On the Nonstationary Response of Stochastically Excited Secondary Systems

1987 ◽  
Vol 54 (3) ◽  
pp. 688-694 ◽  
Author(s):  
W. D. Iwan ◽  
K. S. Smith
Keyword(s):  
Closed Form Expression ◽  
Primary System ◽  
Mean Square ◽  
Stochastic Excitation ◽  
Secondary System ◽  
Form Expression ◽  
Combined System ◽  
Nonstationary Response ◽  
Secondary Systems ◽  
The Mean

The envelope response of a secondary system is derived for the case where the primary system is subjected to nonstationary stochastic excitation. An approximate closed form expression for the mean square envelope response is obtained for the case of transient response to stationary excitation when the primary and secondary systems are noninteracting. When the combined system is classically damped, the effect of the interaction is described by the introduction of an equivalent noninteracting system. The analytical results are compared with results of numerical simulations.

An infinite-server queue subject to an extraneous phase process and related models

1981 ◽  
Vol 18 (1) ◽  
pp. 236-244 ◽  
Author(s):  
P. Purdue ◽  
D. Linton
Keyword(s):  
Original System ◽  
Primary System ◽  
Secondary System ◽  
State Behavior ◽  
Infinite Server ◽  
Server Queue ◽  
Secondary Systems ◽  
Stage System ◽  
The Mean ◽  
Bulk Arrival

We consider an infinite-server queueing system in an extraneous environment. Initially it is shown that the systems of interest can be decomposed into a two-stage system. The primary system is an infinite-server queue with many customer types subject to a clearing mechanism. The secondary system is a special type of bulk-arrival, infinite-server queue. We derive results for the primary and secondary systems separately and combine the results to find the mean steady-state behavior of the original system.

An infinite-server queue subject to an extraneous phase process and related models

1981 ◽  
Vol 18 (01) ◽  
pp. 236-244 ◽  
Author(s):  
P. Purdue ◽  
D. Linton
Keyword(s):  
Original System ◽  
Primary System ◽  
Secondary System ◽  
State Behavior ◽  
Infinite Server ◽  
Server Queue ◽  
Secondary Systems ◽  
Stage System ◽  
The Mean ◽  
Bulk Arrival

We consider an infinite-server queueing system in an extraneous environment. Initially it is shown that the systems of interest can be decomposed into a two-stage system. The primary system is an infinite-server queue with many customer types subject to a clearing mechanism. The secondary system is a special type of bulk-arrival, infinite-server queue. We derive results for the primary and secondary systems separately and combine the results to find the mean steady-state behavior of the original system.

Transient Response of MDOF Systems With Inerters to Nonstationary Stochastic Excitation

2017 ◽  
Vol 84 (10) ◽  
Author(s):  
Sami F. Masri ◽  
John P. Caffrey ◽  
Hui Li
Keyword(s):  
Degrees Of Freedom ◽  
Broad Band ◽  
Primary System ◽  
Mean Square ◽  
Stochastic Excitation ◽  
Mass Ratio ◽  
Tuning Parameters ◽  
Mdof Systems ◽  
Mean Square Response ◽  
Arbitrary Location

Explicit, closed-form, exact analytical expressions are derived for the covariance kernels of a multi degrees-of-freedom (MDOF) system with arbitrary amounts of viscous damping (not necessarily proportional-type), that is equipped with one or more auxiliary mass damper-inerters placed at arbitrary location(s) within the system. The “inerter” is a device that imparts additional inertia to the vibration damper, hence magnifying its effectiveness without a significant damper mass addition. The MDOF system is subjected to nonstationary stochastic excitation consisting of modulated white noise. Results of the analysis are used to determine the dependence of the time-varying mean-square response of the primary MDOF system on the key system parameters such as primary system damping, auxiliary damper mass ratio, location of the damper-inerter, inerter mass ratio, inerter node choices, tuning of the coupling between the damper-inerter and the primary system, and the excitation envelope function. Results of the analysis are used to determine the dependence of the peak transient mean-square response of the system on the damper/inerter tuning parameters, and the shape of the deterministic intensity function. It is shown that, under favorable dynamic environments, a properly designed auxiliary damper, encompassing an inerter with a sizable mass ratio, can significantly attenuate the response of the primary system to broad band excitations; however, the dimensionless “rise-time” of the nonstationary excitation substantially reduces the effectiveness of such a class of devices (even when optimally tuned) in attenuating the peak dynamic response of the primary system.

scholarly journals Seismic Forces in Ancillary Components Supported on Piers and Wharves

2018 ◽  
Vol 34 (2) ◽  
pp. 741-758 ◽  
Author(s):  
Rakesh K. Goel
Keyword(s):  
Simple Procedure ◽  
Single Mode ◽  
Primary System ◽  
Elastic Model ◽  
Secondary System ◽  
Marine Structures ◽  
Acceleration Amplification ◽  
Marine Structure ◽  
Secondary Systems ◽  
Seismic Forces

This paper presents a simple procedure to estimate seismic forces in ancillary components (secondary systems) supported on marine structures such as piers, wharves, and marine oil terminals (primary systems). Since many such marine structures can be idealized as single-degree-of-freedom (SDOF) systems, this study uses a simple linear-elastic model with two DOF, one representing the marine structure and the other representing the ancillary component. This study shows that acceleration at the base of the secondary system is approximately equal to spectral acceleration at the fundamental period of the primary system. It also proposes a formula, which is an improvement over current ASCE 7-10 recommendations, to estimate acceleration amplification in the secondary system due to its flexibility when mass and period ratios of the secondary and primary systems are known. The procedure in this paper is strictly applicable to marine structures for which primarily a single mode contributes to seismic response.

Optimal Performance Comparison of Nonlinear Energy Sinks and Linear Tuned Mass Dampers

2021 ◽  
Author(s):  
Ivan Yegorov (Egorov) ◽  
Austin Uden ◽  
Daniil Yurchenko
Keyword(s):  
Nonlinear Energy Sink ◽  
Free Vibrations ◽  
Performance Comparison ◽  
Optimal Performance ◽  
Primary System ◽  
Secondary System ◽  
Impulsive Excitation ◽  
Secondary Systems ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract This paper studies a targeted energy transfer (TET) mechanism for a two-degree-of-freedom (TDOF) model in free vibration. The model comprises a primary linear system and a secondary system in the form of an energy sink which can be nonlinear. The free vibrations are considered subject to an impulsive excitation exerted on the primary system, leading to a nonzero initial velocity. The goal is to obtain the spring parameters in the nonlinear energy sink (NES) so as to maximize an energy dissipation measure (EDM) representing the percentage of impulsive energy that is absorbed and dissipated in the NES. A global optimization algorithm is used for this purpose. The optimal performance is assessed for the purely linear, linear-cubic, and purely cubic configurations of the spring connecting the primary and secondary systems. The corresponding results are compared with each other. The optimization process is performed for the EDM averaged over given ranges of the initial impulse and natural frequency in the primary system. It is shown that the type of the optimal configuration can vary depending on these ranges.

Acoustic reflections from undulating surfaces

Geophysics ◽  
1986 ◽  
Vol 51 (11) ◽  
pp. 2160-2161 ◽  
Author(s):  
N. R. Hill ◽  
I. Lerche
Keyword(s):  
Closed Form ◽  
Incident Energy ◽  
Wave Reflection ◽  
Mean Field ◽  
Closed Form Expression ◽  
Rough Interface ◽  
Form Expression ◽  
Field Techniques ◽  
The Mean ◽  
Acoustic Speed

We recently investigated the behavior of acoustic wave reflection in a medium with a single rough interface with acoustic speed [Formula: see text] and density[Formula: see text] above (below) the interface (Lerche and Hill, 1985). We used mean‐field techniques (Howe, 1971; Karal and Keller, 1964; Frisch, 1968) to find a closed‐form expression for the mean reflected field, and in particular we examined the case where the roughness is on a much smaller scale than the wavelength of the incident energy. We derived a closed‐form expression which is accurate to second order in roughness height.

Performance Analysis of Cognitive Two-Way Networks with Interference from Primary User over Nakagami-m Fading Channels

2017 ◽  
Vol 3 (1) ◽  
pp. 29
Author(s):  
Hoang Van Toan ◽  
Vo Nguyen Quoc Bao
Keyword(s):  
Fading Channels ◽  
Relay Node ◽  
Primary User ◽  
Relay Network ◽  
Closed Form Expression ◽  
Secondary System ◽  
Form Expression ◽  
Decode And Forward ◽  
System Characteristics ◽  
System Outage Probability

A cognitive underlay two-way relay network taking into account interference links from primary transmitter to secondary receivers over Nakagami-m fading channels is analyzed in this article. In this model, a secondary system including two terminal nodes exchanges data through a decode-and-forward (DF) relay node. Under the underlay approach, all secondary transmitter must adjust transmit power to protect the primary communications. We derive the exact and asymptotic closed-form expression for the secondary system outage probability over Nakagami-m fading channels showing the system diversity. Monte-Carlo simulation are performed to verify the analysis results as well as to show the system characteristics

scholarly journals Optimal Individualized Treatments in Resource-Limited Settings

2016 ◽  
Vol 12 (1) ◽  
pp. 283-303 ◽  
Author(s):  
Alexander R. Luedtke ◽  
Mark J. van der Laan
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression ◽  
Population Mean ◽  
Resource Limited ◽  
Linear Estimators ◽  
Asymptotically Linear Estimators ◽  
Maximum Proportion ◽  
The Mean ◽  
Limited Setting

Abstract An individualized treatment rule (ITR) is a treatment rule which assigns treatments to individuals based on (a subset of) their measured covariates. An optimal ITR is the ITR which maximizes the population mean outcome. Previous works in this area have assumed that treatment is an unlimited resource so that the entire population can be treated if this strategy maximizes the population mean outcome. We consider optimal ITRs in settings where the treatment resource is limited so that there is a maximum proportion of the population which can be treated. We give a general closed-form expression for an optimal stochastic ITR in this resource-limited setting, and a closed-form expression for the optimal deterministic ITR under an additional assumption. We also present an estimator of the mean outcome under the optimal stochastic ITR in a large semiparametric model that at most places restrictions on the probability of treatment assignment given covariates. We give conditions under which our estimator is efficient among all regular and asymptotically linear estimators. All of our results are supported by simulations.

A Stochastic Analysis for Multiple Supported MDOF Secondary Systems

1995 ◽  
Vol 117 (2) ◽  
pp. 182-188 ◽  
Author(s):  
A. Saudy ◽  
T. Aziz ◽  
A. Ghobarah
Keyword(s):  
Dynamic Loading ◽  
Stochastic Analysis ◽  
Dynamic Interaction ◽  
Primary System ◽  
Secondary System ◽  
Theoretical Formulation ◽  
Interaction Forces ◽  
Numerical Examples ◽  
Secondary Systems ◽  
System Properties

A new stochastic analysis is developed to estimate the response of multiple supported mdof secondary systems to dynamic loading. In the proposed stochastic analysis, the effect of the dynamic interaction between the secondary and primary systems is included. An outline for the theoretical formulation of the proposed stochastic analysis is presented. The assumptions adopted in the formulation are discussed. The dynamic interaction is shown to comprise two effects: the effect of the interaction forces arising at the attachment points, and the effect of the changes in the primary system properties resulting from the attachment of the secondary system. In addition, numerical examples are provided to demonstrate the validity of the proposed analysis.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

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