Fluctuations in a controlled vibration insulator subjected to random disturbances

1967 ◽  
Vol 3 (6) ◽  
pp. 598-603
Author(s):  
Yu. P. Maksimovich
Keyword(s):  
Random Disturbances ◽  
Vibration Insulator

scholarly journals Inverse-square law between time and amplitude for crossing tipping thresholds

2019 ◽  
Vol 475 (2222) ◽  
pp. 20180504 ◽  
Author(s):  
Paul Ritchie ◽  
Özkan Karabacak ◽  
Jan Sieber
Keyword(s):  
Dynamical System ◽  
Feedback Loop ◽  
Tipping Point ◽  
Dimensional System ◽  
Stochastic Forcing ◽  
Inverse Square Law ◽  
System A ◽  
Asymptotic Expressions ◽  
Higher Dimensional ◽  
Random Disturbances

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. For the case when the dynamical system is subject to stochastic forcing we give an approximation to the probability of tipping if a parameter changing in time reverses near the tipping point. The derived approximations are valid if the parameter change in time is sufficiently slow. We demonstrate for a higher-dimensional system, a model for the Indian summer monsoon, how numerically observed escape from the equilibrium converge to our asymptotic expressions. The inverse-square law between peak of the parameter forcing and the time the parameter spends above a given threshold is also visible in the level curves of equal probability when the system is subject to random disturbances.

Output Regulation in Bimodal Systems With Application to Surface Tracking in the Presence of Contact Vibrations

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Zhizheng Wu ◽  
Foued Ben Amara
Keyword(s):  
Output Regulation ◽  
Synthesis Algorithm ◽  
Stabilizing Controllers ◽  
Surface Tracking ◽  
Input Signals ◽  
Random Components ◽  
Random Disturbances ◽  
Proposed Regulation ◽  
Regulation Approach ◽  
Contact Vibrations

Motivated by a class of surface tracking problems in mechanical systems subject to contact vibrations, this paper considers a regulation problem for discrete-time switched bimodal linear systems where it is desired to achieve output regulation against exogenous input signals featuring known deterministic and unknown random components. A first step in the regulator design involves constructing a set of observer-based parameterized stabilizing controllers that satisfy a sufficient regulation condition for the switched system against the known deterministic disturbance or reference signals. In the second step, an additional performance constraint is added to identify, from among the already constructed regulators, those that provide the best regulation performance against the unknown random disturbances. A corresponding regulator synthesis algorithm is developed based on iteratively solving properly formulated bilinear matrix inequalities. The proposed regulator is successfully evaluated on an experimental setup involving a switched bimodal mechanical system subject to contact vibrations, hence demonstrating the effectiveness of the proposed regulation approach.

Large Nonlinear Responses of Spatially Nonhomogeneous Stochastic Shell Structures Under Nonstationary Random Excitations

2009 ◽  
Vol 9 (4) ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element ◽  
Shell Structures ◽  
Random Disturbance ◽  
Hybrid Strain ◽  
Central Difference ◽  
Spherical Cap ◽  
Approximation Techniques ◽  
Nonlinear Responses ◽  
Novel Approach ◽  
Random Disturbances

A novel approach for determining large nonlinear responses of spatially homogeneous and nonhomogeneous stochastic shell structures under intensive transient excitations is presented. The intensive transient excitations are modeled as combinations of deterministic and nonstationary random excitations. The emphases are on (i) spatially nonhomogeneous and homogeneous stochastic shell structures with large spatial variations, (ii) large nonlinear responses with finite strains and finite rotations, (iii) intensive deterministic and nonstationary random disturbances, and (iv) the large responses of a specific spherical cap under intensive apex nonstationary random disturbance. The shell structures are approximated by the lower order mixed or hybrid strain based triangular shell finite elements developed earlier by the author and his associate. The novel approach consists of the stochastic central difference method, time coordinate transformation, and modified adaptive time schemes. Computed results of a temporally and spatially stochastic shell structure are presented. Computationally, the procedure is very efficient compared with those entirely or partially based on the Monte Carlo simulation, and it is free from the limitations associated with those employing the perturbation approximation techniques, such as the so-called stochastic finite element or probabilistic finite element method. The computed results obtained and those presented demonstrate that the approach is simple and easy to apply.

The Motion of Floating Systems: Nonlinear Dynamics in Periodic and Random Waves

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Katrin Ellermann
Keyword(s):  
Dynamical Behavior ◽  
Nonlinear Behavior ◽  
Operating Conditions ◽  
Random Waves ◽  
Multiple Components ◽  
Random Disturbances ◽  
Restoring Forces ◽  
Steady State Responses ◽  
External Forces ◽  
Floating Systems

Floating systems, such as ships, barges, or semisubmersibles, show a dynamical behavior, which is determined by their internal structure and the operating conditions caused by external forces e.g., due to waves and wind. Due to the complexity of the system, which commonly includes coupling of multiple components or nonlinear restoring forces, the response can exhibit inherently nonlinear characteristics. In this paper different models of floating systems are considered. For the idealized case of purely harmonic forcing they all show nonlinear behavior such as subharmonic motion or different steady-state responses at constant operating conditions. The introduction of random disturbances leads to deviations from the idealized case, which may change the overall response significantly. Advantages and limitations of the different mathematical models and the applied numerical techniques are discussed.

Optimal Data-Driven Modeling-Free Differential-Inversion-Based Iterative Control: A Wafer Stage Example

2020 ◽  
Author(s):  
Zezhou Zhang ◽  
Qingze Zou
Keyword(s):  
System Dynamics ◽  
High Performance ◽  
Random Noise ◽  
High Accuracy ◽  
Data Driven ◽  
Modeling Process ◽  
Random Disturbances ◽  
Noise Disturbances ◽  
Data Driven Modeling ◽  
Iterative Control

Abstract In this paper, an optimal data-driven modeling-free differential-inversion-based iterative control (OMFDIIC) method is proposed for both high performance and robustness in the presence of random disturbances. Achieving high accuracy and fast convergence is challenging as the system dynamics behaviors vary due to the external uncertainties and the system bandwidth is limited. The aim of the proposed method is to compensate for the dynamics effect without modeling process and achieve both high accuracy and robust convergence, by extending the existed modeling-free differential-inversion-based iterative control (MFDIIC) method through a frequency- and iteration-dependent gain. The convergence of the OMFDIIC method is analyzed with random noise/disturbances considered. The developed method is applied to a wafer stage, and shows a significant improvement in the performance.

Effect of different types of ceilings on floor impact sound insulation performance in CLT model building

2021 ◽  
Vol 263 (2) ◽  
pp. 4402-4409
Author(s):  
Atsuo Hiramitsu ◽  
Susumu Hirakawa ◽  
Takahiro Tsuchimoto ◽  
Takashi Yamauchi
Keyword(s):  
Model Building ◽  
Sound Insulation ◽  
Impact Noise ◽  
Timber Construction ◽  
Stress Relieving ◽  
Measurement Results ◽  
Absorbing Material ◽  
Vibration Insulator ◽  
Effective Use ◽  
Insulation Performance

The floor impact noise generated in a building often causes problems among residents. The floor impact sound insulation performance of timber construction buildings is lower than that of concrete construction. However, due to the large supply of wood and the stress-relieving effects of wood, the use of wood is being promoted around the world. In Japan, the Act on the Promotion of the Utilization of Wood in Public Buildings was enforced to promote the use of CLT (Cross Laminated Timber) for the effective use of wood. We have been experimentally investigating the effect of floor finish structure in CLT model building. In this paper, we report the measurement results of the change in floor impact sound insulation performance when the suspended ceiling structure was changed. As results, it was confirmed that the effect of the sound-absorbing material in the ceiling cavity and the effect of the double-layer ceiling board were effective. In addition, it was clarified that the dry-type double floor structure with rubber vibration insulator on its legs is an effective floor finish structure for improvement of heavy and light weight floor impact sound insulation performances.

Development of a DSM-Based Methodology in an Academic Setting

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
George Platanitis ◽  
Remon Pop-Iliev ◽  
Ahmad Barari
Keyword(s):  
Engineering Design ◽  
Design Process ◽  
Engineering Students ◽  
Design Structure ◽  
Academic Settings ◽  
Task Durations ◽  
Random Disturbances ◽  
Process Convergence ◽  
Work Transformation

This paper proposes the use of a design structure matrix/work transformation matrix (DSM/WTM)-based methodology in academic settings to serve engineering educators as a facilitating tool for predetermining the difficulty and feasibility of design engineering projects they assign, given both the time constraints of the academic term and the expected skill level of the respective learners. By using a third-year engineering design project as a case study, engineering students actively participated in this comprehensive use of DSM methodologies. The engineering design process has been thoroughly analyzed to determine convergence characteristics based on the eigenvalues of the system followed by a sensitivity analysis on the originally determined DSM based on data provided by students in terms of task durations and number of iterations for each task. Finally, an investigation of the design process convergence due to unexpected events or random disturbances has been conducted. The obtained predictive model of the design process was compared to the actual dynamics of the project as experienced by the students and the effect of random disturbances at any point in the design process has thereby been evaluated.

Sign in / Sign up

Export Citation Format

Share Document