scholarly journals Structural optimization for nonlinear dynamic response

2015 ◽  
Vol 373 (2051) ◽  
pp. 20140408 ◽  
Author(s):  
Suguang Dou ◽  
B. Scott Strachan ◽  
Steven W. Shaw ◽  
Jakob S. Jensen
Keyword(s):  
Normal Form ◽  
Resonance Condition ◽  
Nonlinear Resonance ◽  
Computational Method ◽  
Frame Structure ◽  
Nonlinear Behaviour ◽  
Coupled Mode ◽  
Resonant Modes ◽  
Order Of Magnitude ◽  
Micro Systems

Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped–clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.

Influences of Tunnel Excavation Blasting Vibration on Surface High-Rise Building

2010 ◽  
Vol 163-167 ◽  
pp. 2613-2617
Author(s):  
Hai Liang Wang ◽  
Tong Wei Gao
Keyword(s):  
Vibration Frequency ◽  
Vertical Vibration ◽  
Frame Structure ◽  
Vibration Monitoring ◽  
Vibration Velocity ◽  
Blasting Vibration ◽  
Road Tunnel ◽  
Concrete Frame ◽  
High Rise ◽  
Order Of Magnitude

According to the 33 floors high building, blasting vibration monitoring had been carried on. The building, along Yunnan road tunnel of Qingdao Cross-harbor Tunnel Guide Line Project, has concrete frame structure. Monitoring data had been analyzed. Results showed that rules of vertical vibration velocity and main vibration frequency have similar relevance. Amplification effect of them was existed on the middle and top of the building. From the 2nd floor of downward ground to ground, the value of them suddenly decreased. Main vibration frequency is in the range of 101~102 order of magnitude.

Liquid Sloshing Dynamics in a Container Subjected to Coupled Mode Excitation

2008 ◽  
Author(s):  
T. Nasar ◽  
S. A. Sannasiraj ◽  
V. Sundar
Keyword(s):  
Excitation Frequency ◽  
Qualitative Assessment ◽  
Floating Body ◽  
Nonlinear Behaviour ◽  
Wave Excitation ◽  
Coupled Mode ◽  
Sloshing Dynamics ◽  
Time Histories ◽  
Fill Level ◽  
The Individual

An experimental work has been carried out to study the phenomena of sloshing of liquid in a partially filled tank mounted on a barge exposed to regular beam waves. Liquid fill level with aspect ratio (hs/l, where hs is the static liquid depth and l is the tank length) of 0.325 is studied. The time histories of sloshing oscillation are measured along the length of container at predefined locations. The nonlinear behaviour of sloshing oscillation is observed for the regular wave excitation. The spectra of the sloshing oscillation and their qualitative assessment are reported. The individual sway and heave analytical model have been studied in order to substantiate the importance of coupled mode of excitation. Attempts are made to evaluate the harmonics present in the sloshing oscillation and compare with the results of earlier studies. In the present interaction study, it was found that the nonlinear response of the floating body also plays a role to induce violent sloshing oscillation. The effects of wave excitation frequency on the sloshing oscillation are reported.

Nonlinear radio-frequency response of a non-uniform plasma slab–condenser system with realistic density and velocity profiles

1972 ◽  
Vol 8 (2) ◽  
pp. 113-126 ◽  
Author(s):  
R. Ballieu ◽  
A. M. Messiaen ◽  
P. E. Vandenplas
Keyword(s):  
Plasma Sheath ◽  
Nonlinear Behaviour ◽  
Bounded Plasma ◽  
Plasma Slab ◽  
Order Of Magnitude ◽  
Classical Plasma ◽  
Sophisticated Model ◽  
Density Perturbations ◽  
Remarkable Agreement ◽  
Uniform Plasma

The nonlinear behaviour of a realistic one-dimensional bounded plasma (specifically, the classical plasma slab–condenser system) is computed by an iterative perturbation method. The results indicate, somewhat unexpectedly, that the influence of the r.f. field on the static density profile and on the resonance spectrum is much smaller than would have been inferred from a previous analysis of an unbounded plasma. However, this approach is inherently limited by the fact that, even for not too high r.f. fields, the electron density perturbations can become of the same order of magnitude as the static density in the tenuous plasma sheath near the wall. The resonance curves obtained with this sophisticated model show quite remarkable agreement with existing experimental data.

scholarly journals Nonlinear Analysis of a Steel Frame Structure Exposed to Post-Earthquake Fire

Fire ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 73
Author(s):  
Alaa T. Alisawi ◽  
Philip E. F. Collins ◽  
Katherine A. Cashell
Keyword(s):  
Extreme Events ◽  
Human Life ◽  
Significant Risk ◽  
Element Model ◽  
Steel Frame ◽  
Frame Structure ◽  
Structural Safety ◽  
Nonlinear Behaviour ◽  
Design Codes ◽  
Accurate Analysis

The probability of extreme events such as an earthquake, fire or blast occurring during the lifetime of a structure is relatively low but these events can cause serious damage to the structure as well as to human life. Due to the significant consequences for occupant and structural safety, an accurate analysis of the response of structures exposed to these events is required for their design. Some extreme events may occur as a consequence of another hazard, for example, a fire may occur due to the failure of the electrical system of a structure following an earthquake. In such circumstances, the structure is subjected to a multi-hazard loading scenario. A post-earthquake fire (PEF) is one of the major multi-hazard events that is reasonably likely to occur but has been the subject of relatively little research in the available literature. In most international design codes, structures exposed to multi-hazards scenarios such as earthquakes, which are then followed by fires are only analysed and designed for as separate events, even though structures subjected to an earthquake may experience partial damage resulting in a more severe response to a subsequent fire. Most available analysis procedures and design codes do not address the association of the two hazards. Thus, the design of structures based on existing standards may contribute to a significant risk of structural failure. Indeed, a suitable method of analysis is required to investigate the behaviour of structures when exposed to sequential hazards. In this paper, a multi-hazard analysis approach is developed, which considers the damage caused to structures during and after an earthquake through a subsequent thermal analysis. A methodology is developed and employed to study the nonlinear behaviour of a steel framed structure under post-earthquake fire conditions. A three-dimensional nonlinear finite element model of an unprotected steel frame is developed and outlined.

scholarly journals Optical transmission theory for metal-insulator-metal periodic nanostructures

Nanophotonics ◽  
2017 ◽  
Vol 6 (1) ◽  
pp. 349-355 ◽  
Author(s):  
Andre-Pierre Blanchard-Dionne ◽  
Michel Meunier
Keyword(s):  
Dielectric Layer ◽  
Metal Insulator ◽  
Total Transmission ◽  
Coupled Mode ◽  
Transmission And Reflection Coefficients ◽  
Resonant Modes ◽  
Metal Insulator Metal ◽  
Phase Interference ◽  
Multiple Paths ◽  
Transmission And Reflection

AbstractA semi-analytical formalism for the optical properties of a metal-insulator-metal periodic nanostructure using coupled-mode theory is presented. This structure consists in a dielectric layer in between two metallic layers with periodic one-dimensional nanoslit corrugation. The model is developed using multiple-scattering formalism, which defines transmission and reflection coefficients for each of the interface as a semi-infinite medium. Total transmission is then calculated using a summation of the multiple paths of light inside the structure. This method allows finding an exact solution for the transmission problem in every dimension regime, as long as a sufficient number of diffraction orders and guided modes are considered for the structure. The resonant modes of the structure are found to be related to the metallic slab only and to a combination of both the metallic slab and dielectric layer. This model also allows describing the resonant behavior of the system in the limit of a small dielectric layer, for which discontinuities in the dispersion curves are found. These discontinuities result from the out-of-phase interference of the different diffraction orders of the system, which account for field interaction for both inner interfaces of the structure.

Numerical simulations of the nonlinear kink modes in linearly stable supersonic slip surfaces

1991 ◽  
Vol 225 ◽  
pp. 101-120 ◽  
Author(s):  
Jeffrey A. Pedelty ◽  
Paul R. Woodward
Keyword(s):  
Numerical Simulations ◽  
Slip Surface ◽  
Nonlinear Resonance ◽  
Analytic Solutions ◽  
Nonlinear Behaviour ◽  
Sound Waves ◽  
Reflected Waves ◽  
Analytic Work ◽  
Slip Surfaces ◽  
Piecewise Parabolic

We have performed high-resolution numerical simulations of supersonic slip surfaces to confirm and illuminate earlier analytic nonlinear stability calculations of such structures. This analytic work was in turn inspired by earlier computer simulations reported in Woodward (1985) and Woodward et al. (1987). In particular Artola & Majda (1987) examined the response of a supersonic slip surface to an incident train of small-amplitude nonlinear sound waves. They found analytic solutions which indicate that nonlinear resonance occurs at three angles of incidence which depend upon the Mach number of the relative motion. The two-dimensional simulations described here numerically solve this problem for a Mach-4 flow using the piecewise-parabolic method (Colella & Woodward 1984; Woodward & Colella 1984). The simulations show that sound waves incident at a predicted resonance angle excite nonlinear behaviour in the slip surface. At these angles the amplitude of the reflected waves is much greater than the incident wave amplitude (i.e. a shock forms). The observed resonance is fairly broad, but the resonance narrows as the strength of the incident waves is reduced.The nature of the nonlinear kink modes observed in the simulations is similar to that discussed by Artola & Majda. Most of the modes move in either direction with speeds near the predicted value. Speeds of other than this value are observed, but the disagreement is not serious in view of the strongly nonlinear behaviour seen in the simulations but not treated in the analytic work. The stationary modes seen in the analytic results are perhaps observed as transient structures. They may eventually dominate the flow at late times (Woodward et al. 1987).The role of the kink modes in the stability of slab jets is discussed, and it is argued that the stationary modes are more disruptive than the propagating modes.

Necessary Height of the Vertical Stiffeners in Steel Silos on Discrete Supports with Accounting of Imperfections

2020 ◽  
Vol 61 (3) ◽  
pp. 201-210
Author(s):  
Lyubomir A. Zdravkov
Keyword(s):  
Thin Shell ◽  
Frame Structure ◽  
Nonlinear Behaviour ◽  
Normal Stresses ◽  
Critical Height ◽  
Local Loss ◽  
Ideal Position ◽  
Supporting Frame ◽  
Steel Silos ◽  
The Ideal

To ensure unloading of the whole amount of stored product by gravity, the steel silos are often placed on supporting frame structure. The values of stresses in the joints between the thin shell and supporting frame elements are extremely high. It can cause local loss of stability in the shell. To prevent it, many designers place stiffening elements above the supports. Here the question is how high should be the stiffening elements? The appropriate solution is that they should rise to that level till which the values of meridional normal stresses above the supports and in the middle between them are equalized. But where is this level? Many researchers worked on values and ways of distribution of normal meridional stresses above the supports of the cylindrical shells. As a result of their efforts are determined critical height Hcr of the shell and the ideal position HI of intermediate stiffening ring. But these heights are considerably different between each other. To which of them our vertical stiffening elements should achieve? Considering the nonlinear behaviour of the steel, the effects of changes in geometry during loading and imperfections caused by welding works, the author tried to obtain an answer to this question.

scholarly journals Bound states in the continuum in open acoustic resonators

2015 ◽  
Vol 780 ◽  
pp. 370-387 ◽  
Author(s):  
A. A. Lyapina ◽  
D. N. Maksimov ◽  
A. S. Pilipchuk ◽  
A. F. Sadreev
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Life Time ◽  
Three Dimensions ◽  
Destructive Interference ◽  
Acoustic Resonators ◽  
Coupled Mode ◽  
Resonant Modes ◽  
Axisymmetric Duct ◽  
The Continuum

We consider bound states in the continuum (BSCs) or embedded trapped modes in two- and three-dimensional acoustic axisymmetric duct–cavity structures. We demonstrate numerically that, under variation of the length of the cavity, multiple BSCs occur due to the Friedrich–Wintgen two-mode full destructive interference mechanism. The BSCs are detected by tracing the resonant widths to the points of the collapse of Fano resonances where one of the two resonant modes acquires infinite life-time. It is shown that the approach of the acoustic coupled mode theory cast in the truncated form of a two-mode approximation allows us to analytically predict the BSC frequencies and shape functions to a good accuracy in both two and three dimensions.

Application of the Lie Group Transformations to Nonlinear Dynamical Systems

1999 ◽  
Vol 66 (2) ◽  
pp. 439-447 ◽  
Author(s):  
V. N. Pilipchuk ◽  
R. A. Ibrahim
Keyword(s):  
Normal Form ◽  
Lie Group ◽  
Internal Resonance ◽  
Differential Operators ◽  
Nonlinear Dynamical Systems ◽  
Resonance Condition ◽  
Equations Of Motion ◽  
Double Pendulum ◽  
Parametrically Excited ◽  
Linear Differential

This paper describes the theory of Lie group operators in a form suitable for the applied dynamics community. In particular, it is adapted to analyzing the dynamic behavior of nonlinear systems in the presence of different resonance conditions. A key ingredient of the theory is the Hausdorff formula, which is found to be implicitly reproduced in most averaging techniques during the transformation process of the equations of motion. The method is applied to examine the nonlinear modal interaction in a coupled oscillator representing a double pendulum. The system equations of motion are reduced to their simplest (normal) form using operations with the linear differential operators according to Hausdorff's formula. Based on the normal form equations, different types of resonance regimes are considered. It is shown that the energy of the parametrically excited first mode can be regularly (or nonregularly) shared with the other mode due to the internal resonance condition. If the second mode is parametrically excited, its energy is localized and is not transferred to the first mode, even in the presence of internal resonance.

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