Contribution Of Higher-order Modes Research Articles

The contribution of higher order modes in the dynamic response of slender vertical structures with application to wind turbine towers

Understanding the contribution of the vibration modes to the response of a tower-like structure subjected to base excitations is crucial for a safe and optimized design. The modal contributions to the structural response are generally assessed through modal participation factors and effective masses; however, relatively recent studies pointed out the variability of the modal contributions depending on the response effect (e.g., top displacement, base shear force, base bending moment). The formulation proposed here derives the shear force and the bending moment at the base of a tower-like structure by combining the influence function technique with the quasi-static equivalent forces technique. The resulting formulation of the tower response relies on the concept of modal contribution factors, which provides a straightforward indication of the modal contributions associated with a given response effect. The proposed methodology is applied to the case of wind turbine towers erected on temporary foundations at the port quayside without rotor nacelle assembly to assess the forces on the foundations due to the seismic loading on the towers. This technique may be of great relevance for assessing the tower integrity during installation and for the design of the temporary foundations at the quayside of harbors in seismic area, also considering the quick expansion of the offshore wind energy in countries prone to earthquakes.

Extended component mode synthesis method for dynamic analysis of mechanical systems with local nonlinearities

Engineering structures are generally designed based on linear elasticity assumptions. However, it is difficult to describe the connected structures using a simple linear system, due to factors such as sliding and friction at interfaces, and variations in contact areas during vibration processes. Therefore, it is necessary to develop an approach to tackle such systems with interface nonlinearities. In this paper, we proposed an extended free-interface component mode synthesis method. According to the proposed method, the substructures are separated at the nonlinear interfaces. Then the component mode synthesis procedure is carried out. By reasonably neglecting the contributions of higher order modes to the damping and inertia terms, it is demonstrated that the nonlinear interface forces and their time derivatives can be expressed as functions of themselves, as well as modal displacements and velocities. This characteristic facilitates the synthesis of the reduced order models for substructures in the state space. Also owing to this operation, the original properties of nonlinear interface forces can be preserved as much as possible, without any linearization. This method is suitable for non-proportionally damped structures with local nonlinearities such as mechanical structures with nonlinear spring and dashpot connections, rotor-bearing systems and so on. It also may be an alternative for the dynamic analysis of jointed structures with contact nonlinearities. Two numerical examples are presented to demonstrate the capability of the proposed method: (1) an eighteen degrees of freedom spring-dashpot-mass system with cubic spring and cubic dashpot interface connections is studied and (2) a more complex mechanical structure: a dual-rotor system with deep-groove ball bearing inter-shaft support. The numerical simulation results indicate that the dynamic responses of the reduced order model match very well with that of the full model, revealing the high accuracy of the proposed method with low computational costs.

Modelling and Evaluation of the Seismic Capacity of Typical Brick URM Buildings of the Historical Center of Cuenca- Ecuador

The Historic Center of Cuenca (HCC) is located in the southern region of Ecuador. It is well known that our country is located on the so-called belt of fire of the Pacific Ocean, this area is characterized by having generated the most important seismic events in the history of mankind. More specifically, there are records that show that in the last 200 years the city of Cuenca has been exposed to earthquakes that have produced moderate to severe damage. These reasons make it possible to establish that the city of Cuenca and specifically its historic center could present important problems in the face of significant seismic events. Most of the buildings in the HCC date back to the middle of the 20th century and have used unreinforced brick masonry (brick-URM) to build their walls. This work is part of the Seismic Vulnerability Project: Seismic Damage Scenarios of the Built Heritage of the Historic Center of Cuenca. In the context of this vulnerability project, the objective of this work was to establish a family of pushover curves for three unreinforced brick masonry buildings typical of the HCC, based on a parametric pushover analysis. The definition of the typical buildings was based on an extensive work of architectural and geometric characterization of the traditional built heritage of HCC. On the basis of focusing the study on two-story buildings (the most common), the size of the floor area of the buildings (small, medium and large area) was assumed as a base parameter. Based on an analysis of the variability of different geometric and mechanical characteristics, and in order to study their influence on the pushover curves of the three typical brick URM buildings, the following study parameters were defined: 1) compressive strength of brick masonry, 2) lateral displacement capacity of brick-URM elements, 3) wall thickness. The pushover analysis was carried out with the Ruaumoko program. The model of the buildings responds to an equivalent portal frame macro-model scheme that has been formulated and validated by the authors of this paper. In order to consider the effects of the flexible floor on the dynamic response of this type of structures, a lateral load pattern that takes into account the contribution of higher order modes of vibration will be used in pushover analysis. The results will be discussed in terms of the incidence of the variability of the study parameters on the basic characteristics of the pushover curves. These results will be an essential input for the next stage of the project consisting of damage estimation for different levels of seismic action expected in the city.

Characteristic Mode Analysis of Antenna Mutual Coupling in the Near Field

Characteristic mode analysis (CMA) has been widely used for guiding antenna design and mitigating antenna mutual coupling in the far field. However, antenna mutual coupling in the near field is still an intractable problem. In this communication, CMA is adopted to analyze and mitigate the near-field coupling between antennas. It is found that more modes are required in CMA as the contributions of higher order modes are more significant in the near-field region. In addition, the modal near-field distributions are proposed to discriminate the unwanted modes along with the modal admittance and eigencurrent distributions. Inductive loads are used to suppress the unwanted modes for mitigating the out-of-band mutual coupling while the in-band radiation property is mostly retained. The design procedures are elaborated through a two-dipole-antenna system, and the effectiveness of the proposed method is verified through fabricated prototypes. Based on the measured results, a significant reduction, more than 10 dB, of mutual coupling in the near field is obtained compared with those without optimization.

A physical domain-based substructuring as a framework for dynamic modeling and reanalysis of systems

A comprehensive physical domain-based formulation of reduced-order models based on dominant and residual normal modes and interface reduction is presented. The dynamic behavior of the substructures is characterized by the dominant fixed interface normal modes and by the static contribution of higher order modes. Interface reduction is accomplished by using a reduced number of interface modes. Special attention is considered to the proper treatment of residual normal modes in the context of system reanalyses and sensitivity analyses. The efficiency of the resultant formulation is evaluated in the framework of dynamic response characterization, modal sensitivity analysis and uncertainty propagation analysis. The effectiveness of the proposed model reduction technique is demonstrated by means of numerical examples involving two structural models. Numerical results show that the technique allows an effective dynamic modeling and reanalysis of a class of structural models.

New refractive index profiles of dispersion-flattened highly nonlinear fibers for future all-optical signal processing in wdm optical networks

In this paper, we demonstrate new dissimilar refractive index profiles for highly nonlinear ultra-flattened dispersion fibers with noteworthy effective area $$(A_\mathrm{eff})$$(Aeff) for future optical signal processing. The newly proposed fibers named from Type 1 to Type 5 have a flattened dispersion over S, C, L and U bands. Predominantly, few-mode HNL-UFF fiber of Type 3 yields dispersion-flattened characteristics over a range of 250 nm of optical communication spectrum with a mere 0.2 ps/nm km variation in dispersion and a dispersion slope of $$0.0057\hbox { ps}/\hbox {nm}^{2}$$0.0057ps/nm2 km due to the contribution of higher-order modes to the dispersion characteristics of the fiber. Moreover, it has a moderate nonlinear coefficient of $$8.03\hbox { W}^{-1}\,\hbox {km}^{-1}$$8.03W-1km-1. By modifying the refractive index profile of Type 3 fiber, Type 4 and Type 5 fibers are obtained in order to ensure single-mode operation, while the zero flattened dispersion characteristics of the fiber are compromised. Among the newly proposed fibers, Type 4 fiber offers a very low ITU-T cutoff wavelength of $$1.33~\upmu \hbox {m}$$1.33μm, whereas in the case of Type 5 fiber it is $$1.38~\upmu \hbox {m}$$1.38μm. Moreover, Type 4 and Type 5 fibers have good nonlinear coefficients of $$12.26\hbox { W}^{-1}\,\hbox {km}^{-1}$$12.26W-1km-1 and $$11.45\hbox { W}^{-1}\,\hbox {km}^{-1}$$11.45W-1km-1, respectively. By virtue of the proposed optimized index profile, an insensitive behavior toward bending is displayed by Type 3, Type 4 and Type 5 fibers. In addition, Type 4 fiber provides a better splice loss of 0.25 dB.

Tunable plasmon resonance coupling in coaxial gold nanotube arrays

The optical properties and plasmon resonance coupling of double coaxial gold nanotube arrays are investigated. The results show that the optical transmission is highly tunable by varying the thicknesses of the inner and outer nanotubes, the separation between the inner and outer nanotubes, and the dielectric parameters inside, between, and outside the two nanotubes. The shorter-wavelength transmission bands are very sensitive to the modification of the wall thickness of the outer nanotube, the separation, and the dielectric parameters between the double nanotubes. The dipole and multipolar plasmon modes are excited in our model. However, for small separation and refractive index, the dipole normal mode has a leading function in the transmission properties. Compared with the dipolar modes, the contribution of higher-order modes becomes larger as the parameters increase.

Quality factors of nonideal micro pillars

The influence of fabrication-induced imperfections and material absorption on the quality (Q) factor of a microcavity pillar is studied numerically. The dependence on sidewall inclination, selective underetch, and intrinsic loss is quantified. The authors show that imperfections can lead to an improvement in Q and that a sidewall inclination angle of less than 1° causes a dramatic change in the Q factor. The variations in Q can be attributed to a delicate balance between effective index contrasts, mode overlap, and higher-order mode contributions.

Optimal truncated model for vibration control design within a specified bandwidth

The work in this paper is directed at developing correction terms for a truncated structural dynamic model, which includes the effect on the structural response of both low and high frequency unmodelled vibration modes. The proposed model correction approach considers the corrected truncated model that only takes into account resonant modes within the bandwidth of interest and the optimised correction terms. The proposed approach is in contrast to the standard model correction approach that normally utilises a feedthrough correction term, taking into account only the unmodelled high frequency modes, while including all low frequency resonant modes into the truncated model. Thus, when one only interested in controlling vibration associated with a specified bandwidth of interest, the order of the corrected truncated model can be kept sufficiently low since the model does not have to include low and high frequency modes, leading to less complicated control design problems. Such active control within the specified bandwidth can be crucial for control tasks in the vibration minimisation at localised structural regions or in the noise reduction due to some coupled structural–acoustic modes. The procedures for calculating the optimal correction terms which include the lower and higher order mode contributions are outlined for both analytical and experimental models, allowing the procedures to be used for a wide range of theoretical and practical applications.

High frequency spatial vibration control using [formula omitted] method

A general feedback control approach has been developed to reduce the amplitude of high-frequency structural vibration modes without spending any control effort on reducing the vibration level of low-frequency modes. A procedure is outlined for developing a truncated structural model, which only includes the vibration modes of interest and takes account of the contributions of lower and higher-order modes in the frequency band of interest. Procedures for calculating the lower and higher order mode contributions are outlined, and a better model for estimating the contributions from the lower-order modes is developed by introducing a second-order term. The new controller so obtained has a lower order than standard feedback controllers and is also able to concentrate all the control energy on the modes resonant in the frequency band of interest. The control approach is further developed by using spatial output control to achieve a global attenuation of the structure for the desired frequencies and to allow the distribution of control energy among the controlled frequencies in any desired way. The general theory developed in this paper is validated experimentally using a cantilevered beam as a representative structure and controlling the fourth to the seventh-order vibration modes over a frequency range from 342 to 1125 Hz. Piezoelectric patches are used as a sensor and actuator and the global attenuation is measured using a scanning laser vibrometer.

A TROPICAL PACIFIC PREDICTION SYSTEM OF INTERMEDIATE COMPLEXITY: ROLE OF THE VERTICAL STRUCTURE VARIABILITY

An intermediate ocean-atmosphere coupled model of the tropical Pacific is used to investigate the sensitivity of the seasonal forecasts to the configuration of the oceanic vertical structure. The models consist in a three baroclinic mode tropical Pacific Ocean model and a Gill (1980)'s tropical atmosphere. The predictive skill of the model using a simple nudging method for the initialization is first presented from 1970 and compared to the results of other prediction system of similar complexity, which emphasizes the modulation of the skill on decadal timescales. It is then demonstrated that the skill is critically dependant on the energy distribution on the baroclinic mode, higher-order mode contributions being favored at some period and not at others. Linear Green’s function are used to assimilate satellite observations (SST and wind) and derive the optimized set of parameters that determines the vertical structure in the model for a particular period of time. The scheme is first tested for the period prior to the development of the 1997 El Nino. It is shown that substantial improvement in forecasting the event is realized for an increase of the relative contribution of the higher-order modes through the model parameters setting. Assimilation experiments of satellite data for the September 2003-February 2004 period are carried for producing initial conditions for the coupled model. Results of forecasts runs for 2004 are presented and discussed.

Frequency and time domain analysis of microstrip lines with multiple right-angle bend discontinuities

Frequency-dependent scattering matrices for the composite transmission structures of single microstrip lines having two right-angle bend discontinuities have been determined. The scattering parameters found by a mode-matching technique are used in the computations of the time domain responses for trapezoidal pulse inputs. From the time domain responses the delays, distortions and reflections are found. The contributions of higher-order modes, which may be significant in deciding the signal flow behaviour in these types of transmission structure, are also identified.

Tyre Models for the Study of In-Plane Dynamics

SUMMARY A flexible ring model of the tyre is presented in this paper. The natural frequencies and mode shapes of the tyre are obtained from this ring model. The vibration transmission properties of the tyre between the tyre-road contact point and the wheel axle are analysed. Based on the results of this flexible ring model, a simplified tyre model is developed, which is able to describe the zeroth and first order vibration modes of the tyre. Residual stiffnesses are introduced to take into account the contribution of higher order modes on the total deformation of the tyre. A tyre-road interface model based on the well-known brush model is also developed and integrated into the simplified tyre model. The parameters of both models are established for two different tyres. Finally some numerical results are presented.

Sound radiation from single and annular stream nozzles, with modal decomposition of in-duct acoustic power

An experimental program was carried out to study the acoustic characteristics of single and annular stream duct-nozzle systems at various flow conditions by using a refined acoustic impulse technique developed recently by Salikuddin et al. [1–3] at Lockheed-Georgia Company. In this technique signal synthesis [4] and signal averaging processes are incorporated to generate a desired impulsive signal from acoustic driver(s) and to eliminate background noise (flow noise) from in-duct and far field signals, respectively. The contribution of higher order modes to incident reflected and transmitted acoustic powers is accounted for by using a modal decomposition process described in references [1, 5]. The single stream nozzles include a 12-lobe, 24-tube suppressor nozzle with an equivalent exit diameter of 6.2 cm and a reference round convergent nozzle of equal area. These nozzles were connected to a 10 cm diameter supply duct and were tested statically as well as with simulated flight. The annular stream nozzles include two outer nozzle configurations, a 10 cm diameter duct and a 6·2 cm diameter conical nozzle, both connected to a 10 cm diameter supply duct. A 3·34 cm diameter straight duct, blocked at the upstream end, was used as the inner stream nozzle for both the configurations. These annular stream terminations were tested statically at various annular stream flow velocities with no inner stream flow. The results derived from the experiments include in-duct acoustic powers, termination reflection coefficients, transmission coefficients, far field power, and acoustic dissipation.