Polynomial Approximations of Wave Loading and Superharmonic Responses of Fixed Structures

2003 ◽  
Vol 125 (3) ◽  
pp. 161-167 ◽  
Author(s):  
Chih Young Liaw ◽  
Xiang Yuan Zheng
Keyword(s):  
Drag Force ◽  
Volterra Series ◽  
Least Squares Method ◽  
Series Representation ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Wave Forces ◽  
Wave Loading ◽  
Wave Kinematics ◽  
Structural Responses

Besides the commonly considered drag force, inundation due to variable water surface is another important nonlinear effect of wave loading. Quadratic and quartic approximations of the inundation drag force are derived using the least squares method. Other nonlinear effects, including the second-order wave kinematics and nonlinear inertia wave forces, are also considered. Superharmonic forces and the corresponding structural responses due to different nonlinear effects are compared using a single mode representation of the fixed offshore structural system. The appropriate expressions that can serve as the basis for the Volterra series representation of the nonlinear wave forces are presented.

scholarly journals A theory of nonlinear wave loading on offshore structures

1981 ◽  
Vol 4 (3) ◽  
pp. 589-613 ◽  
Author(s):  
Lokenath Debnath ◽  
Matiur Rahman
Keyword(s):  
Nonlinear Wave ◽  
Vertical Cylinder ◽  
Nonlinear Effects ◽  
Diffraction Theory ◽  
Offshore Structures ◽  
The Body ◽  
Wave Number ◽  
Wave Forces ◽  
Wave Loading ◽  
Nonlinear Contribution

A theoretical study is made of the nonlinear wave loading on offshore structures using the diffraction theory of hydrodynamics. A nonlinear modification of the classical Morison equation,D≡Fℓ+FDfor estimating wave forces on offshore structures is suggested in this paper. The modified equation is found in the formD≡Fℓ+Fnℓ+FDwhereFnℓ≡Fd+Fw+Fqis the nonlinear contribution made up of the dynamic, waterline, and the quadratic forces associated with the irrotational-flow part of the wave loading on structures. The study has then been applied to calculate the linear and the nonlinear wave loadings on a large vertical cylinder partially immersed in an ocean of arbitrary uniform depth. All the linear and nonlinear forces exerting on the cylinder are determined explicitly. A comparison is made between these two kinds of forces. Special attention is given to the nonlinear wave loadings on the cylinder. It is shown that all nonlinear effects come from the interaction between the body's responses to the oncoming wave's fluctuating velocity and its fluctuating extension. It is found that the nonlinear effects are dominated by the sum of the dynamic and waterline forces. The nonlinear correction to Morison's equation increases with increasingkbwherebis the characteristic dimension of the body andkis the wave number. This prediction is shown to be contrary to that of the linear diffraction theory which predicted that the Morison coefficient decreases with increasingkb. Several interesting results and limiting cases are discussed in some detail.

scholarly journals AN EXPERIMENTAL STUDY OF A SOLITARY WAVE IMPACTING A VERTICAL SLENDER CYLINDER

2020 ◽  
pp. 8
Author(s):  
Bing Tai ◽  
Yuxiang Ma ◽  
Guohai Dong ◽  
Marc Perlin
Keyword(s):  
Solitary Wave ◽  
Structural Response ◽  
Equation Of Motion ◽  
Temporal Variations ◽  
Wave Forces ◽  
Wave Loads ◽  
Coastal Structures ◽  
High Wave ◽  
Wave Kinematics ◽  
Structural Responses

Solitary waves can evolve into plunging breakers during shoaling, inducing high wave loads on coastal structures. Meanwhile, plunging waves propagate with rapid spatial-temporal variations both in wave geometry and wave kinematics, causing varying forces on structures for different breaking stages (Chan et al., 1995). Although there have been numerous experiments for wave forces on cylinders, to our knowledge no experiments have studied the forces at different breaking stages of a plunging solitary wave. Thus, in our study, experiments are conducted to investigate the force due to a plunging solitary wave impacting a circular cylinder as a function of the wave's phase. Due to these forces, as expected structural responses are induced (Paulsen et al., 2019); to eliminate the effect of the structural response, the equation of motion is proposed to facilitate extracting only the isolated hydrodynamic forces.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/P07Cdlnxe7s

Ultrashort pulses propagation through different approaches of the Split-Step Fourier method

2018 ◽  
Vol 1 (3) ◽  
pp. 2
Author(s):  
José Stênio De Negreiros Júnior ◽  
Daniel Do Nascimento e Sá Cavalcante ◽  
Jermana Lopes de Moraes ◽  
Lucas Rodrigues Marcelino ◽  
Francisco Tadeu De Carvalho Belchior Magalhães ◽  
...  
Keyword(s):  
Energy Conservation ◽  
Optical Pulse ◽  
Time Window ◽  
Fourier Method ◽  
Ultrashort Pulses ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Time Algorithm ◽  
Optical Pulses ◽  
Running Time

Simulating the propagation of optical pulses in a single mode optical fiber is of fundamental importance for studying the several effects that may occur within such medium when it is under some linear and nonlinear effects. In this work, we simulate it by implementing the nonlinear Schrödinger equation using the Split-Step Fourier method in some of its approaches. Then, we compare their running time, algorithm complexity and accuracy regarding energy conservation of the optical pulse. We note that the method is simple to implement and presents good results of energy conservation, besides low temporal cost. We observe a greater precision for the symmetrized approach, although its running time can be up to 126% higher than the other approaches, depending on the parameters set. We conclude that the time window must be adjusted for each length of propagation in the fiber, so that the error regarding energy conservation during propagation can be reduced.

scholarly journals Amplification characteristics in active tapered segmented cladding fiber with large mode area

2021 ◽  
Vol 9 ◽  
Author(s):  
Caijian Xie ◽  
Tigang Ning ◽  
Jingjing Zheng ◽  
Li Pei ◽  
Jianshuai Wang ◽  
...  
Keyword(s):  
High Power ◽  
Heat Load ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Large Mode Area ◽  
High Loss ◽  
Effective Mode Area ◽  
Steady State Rate ◽  
State Rate ◽  
Mode Area

Abstract A kind of tapered segmented cladding fiber (T-SCF) with large mode area (LMA) is proposed, and the mode and amplification characteristics of T-SCFs with concave, linear, and convex tapered structures are investigated based on finite-element method (FEM) and few-mode steady-state rate equation. Simulation results indicate that the concave tapered structure can introduce high loss for high-order modes (HOMs) that is advantageous to achieve single-mode operation, whereas the convex tapered structure provides large effective mode area that can help to mitigate nonlinear effects. Meanwhile, the small-to-large amplification scheme shows further advantages on stripping off HOMs, and the large-to-small amplification scheme decreases the heat load density induced by the high-power pump. Moreover, single-mode propagation performance, effective mode area, and heat load density of the T-SCF are superior to those of tapered step index fiber (T-SIF). These theoretical model and numerical results can provide instructive suggestions for designing high-power fiber lasers and amplifiers.

Second Order Averaging Study of an Autoparametric System

1993 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj ◽  
Patricia Davies
Keyword(s):  
Dynamical Behavior ◽  
Period Doubling ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Pitchfork Bifurcation ◽  
Second Order ◽  
System Response ◽  
Response Curves ◽  
Vibratory System ◽  
First Order

Abstract The autoparametric vibratory system consisting of a primary spring-mass-dashpot system coupled with a damped simple pendulum serves as an useful example of two degree-of-freedom nonlinear systems that exhibit complex dynamic behavior. It exhibits 1:2 internal resonance and amplitude modulated chaos under harmonic forcing conditions. First-order averaging studies of this system using AUTO and KAOS have yielded useful information about the amplitude dynamics of this system. Response curves of the system indicate saturation and the pitchfork bifurcation sets are found to be symmetric. The period-doubling route to chaotic solutions is observed. However questions about the range of the small parameter ε (a function of the forcing amplitude) for which the solutions are valid cannot be answered by a first-order study. Some observed dynamical behavior, like saturation, may not persist when higher-order nonlinear effects are taken into account. Second-order averaging of the system, using Mathematica (Maeder, 1991; Wolfram, 1991) is undertaken to address these questions. Loss of saturation is observed in the steady-state amplitude responses. The breaking of symmetry in the various bifurcation sets becomes apparent as a consequence of ε appearing in the averaged equations. The dynamics of the system is found to be very sensitive to damping, with extremely complicated behavior arising for low values of damping. For large ε second-order averaging predicts additional Pitchfork and Hopf bifurcation points in the single-mode response.

Instantaneous Identification of Polynomial Nonlinearity Based on Volterra Series Representation

2005 ◽  
Vol 293-294 ◽  
pp. 703-710 ◽  
Author(s):  
Giacomo V. Demarie ◽  
Rosario Ceravolo ◽  
Alessandro de Stefano
Keyword(s):  
Structural Engineering ◽  
Volterra Series ◽  
Series Representation ◽  
Consistent Estimate ◽  
Short Time Fourier Transform ◽  
Dynamic Identification ◽  
Polynomial Nonlinearity ◽  
Definition Of ◽  
Short Time

In structural engineering applications a sufficient quantity of experimental data to be able to achieve a consistent estimate of nonlinear quantities is seldom available: this applies in particular when the structures are to be tested in situ. This report discusses the definition of instantaneous estimators to be used in the dynamic identification of invariant nonlinear systems on the basis of Short-Time Fourier Transform representation of excitation and system’s response and within the framework of a Volterra series representation of the input/output relationship. An estimation of the parameters of a dynamic system can be worked out from the evolution of such instantaneous estimators.

Analysis of a Microwave Feedforward Amplifier Using Volterra Series Representation

1977 ◽  
Vol 25 (3) ◽  
pp. 355-360 ◽  
Author(s):  
A. Javed ◽  
P. Goud ◽  
B. Syrett
Keyword(s):  
Volterra Series ◽  
Series Representation

On Random Field Discretization in Stochastic Finite Elements

1998 ◽  
Vol 65 (2) ◽  
pp. 320-327 ◽  
Author(s):  
B. A. Zeldin ◽  
P. D. Spanos
Keyword(s):  
Random Field ◽  
Volterra Series ◽  
Interpolation Method ◽  
Series Representation ◽  
Stochastic Mechanics ◽  
Discretization Methods ◽  
Nonlinear Input ◽  
Midpoint Method ◽  
Stochastic Finite Elements ◽  
Theoretical Developments

Several traditional methods for discretizing random fields in stochastic mechanics applications are considered; they are the midpoint method, the interpolation method, and the local averaging method. A simple and computationally convenient criterion for estimating the accuracy of these discretization methods is developed. Also, the Volterra series representation of nonlinear input/output relationships is utilized to assess the effect of the random field discretization methods on the response variability of stochastic mechanics problems. The theoretical developments are elucidated by a numerical example involving a beam problem.

An Experimental Method to Identify the Effects of Joints on Structures Using Laser Vibrometry

2001 ◽  
Author(s):  
Xianghong Ma ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman
Keyword(s):  
Complex Modulus ◽  
Nonlinear Effects ◽  
Mode Shapes ◽  
Joint Interface ◽  
Laser Vibrometry ◽  
Post Process ◽  
Structural Responses ◽  
The Difference ◽  
As Effects ◽  
Dynamic Phenomena

Abstract A technique based on laser vibrometry is outlined for identifying the effects of bolted joints on the structural dynamics. The method is based on the comparison of the dynamics of the bolted structure to that of a “baseline” structure; e.g., a structure with similar geometry and material characteristics but no jointed interface. Hence, under identical forcing conditions, the difference in the dynamics between the actual and baseline structures can be attributed solely to the joint interface effects. Non-contacting laser vibrometry is utilized to experimentally measure these differences in the structural responses at specific frequencies. A numerical algorithm is then developed to post-process the experimental data and identify the joint effects on the dynamics. The method provides estimates for the equivalent, frequency and amplitude dependent complex modulus of the joint interface. The laser scans of the mode shapes of the systems under consideration reveal interesting dynamic phenomena such as nonlinear effects due to micro-impacts at the bolted joint as well as effects due to non-proportional damping distribution.

Sign in / Sign up

Export Citation Format

Share Document