Complex Modal Extraction for Estimating Wave Parameters in One-Dimensional Media

2010 ◽  
Author(s):  
B. F. Feeny
Keyword(s):  
Group Velocity ◽  
Traveling Waves ◽  
Random Noise ◽  
Mode Shapes ◽  
Transient Wave ◽  
Wave Speeds ◽  
One Dimensional ◽  
Wave Numbers ◽  
Displacement Profile ◽  
Complex Modal

A method of complex orthogonal decomposition is applied to the extraction of modes from simulation data of multi-modal traveling waves in one-dimensional continua. The decomposition of a transient wave is performed on a nondispersive pulse. Complex wave modes are then extracted from a two-harmonic simulation of a dispersive medium. The wave frequencies and wave numbers are obtained by looking at the whirl of the complex modal coordinate, and the complex modal function, respectively, in the complex plane. From the frequencies and wave numbers, the wave speeds are then estimated, as well as the group velocity associated with the two waves. The group velocity is also extracted directly from a decomposition of the traveling envelope of the waveform. The observations from the first two examples are used to help interpret the decomposition of a simulation of the traveling waves produced by a Gaussian initial displacement profile in an Euler-Bernoulli beam. While such a disturbance produces a continuous spectrum of wave components, the sampling conditions limit the range of wave components (i.e. mode shapes and modal coordinates) to be extracted. Within this working range, the wave numbers and frequencies are obtained from the extraction, and compared to theory. The frequency distribution is then approximated. The results are robust to random noise.

Complex Modal Decomposition for Estimating Wave Properties in One-Dimensional Media

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
B. F. Feeny
Keyword(s):  
Traveling Waves ◽  
Random Noise ◽  
Mode Shapes ◽  
Wave Speeds ◽  
One Dimensional ◽  
Wave Numbers ◽  
Displacement Profile ◽  
The Time Domain ◽  
Euler Bernoulli Beam ◽  
Complex Modal

A method of complex orthogonal decomposition is summarized for the time-domain, and then formulated and justified for application in the frequency-domain. The method is then applied to the extraction of modes from simulation data of sampled multimodal traveling waves for estimating wave parameters in one-dimensional continua. The decomposition is first performed on a transient nondispersive pulse. Complex wave modes are then extracted from a two-harmonic simulation of a dispersive medium. The wave frequencies and wave numbers are obtained by looking at the whirl of the complex modal coordinate, and the complex modal function, respectively, in the complex plane. From the frequencies and wave numbers, the wave speeds are then estimated, as well as the group velocity associated with the two waves. The decomposition is finally applied to a simulation of the traveling waves produced by a Gaussian initial displacement profile in an Euler–Bernoulli beam. While such a disturbance produces a continuous spectrum of wave components, the sampling conditions limit the range of modal components (i.e., mode shapes and modal coordinates) to be extracted. Within this working range, the wave numbers and frequencies are obtained from the extraction, and compared to theory. Modal signal energies are also quantified. The results are robust to random noise.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Straked Riser Design With VIVA

2010 ◽  
Author(s):  
Dhyanjyoti Deka ◽  
Paul R. Hays ◽  
Kamaldev Raghavan ◽  
Mike Campbell
Keyword(s):  
Traveling Waves ◽  
Oil And Gas ◽  
Cross Flow ◽  
Oil And Gas Industry ◽  
Response Prediction ◽  
Design Tool ◽  
Mode Shapes ◽  
Fe Model ◽  
Viv Suppression ◽  
Modal Solution

VIVA is a vortex induced vibration (VIV) analysis software that to date has not been widely used as a design tool in the offshore oil and gas industry. VIVA employs a hydrodynamic database that has been benchmarked and calibrated against test data [1]. It offers relatively few input variables reducing the risk of user induced variability of results [2]. In addition to cross flow current induced standing wave vibration, VIVA has the capability of predicting traveling waves on a subsea riser, or a combination of standing and traveling waves. Riser boundary conditions including fixed, pinned, flex joint or SCR seabed interaction can be modeled using springs and dashpots. VIVA calculates riser natural frequencies and mode shapes and also has the flexibility to import external modal solutions. In this paper, the applicability of VIVA for the design of straked steel catenary risers (SCR) and top tensioned risers (TTR) is explored. The use of linear and rotational springs provided by VIVA to model SCR soil interaction and flex joint articulation is evaluated. Comparisons of the VIV fatigue damage output with internal and external modal solution is presented in this paper. This paper includes validation of the VIVA generated modal solution by comparing the modal frequencies and curvatures against a finite element (FE) model of the risers. Fatigue life is calculated using long term Gulf of Mexico (GoM) currents and is compared against the industry standard software SHEAR7. Three different lift curve selections in SHEAR7 are used for this comparison. The differences in riser response prediction by the two software tools are discussed in detail. The sensitivity of the VIVA predicted riser response to the absence of VIV suppression devices is presented in this paper. The riser VIV response with and without external FE generated modal input is compared and the relative merits of the two modeling approaches are discussed. Finally, the recommended approach for VIVA usage for SCR and TTR design is given.

Complex Modal Analysis of Non-Self-Adjoint Hybrid Serpentine Belt Drive Systems

2000 ◽  
Vol 123 (2) ◽  
pp. 150-156 ◽  
Author(s):  
Lixin Zhang ◽  
Jean W. Zu ◽  
Zhichao Hou
Keyword(s):  
Modal Analysis ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mode Shapes ◽  
Belt Drive ◽  
Serpentine Belt ◽  
Complex Modal Analysis ◽  
Drive Systems ◽  
Complex Modal

A linear damped hybrid (continuous/discrete components) model is developed in this paper to characterize the dynamic behavior of serpentine belt drive systems. Both internal material damping and external tensioner arm damping are considered. The complex modal analysis method is developed to perform dynamic analysis of linear non-self-adjoint hybrid serpentine belt-drive systems. The adjoint eigenfunctions are acquired in terms of the mode shapes of an auxiliary hybrid system. The closed-form characteristic equation of eigenvalues and the exact closed-form solution for dynamic response of the non-self-adjoint hybrid model are obtained. Numerical simulations are performed to demonstrate the method of analysis. It is shown that there exists an optimum damping value for each vibration mode at which vibration decays the fastest.

scholarly journals Slow light bimodal interferometry in one-dimensional photonic crystal waveguides

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Luis Torrijos-Morán ◽  
Amadeu Griol ◽  
Jaime García-Rupérez
Keyword(s):  
Photonic Crystal ◽  
Group Velocity ◽  
Communication Networks ◽  
Slow Light ◽  
Single Channel ◽  
Point Of Care ◽  
Semiconductor Industry ◽  
Optical Modulator ◽  
One Dimensional ◽  
Dimensional Photonic Crystal

AbstractStrongly influenced by the advances in the semiconductor industry, the miniaturization and integration of optical circuits into smaller devices has stimulated considerable research efforts in recent decades. Among other structures, integrated interferometers play a prominent role in the development of photonic devices for on-chip applications ranging from optical communication networks to point-of-care analysis instruments. However, it has been a long-standing challenge to design extremely short interferometer schemes, as long interaction lengths are typically required for a complete modulation transition. Several approaches, including novel materials or sophisticated configurations, have been proposed to overcome some of these size limitations but at the expense of increasing fabrication complexity and cost. Here, we demonstrate for the first time slow light bimodal interferometric behaviour in an integrated single-channel one-dimensional photonic crystal. The proposed structure supports two electromagnetic modes of the same polarization that exhibit a large group velocity difference. Specifically, an over 20-fold reduction in the higher-order-mode group velocity is experimentally shown on a straightforward all-dielectric bimodal structure, leading to a remarkable optical path reduction compared to other conventional interferometers. Moreover, we experimentally demonstrate the significant performance improvement provided by the proposed bimodal photonic crystal interferometer in the creation of an ultra-compact optical modulator and a highly sensitive photonic sensor.

scholarly journals Study of Abnormal Group Velocities in Flexural Metamaterials

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Hong Woo Park ◽  
Joo Hwan Oh
Keyword(s):  
Group Velocity ◽  
Periodic Structure ◽  
Three Dimensional ◽  
Wave Dispersion ◽  
Abnormal Behavior ◽  
Flexural Wave ◽  
Negative Group ◽  
One Dimensional ◽  
Optical Branch ◽  
Negative Group Velocity

Abstract Generally, it has been known that the optical branch of a simple one-dimensional periodic structure has a negative group velocity at the first Brillouin zone due to the band-folding effect. However, the optical branch of the flexural wave in one-dimensional periodic structure doesn’t always have negative group velocity. The problem is that the condition whether the group velocity of the flexural optical branch is negative, positive or positive-negative has not been studied yet. In consequence, who try to achieve negative group velocity has suffered from trial-error process without an analytic guideline. In this paper, the analytic investigation for this abnormal behavior is carried out. In particular, we discovered that the group velocity of the optical branch in flexural metamaterials is determined by a simple condition expressed in terms of a stiffness ratio and inertia ratio of the metamaterial. To derive the analytic condition, an extended mass-spring system is used to calculate the wave dispersion relationship in flexural metamaterials. For the validation, various numerical simulations are carried out, including a dispersion curve calculation and three-dimensional wave simulation. The results studied in this paper are expected to provide new guidelines in designing flexural metamaterials to have desired wave dispersion curves.

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