scholarly journals Implications of Buckingham's Pi Theorem to the Study of Similitude in Discrete Structures: Introduction of the RFN, μN and the SN Dimensionless Numbers and the Concept of Structural Speed

2021 ◽  
pp. 1-20
Author(s):  
Ares J. Rosakis ◽  
Jose Andrade ◽  
Vahe Gabuchian ◽  
John Harmon ◽  
Joel P. Conte ◽  
...  
Keyword(s):  
Signal Transmission ◽  
Discrete Systems ◽  
Dimensionless Numbers ◽  
Restoring Force ◽  
Need To Evaluate ◽  
Time Histories ◽  
Restoring Forces ◽  
Pi Theorem ◽  
Inertial Loading ◽  
Dynamic Time

Abstract Motivated by the need to evaluate the seismic response of large capacity gravity energy storage systems (potential energy batteries) such as the proposed frictional Multiblock Tower Structures (MTS) recently discussed by Andrade et al. [1], we apply Buckingham's Pi Theorem [2] to identify the most general forms of dimensionless numbers and dynamic similitude laws appropriate for scaling discontinuous multiblock structural systems involving general restoring forces resisting inertial loading. We begin by introducing the dimensionless “mu-number” (μN) appropriate for both gravitational and frictional restoring forces and then generalize by introducing the “arbitrary restoring force number” (RFN). RFN is subsequently employed to study similitude in various types of discontinuous or discrete systems featuring frictional, gravitational, cohesive, elastic and mixed restoring forces acting at the block interfaces. In the process, we explore the additional consequences of inter and intra-block elasticity on scaling. We also formulate a model describing the mechanism of structural signal transmission for the case of rigid MTS featuring inter-block restoring forces composed of elastic springs and interfacial friction, introducing the concept of “structural speed”. Finally, we validate our results by demonstrating that dynamic time-histories of field quantities and structural speeds between MTS models at various scales are governed by our proposed similitude laws, thus demonstrating the consistency of our approach.

An Advanced Test Method to Determine Viscous Damping of Floating Structures

2010 ◽  
Author(s):  
Z. J. Huang ◽  
B. J. O’Donnell ◽  
T. W. Yung ◽  
S. T. Slocum
Keyword(s):  
Low Frequency ◽  
Test Method ◽  
Total Force ◽  
Viscous Damping ◽  
Damping Force ◽  
Restoring Force ◽  
Viscous Forces ◽  
Motion Time ◽  
Research Company ◽  
Time Histories

ExxonMobil Upstream Research Company developed an advanced model test method to determine reliable damping values for predicting low frequency motions of an FLNG barge and an LNG carrier. Since viscous damping forces are a very small portion of the total force on the model, how to separate the viscous forces from the total forces is the key technical challenge. To better isolate viscous damping forces, an inertial compensation system consisting of springs was employed in the test. The spring stiffness was designed such that the restoring force cancelled the large inertial loads at the oscillation frequency. Furthermore, double-body models were built and were deeply submerged to minimize surface wave damping. With such an experimental setup, the total force measured was mainly the viscous damping force. Viscous damping was derived from the measured force and motion time histories.

Load Optimization of a Nonlinear Mono-Stable Duffing-Type Harvester Operating in a White Noise Environment

2013 ◽  
Author(s):  
Qifan He ◽  
Mohammed F. Daqaq
Keyword(s):  
Performance Enhancement ◽  
The Other ◽  
Statistical Linearization ◽  
Restoring Force ◽  
Approximate Analytical Expression ◽  
Load Optimization ◽  
Energy Harvesters ◽  
Equivalent Linear ◽  
Optimal Load ◽  
Restoring Forces

This paper investigates electric load optimization of nonlinear mono-stable Duffing energy harvesters subjected to white Gaussian excitations. Both symmetric and asymmetric nonlinear restoring forces are considered. Statistical linearization is utilized to obtain an approximate analytical expression for the optimal load as function of the other systems parameters. It is shown that the optimal load is dependent on the nonlinearity unless the ratio between the harvesting circuit time constant and the period of the mechanical oscillator is very large. Under optimal loading conditions, a harvester with a symmetric nonlinear restoring force can never produce more power than an equivalent linear harvester regardless of the magnitude or nature of the nonlinearity. On the other hand, asymmetries in the restoring force are shown to provide performance enhancement over an equivalent linear harvester.

Chemomechanics with molecular force probes

2010 ◽  
Vol 82 (4) ◽  
pp. 931-951 ◽  
Author(s):  
Zhen Huang ◽  
Roman Boulatov
Keyword(s):  
Materials Science ◽  
Reaction Rates ◽  
Restoring Force ◽  
Strained Molecules ◽  
Multiple Length Scales ◽  
Molecular Force ◽  
Directional Motion ◽  
Restoring Forces ◽  
Highly Strained ◽  
Force Probes

Chemomechanics is an emerging area at the interface of chemistry, materials science, physics, and biology that aims at quantitative understanding of reaction dynamics in multiscale phenomena. These are characterized by correlated directional motion at multiple length scales—from molecular to macroscopic. Examples include reactions in stressed materials, in shear flows, and at propagating interfaces, the operation of motor proteins, ion pumps, and actuating polymers, and mechanosensing. To explain the up to 1015-fold variations in reaction rates in multiscale phenomena—which are incompatible within the standard models of chemical kinetics—chemomechanics relies on the concept of molecular restoring force. Molecular force probes are inert molecules that allow incremental variations in restoring forces of diverse reactive moieties over hundreds of piconewtons (pN). Extending beyond the classical studies of reactions of strained molecules, molecular force probes enable experimental explorations of how reaction rates and restoring forces are related. In this review, we will describe the utility of one such probe—stiff stilbene. Various reactive moieties were incorporated in inert linkers that constrained stiff stilbene to highly strained macrocycles. Such series provided the first direct experimental validation of the most popular chemomechanical model, demonstrated its predictive capabilities, and illustrated the diversity of relationships between reaction rates and forces.

scholarly journals Restoring Force Surface Analysis of Nonlinear Vibration Data From Micro-Cantilever Beams

2006 ◽  
Author(s):  
Matthew S. Allen ◽  
Hartono (Anton) Sumali ◽  
David S. Epp
Keyword(s):  
Functional Form ◽  
Piecewise Linear ◽  
Cantilever Beams ◽  
Restoring Force ◽  
Vibration Data ◽  
Surface Method ◽  
Highly Nonlinear ◽  
Nonlinear Dynamic Characteristics ◽  
Restoring Forces ◽  
Micro Cantilever

The responses of micro-cantilever beams, with lengths ranging from 100-1500 microns, have been found to exhibit nonlinear dynamic characteristics at very low vibration amplitudes and in near vacuum. This work seeks to find a functional form for the nonlinear forces acting on the beams in order to aide in identifying their cause. In this paper, the restoring force surface method is used to non-parametrically identify the nonlinear forces acting on a 200 micron long beam. The beam response to sinusoidal excitation contains as many as 19 significant harmonics within the measurement bandwidth. The nonlinear forces on the beam are found to be oscillatory and to depend on the beam velocity. A piecewise linear curve is fit to the response in order to more easily compare the restoring forces obtained at various amplitudes. The analysis illustrates the utility of the restoring force surface method on a system with complex and highly nonlinear forces.

Dynamic Response of Nonlinear Oscillators With Hysteresis

2015 ◽  
Author(s):  
Biagio Carboni ◽  
Walter Lacarbonara
Keyword(s):  
Hysteresis Loops ◽  
Base Excitation ◽  
Response Curves ◽  
Restoring Force ◽  
Single Degree Of Freedom ◽  
Wire Ropes ◽  
Dynamical Behaviors ◽  
Nonlinear Features ◽  
Restoring Forces ◽  
Force Displacement

The nonlinear features of the steady-state periodic response of hysteretic oscillators are investigated. Frequency-response curves of base-excited single-degree-of-freedom (SDOF) systems possessing different hysteretic restoring forces are numerically obtained employing a continuation procedure based on the Jacobian of the Poincaré map. The memory-dependent restoring forces are expressed as a direct summation of linear and cubic elastic components and a hysteretic part described by a modified version of the Bouc-Wen law. The resulting force-displacement curves feature a pinching around the origin. Depending on the hysteresis material parameters (which regulate the shapes of the hysteresis loops), the oscillator exhibits hardening, softening and softening-hardening behaviors in which the switching from softening to hardening takes place above certain base excitation amplitudes. A comprehensive analysis in the parameters space is performed to identify the thresholds of these different behaviors. The restoring force features here considered have been experimentally obtained by means of an original rheological device comprising assemblies of steel and shape memory wire ropes. This study is carried out also with the aim of designing the restoring forces which give rise to dynamical behaviors useful for a variety of applications.

Identification of model-free structural nonlinear restoring forces using partial measurements of structural responses

2016 ◽  
Vol 20 (1) ◽  
pp. 69-80 ◽  
Author(s):  
Y Lei ◽  
SJ Luo ◽  
MY He
Keyword(s):  
Power Series ◽  
Structural Parameters ◽  
Structural System ◽  
Restoring Force ◽  
Model Free ◽  
Nonlinear Structural ◽  
Structural Nonlinearities ◽  
Restoring Forces ◽  
Structural Responses ◽  
Nonlinear Behaviors

Identification of nonlinear structural system is an important but challenging task for structural health monitoring. Due to the complexities of structural nonlinearities, it is hard to establish proper mathematical models for some structural nonlinear behaviors. Moreover, only partial structural responses can be measured in practice; it is essential to conduct identification of nonlinear structural systems using only partial measurements of structural responses. To cope with these issues, an algorithm is proposed in this article for the identification of some model-free structural nonlinear restoring forces using only partial measurements of structural responses. First, an equivalent linear structural system is introduced for the identification of the locations of structural nonlinearities. Then, a model-free structural nonlinear restoring force is approximated by a power series polynomial. The unknown coefficients of the power series polynomials together with other structural parameters are identified by the extended Kalman filter so that the characteristics of the behaviors of the model-free of nonlinear restoring forces can be identified. Some numerical examples including the identification of two nonlinear multi-story shear frames and a planar nonlinear truss with different structural nonlinear restoring forces are used to validate the proposed algorithm.

A Comprehensive Metric for Comparing Time Histories in Validation of Simulation Models With Emphasis on Vehicle Safety Applications

2008 ◽  
Author(s):  
H. Sarin ◽  
M. Kokkolaras ◽  
G. Hulbert ◽  
P. Papalambros ◽  
S. Barbat ◽  
...  
Keyword(s):  
Time History ◽  
Simulation Models ◽  
Experimental Tests ◽  
Vehicle Safety ◽  
Subject Matter Experts ◽  
Time Warping ◽  
Time Histories ◽  
Dynamic Time ◽  
Safety Considerations ◽  
Safety Applications

Computer modeling and simulation are the cornerstones of product design and development in the automotive industry. Computer-aided engineering tools have improved to the extent that virtual testing may lead to significant reduction in prototype building and testing of vehicle designs. In order to make this a reality, we need to assess our confidence in the predictive capabilities of simulation models. As a first step in this direction, this paper deals with developing a metric to compare time histories that are outputs of simulation models to time histories from experimental tests with emphasis on vehicle safety applications. We focus on quantifying discrepancy between time histories as the latter constitute the predominant form of responses of interest in vehicle safety considerations. First we evaluate popular measures used to quantify discrepancy between time histories in fields such as statistics, computational mechanics, signal processing, and data mining. Then we propose a structured combination of some of these measures and define a comprehensive metric that encapsulates the important aspects of time history comparison. The new metric classifies error components associated with three physically meaningful characteristics (phase, magnitude and topology), and utilizes norms, cross-correlation measures and algorithms such as dynamic time warping to quantify discrepancies. Two case studies demonstrate that the proposed metric seems to be more consistent than existing metrics. It is also shown how the metric can be used in conjunction with ratings from subject matter experts to build regression-based validation models.

Prediction of Hydrodynamic Damping of Moored Offshore Structures Using CFD

2019 ◽  
Author(s):  
Changqing Jiang ◽  
Ould el Moctar ◽  
Thomas E. Schellin
Keyword(s):  
Offshore Structures ◽  
Least Square ◽  
Navier Stokes ◽  
Coupled Analysis ◽  
Total System ◽  
Mooring System ◽  
Restoring Force ◽  
Hydrodynamic Damping ◽  
Restoring Forces ◽  
Decay Tests

Abstract Usually, mooring system restoring forces acting on floating offshore structures are obtained from a quasi-static mooring model alone or from a coupled analysis based on potential flow solvers that do not always consider nonlinear mooring-induced phenomena or fluid-structure interactions and the associated viscous damping effects. By assuming that only the mooring system influences the restoring force characteristics, the contribution of mooring-induced damping to total system damping is neglected. This paper presents a technique to predict hydrodynamic damping of moored structures based on coupling the dynamic mooring model with a Reynolds-averaged Navier-Stokes (RANS) equations solver. We obtained hydrodynamic damping coefficients using a least-square algorithm to fit the time trace of decay tests. We analyzed a moored offshore buoy and validated our predictions against experimental measurements. The mooring system consisted of three catenary chains. The analyzed response comprised the decaying oscillating buoy motions, the natural periods, and the associated linear and quadratic damping characteristics. Predicted motions, natural periods, and hydrodynamic damping generally well agreed to comparable experimental data.

GENERATION OF A PAIR OF SURFACE TIME HISTORIES FOR JAKARTA USED FOR EARTHQUAKE RESISTANCE DESIGN OF INFRASTRUCTURES

2015 ◽  
Vol 77 (11) ◽  
Author(s):  
B.M. Hutapea ◽  
M. Asrurifak ◽  
Hendriyawan Hendriyawan ◽  
Masyhur Irsyam
Keyword(s):  
Ground Surface ◽  
Time History ◽  
Hazard Maps ◽  
Surface Time ◽  
History Analysis ◽  
Earthquake Design ◽  
Time Histories ◽  
Design Loads ◽  
Dynamic Time ◽  
The Impact

It is not the earthquake but the collapse of the building and infrastructure that will cause the damage and the loss of human lives. To mitigate these hazards, the building and infrastructure need to be designed such that will not collapse due to earthquake. This paper presents the procedure for generating time histories at ground surface for Jakarta area. Required data to generate these modified time histories were extracted from the Team for Revision of Seismic Hazard Maps of Indonesia 2010. The results are used as input motions in dynamic time history analysis for predicting earthquake design loads for infrastructures, such as bridges such that those structures can be designed to bear the impact of an earthquake and prevent collapse

scholarly journals Alternative diastolic function models of ventricular longitudinal filling velocity are mathematically identical

2020 ◽  
Vol 318 (5) ◽  
pp. H1059-H1067 ◽  
Author(s):  
Druv Bhagavan ◽  
William M. Padovano ◽  
Sándor J. Kovács
Keyword(s):  
Diastolic Function ◽  
Longitudinal Velocity ◽  
Force Balance ◽  
Balance Model ◽  
Diastolic Filling ◽  
Restoring Force ◽  
Suction Pump ◽  
Restoring Forces ◽  
Pdf Model

The spatiotemporal features of normal in vivo cardiac motion are well established. Longitudinal velocity has become a focus of diastolic function (DF) characterization, particularly the tissue Doppler e′-wave, manifesting in early diastole when the left ventricle (LV) is a mechanical suction pump (dP/dV < 0). To characterize DF and elucidate mechanistic features, several models have been proposed and have been previously compared algebraically, numerically, and in their ability to fit physiological velocity data. We analyze two previously noncompared models of early rapid-filling lengthening velocity (Doppler e′-wave): parametrized diastolic filling (PDF) and force balance model (FBM). Our initial numerical experiments sampled FBM-generated e′( t) contours as input to determine PDF model predicted fit. The resulting exact numerical agreement [standard error of regression (SER) = 9.06 × 10−16] was not anticipated. Therefore, we analyzed all published FBM-generated e′( t) contours and observed identical agreement. We re-expressed FBM’s algebraic expressions for e′( t) and observed for the first time that model-based predictions for lengthening velocity by the FBM and the PDF model are mathematically identical: e′( t) = γe−α tsinh(β t), thereby providing exact algebraic relations between the three PDF parameters and the six FBM parameters. Previous pioneering experiments have independently established the unique determinants of e′( t) to be LV relaxation, restoring forces (stiffness), and load. In light of the exact intermodel agreement, we conclude that the three PDF parameters, relaxation, stiffness (restoring forces), and load, are unique determinants of DF and e′( t). Thus, we show that only the PDF formalism can compute the three unique, independent, physiological determinants of long-axis LV myocardial velocity from e′( t). NEW & NOTEWORTHY We show that two separate, independently derived physiological (kinematic) models predict mathematically identical expressions for LV-lengthening velocity (Doppler e′-wave), indicating that damped harmonic oscillatory motion is a physiologically accurate model of diastolic function. Although both models predict the same “overdamped” velocity contour, only one model solves the “inverse problem” and generates unique, lumped parameters of relaxation, stiffness (restoring force), and load from the e′-wave.

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