Estimation of Ship Roll Parameters in Random Waves

1992 ◽  
Vol 114 (2) ◽  
pp. 114-121 ◽  
Author(s):  
J. B. Roberts ◽  
J. F. Dunne ◽  
A. Debonos
Keyword(s):  
Markov Property ◽  
Simulated Data ◽  
Wide Band ◽  
Equation Of Motion ◽  
Roll Motion ◽  
Random Waves ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Ship Roll ◽  
Stochastic Input

The problem of estimating the parameters in an equation of roll motion from roll measurements only, taken in an irregular sea, is discussed. A single degree of freedom equation of motion is assumed, with a wide-band stochastic input and with a linear-in-the-parameters representation of both the damping and restoration terms. A method based on the Markov property of the energy envelope process, associated with the roll motion, is developed which enables all the relevant parameters to be estimated. The method is validated by applying it to some simulated data, for which the true parameters are known.

Nonlinear Oscillators with a Power-Form Restoring Force: Non-Isochronous and Isochronous Case

2013 ◽  
Vol 430 ◽  
pp. 14-21
Author(s):  
Ivana Kovacic
Keyword(s):  
Kinetic Energy ◽  
Constant Coefficient ◽  
Nonlinear Term ◽  
Nonlinear Oscillators ◽  
Equation Of Motion ◽  
Constant Amplitude ◽  
Restoring Force ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
First Case

This work is concerned with single-degree-of-freedom conservative nonlinear oscillators that have a fixed restoring force, which comprises a linear term and an odd-powered nonlinear term with an arbitrary magnitude of the coefficient of nonlinearity. There are two cases of interest: i) non-isochronous, when the system has an amplitude-dependent frequency and ii) isochronous, when the frequency of oscillations is constant (amplitude-independent). The first case is associated with the constant coefficient of the kinetic energy, while the frequency-amplitude relationship and the solution for motion need to be found. To that end, the equation of motion is solved by introducing a new small expansion parameter and by adjusting the Lindstedt-Poincaré method. In the second case, the condition for the frequency of oscillations to be constant is derived in terms of the expression for the position-dependent coefficient of the kinetic energy. The corresponding solution for isochronous oscillations is obtained. Numerical verifications of the analytical results are also presented.

Dynamics of High-Speed Cam-Driven Mechanisms—Part 2: Nonlinear System Models

1975 ◽  
Vol 97 (3) ◽  
pp. 777-781 ◽  
Author(s):  
F. Y. Chen ◽  
N. Polvanich
Keyword(s):  
Nonlinear System ◽  
High Speed ◽  
Phase Plane ◽  
Response Spectra ◽  
Equation Of Motion ◽  
Dynamic Responses ◽  
System Model ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Shock Response

The dynamic responses of the cam-driven mechanism are investigated, based on a non-linear lumped system model. The nonlinearity is an energy-dissipating element which consists of viscous, quadratic, Coulomb and static frictions combined. The nonlinear equation of motion of a single degree of freedom is first analyzed using a numerical method and the results of time responses are presented and characterized in the phase-plane. The primary and residual shock response spectra in nondimensional form for a number of typical cam input excitations are presented and compared with those of the associated linear cases.

Parametric Identification of Nonlinear Ship Roll Motion from Forced Roll Data

1988 ◽  
Vol 32 (02) ◽  
pp. 101-111 ◽  
Author(s):  
P. J. Gawthrop ◽  
A. Kountzeris ◽  
J. B. Roberts
Keyword(s):  
Simulated Data ◽  
Real Data ◽  
Estimation Procedure ◽  
Parametric Identification ◽  
Efficient Estimation ◽  
General Nature ◽  
Roll Motion ◽  
Forced Roll ◽  
Ship Roll ◽  
Ship Roll Motion

A method of estimating the parameters in a nonlinear, single-degree-of-freedom model of ship roll motion is described. It is shown that the "linear-in-the-parameters" nature of the model allows formulation of a relatively simple, and computationally very efficient, estimation procedure, based on a recursive, linear least-squares algorithm. The method is applied to the case of forced roll, where the roll moment excitation can be accurately determined. The general nature of the estimation scheme allows the combining of data from a sequence of experiments with sinusoidal forcing of varying frequency, and also allows the use of data arising from a nonsinusoidal forcing moment. In the latter case all the required parameters in the ship motion model can be estimated from a single test. The technique is illustrated by applying it to both digitally simulated data (where the parameters are known, a priori) and to real data, obtained from a model ship. In the latter case the parameter values obtained by the proposed method are shown to agree well with estimates obtained by alternative, independent methods.

Analysis of the Quality Factor and Response Time of Resonant Biosensor

2016 ◽  
Author(s):  
Pezhman A. Hassanpour
Keyword(s):  
Response Time ◽  
Quality Factor ◽  
Governing Equation ◽  
Dynamic Effect ◽  
Equation Of Motion ◽  
Measured Parameter ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
The Relationship

The relationship between the overall damping and response time of resonant biosensors is investigated in this paper. The governing equation of motion is derived using a single degree-of-freedom model of the resonator considering the dynamic effect of adsorption of the measured parameter. It is shown that the adsorption leads to a damping force on the resonant sensor. If not taken into account, this damping force results in misinter-pretation of the sensor readings.

Influence of Cam Motions on the Dynamic Behavior of Return Springs

1998 ◽  
Vol 120 (2) ◽  
pp. 305-310 ◽  
Author(s):  
Q. Yu ◽  
H. P. Lee
Keyword(s):  
Analytical Solution ◽  
Dynamic Response ◽  
Dynamic Behavior ◽  
Response Spectrum ◽  
Equation Of Motion ◽  
Simple Expression ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Input Motion ◽  
Selection Of

Based on the analytical solution of the equation of motion for a single degree-of-freedom model of a spring, the relation between the dynamic behavior and the kinematic features of input cam motions is discussed in this paper. A simple expression for the dynamic response spectrum of the vibration excited by the input motion is presented. It provides a useful tool to estimate the effect of cam motions on the dynamic behavior of springs. A method for the selection of cam motion curves based on this response spectrum is also presented in the paper. Examples are given to illustrate the method.

Seismic Reliability Analysis of Single-Degree-of-Freedom System when Structural Response is with Markov Property

2012 ◽  
Vol 204-208 ◽  
pp. 2690-2693
Author(s):  
Zhen Hao Zhang ◽  
Wei Jun Yang
Keyword(s):  
Reliability Analysis ◽  
Markov Property ◽  
Structural Response ◽  
Degree Of Freedom ◽  
Superposition Method ◽  
Structural System ◽  
Single Degree Of Freedom ◽  
Seismic Reliability ◽  
Single Degree ◽  
Mode Superposition Method

The stationary responses process of single-degree-of-freedom structural system is a stationary process with Markov property in displacement-speed space when the random earthquake load is simulated as flat noise or nearly flat noise. In this paper, the seismic reliability of singe-degree-of-freedom structural system of which the structural responses is with Markov property is studied according to first excursion mechanism. The explicit solution method of the structural seismic reliability is deduced. It is shown from the example that the method of this paper is correct. For the seismic reliability analysis of multiple-degree-of-freedom system, the mode-superposition method can be adopted to transform multiple-degree-of-freedom system into a series of generalized single-degree-of-freedom systems, so the method of this paper is also applicable in the theory.

The Dynamics of a Harmonically Excited System Having Rigid Amplitude Constraints, Part 1: Subharmonic Motions and Local Bifurcations

1985 ◽  
Vol 52 (2) ◽  
pp. 453-458 ◽  
Author(s):  
S. W. Shaw
Keyword(s):  
Simple Model ◽  
Piecewise Linear ◽  
Equation Of Motion ◽  
Harmonic Excitation ◽  
Coefficient Of Restitution ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Local Bifurcations ◽  
Excited System ◽  
Double Impact

A simple model for the response of mechanical systems having two-sided amplitude constraints is considered. The model consists of a piecewise-linear single degree-of-freedom oscillator subjected to harmonic excitation. Encounters with the constraints are modeled using a simple impact rule employing a coefficient of restitution, and excursions between the constraints are assumed to be governed by a linear equation of motion. Symmetric double-impact motions, both harmonic and subharmonic, are studied by means of a mapping that relates conditions at subsequent impacts. Stability and bifurcation analyses are carried out for these motions and regions are found in which no stable symmetric motions exist. The possible motions that can occur in such regions are discussed in the following paper, Part 2.

Chaos and Three-Dimensional Horseshoes in Slowly Varying Oscillators

1988 ◽  
Vol 55 (4) ◽  
pp. 959-968 ◽  
Author(s):  
Stephen Wiggins ◽  
Steven W. Shaw
Keyword(s):  
Chaotic Dynamics ◽  
Three Dimensional ◽  
Equation Of Motion ◽  
Necessary Condition ◽  
Stable And Unstable Manifolds ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Unstable Manifolds ◽  
Additional Equation

We present general results pertaining to chaotic motions in a class of systems termed slowly varying oscillators which consist of weakly perturbed single-degree-of-freedom systems in which parameters vary slowly in time according to an additional equation of motion. Our results include an analytical method for detecting transversal intersections of stable and unstable manifolds (typically a necessary condition for chaotic motions to exist) and a detailed description of the chaotic dynamics that occur when this situation exists.

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