the effect of the FPSO heaving. The equation of motion of the fluid-carrying pipeline is derived by assuming small amplitude displacements, modeling the empty pipeline as a Bernoulli-Euler beam, and adopting the so-called “plug-flow” approximation for the fluid (Pai¨doussis, 1998). Random vibration analysis is carried out by the Galerkin method selecting as basis functions the natural modes of a beam with the same boundary conditions as the pipeline. The discretized equations of motion are used in conjunction with linear random vibration theory to compute the stress spectrum for a generic section of the pipeline. For this purpose, the power spectrum of the acceleration at the deck level is determined by using the Response Amplitude Operator of the FPSO hull. Finally, the computed stress spectrum is used to estimate the pipeline fatigue life employing an appropriate S-N fatigue curve of the material. An illustrative example concerning a pipeline simply-supported at both ends is included in the paper.

Efficient Dynamic Analysis of a Nonlinear Wave Energy Harvester Model

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Pol D. Spanos ◽  
Felice Arena ◽  
Alessandro Richichi ◽  
Giovanni Malara
Keyword(s):  
Monte Carlo ◽  
Linear System ◽  
Wave Energy ◽  
Alternative Energy ◽  
Energy Harvester ◽  
Single Point ◽  
Computational Cost ◽  
Complex Problem ◽  
Statistical Linearization ◽  
Monte Carlo Techniques

In recent years, wave energy harvesting systems have received considerable attention as an alternative energy source. Within this class of systems, single-point harvesters are popular at least for preliminary studies and proof-of-concept analyses in particular locations. Unfortunately, the large displacements of a single-point wave energy harvester are described by a set of nonlinear equations. Further, the excitation is often characterized statistically and in terms of a relevant power spectral density (PSD) function. In the context of this complex problem, the development of efficient techniques for the calculation of reliable harvester response statistics is quite desirable, since traditional Monte Carlo techniques involve nontrivial computational cost. The paper proposes a statistical linearization technique for conducting expeditiously random vibration analyses of single-point harvesters. The technique is developed by relying on the determination of a surrogate linear system identified by minimizing the mean square error between the linear system and the nonlinear one. It is shown that the technique can be implemented via an iterative procedure, which allows calculating statistics, PSDs, and probability density functions (PDFs) of the response components. The reliability of the statistical linearization solution is assessed vis-à-vis data from relevant Monte Carlo simulations. This novel approach can be a basis for constructing computationally expeditious assessments of various design alternatives.

Statistical Linearization of Nonlinear Stiffness Matrix of Planetary Gear Train

2017 ◽  
Author(s):  
Jalal Taheri Kahnamouei ◽  
Jianming Yang
Keyword(s):  
Stiffness Matrix ◽  
Random Vibration ◽  
Planetary Gear ◽  
Small Time ◽  
Gear Train ◽  
Statistical Linearization ◽  
Stochastic Dynamic ◽  
Nonlinear Stiffness ◽  
Time Step ◽  
Planetary Gear Train

Stochastic dynamic analysis of the planetary gear train is complicated and it becomes more challenging when the nonlinear term is considered in the equation. A backlash between gears’ teeth is one of the nonlinearity sources in the gearbox which changes the equation of random vibration to nonlinear. In this paper, the linearization of the random vibration of multi-degrees of freedom (MDOF) with nonlinear stiffness is examined for planetary gear trains. The method used to treat nonlinearity is the statistical linearization method (SL). At first, to achieve adequate accuracy, the time domain is divided into very small time intervals then SL is utilized in each time step. For each time step an equivalent linear stiffness matrix is calculated and replacs the nonlinear stiffness matrix. The comparison between equivalent stiffness and linear stiffness at each step has shown a good agreement.

Phenomenological renormalisation of Monte Carlo data

1982 ◽  
Vol 15 (11) ◽  
pp. L617-L623 ◽  
Author(s):  
M N Barber ◽  
W Selke
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Data

scholarly journals Relativistic equations for elementary particles

1948 ◽  
Vol 192 (1029) ◽  
pp. 195-218 ◽  
Keyword(s):  
Elementary Particle ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Wave Form ◽  
Total Charge ◽  
Field Equations ◽  
Relativistic Approximation ◽  
Special Cases ◽  
Linear Differential

From the general principles of quantum mechanics it is deduced that the wave equation of a particle can always be written as a linear differential equation of the first order with matrix coefficients. The principle of relativity and the elementary nature of the particle then impose certain restrictions on these coefficient matrices. A general theory for an elementary particle is set up under certain assumptions regarding these matrices. Besides, two physical assumptions concerning the particle are made, namely, (i) that it satisfies the usual second-order wave equation with a fixed value of the rest mass, and (ii) either the total charge or the total energy for the particle-field is positive definite. It is shown that in consequence of (ii) the theory can be quantized in the interaction free case. On introducing electromagnetic interaction it is found that the particle exhibits a pure magnetic moment in the non-relativistic approximation. The well-known equations for the electron and the meson are included as special cases in the present scheme. As a further illustration of the theory the coefficient matrices corresponding to a new elementary particle are constructed. This particle is shown to have states of spin both 3/2 and 1/2. In a certain sense it exhibits an inner structure in addition to the spin. In the non-relativistic approximation the behaviour of this particle in an electromagnetic field is the same as that of the Dirac electron. Finally, the transition from the particle to the wave form of the equations of motion is effected and the field equations are given in terms of tensors and spinors.

Stochastic Dynamic Analysis and Reliability of a Vessel Rolling in Random Beam Seas

2015 ◽  
Vol 59 (02) ◽  
pp. 113-131
Author(s):  
Wei Chai ◽  
Arvid Naess ◽  
Bernt J. Leira
Keyword(s):  
Dynamic System ◽  
Markov Property ◽  
Planck Equation ◽  
Linear Filter ◽  
Stochastic Dynamic ◽  
Theoretical Principle ◽  
Pi Method ◽  
Beam Seas ◽  
Stochastic Dynamic Analysis ◽  
High Level

This article presents a four-dimensional (4D) path integration (PI) approach to study the stochastic roll response and reliability of a vessel in random beam seas. Specifically, a 4D Markov dynamic system is established by combing the single-degree-of freedom model used to represent the ship rolling behavior in random beam seas with a second-order linear filter used to approximate the stationary roll excitation moment. On the basis of the Markov property of the coupled 4D dynamic system, the response statistics of roll motion can be obtained by solving the Fokker-Planck equation of the dynamic system via the 4D PI method. The theoretical principle and numerical implementation of the current state of the art 4D PI method are presented. Moreover, the numerical robustness and accuracy of the 4D PI method are evaluated by comparing with the results obtained by the application of Monte Carlo simulation (MCS). The influence of the restoring terms and the damping terms on the stochastic roll response are investigated. Furthermore, based on the well-known Poisson assumption and the response statistics yielded by the 4D PI technique, evaluation of the reliability associated with high-level response is performed. The performance of the Poisson estimate for different levels of external excitations is evaluated by the versatile MCS technique.

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