A Discretized Optimization Strategy for Rest-to-Rest Maneuvers of Overhead Cranes Considering the Effect of Damping

2015 ◽  
Author(s):  
Khaled A. Alghanim ◽  
Khaled A. Alhazza ◽  
Ziyad N. Masoud
Keyword(s):  
Damping Ratio ◽  
Equations Of Motion ◽  
Maximum Velocity ◽  
System Response ◽  
Optimization Strategy ◽  
Time Step ◽  
Natural Period ◽  
Overhead Cranes ◽  
Finite Step ◽  
Acceleration Profile

An optimization strategy to reduce residual vibration of rest-to-rest maneuvers of overhead cranes is proposed. The proposed technique is based on generating shaped acceleration commands for a simple harmonic oscillator with damping included. Furthermore, the proposed technique solves the problem of discrete signal commands that result from using slow digital to analog convertors on real cranes. A discretized acceleration profile is derived analytically using finite step segments. These segments are integrated into a matrix, which is then coupled with a system response matrix through the system’s equations of motion. The resulting input acceleration matrix is then optimized to satisfy rest-to-rest maneuver conditions. The profile designer can control many parameters such as maneuver duration, discrete time step, hoisting speed, damping ratio, maximum velocity and acceleration. Unlike traditional command shapers, the proposed shaped profiles are independent of the natural period of the system, i.e., the acceleration profile duration is designer selectable. Through several examples, the performance of the proposed controller is validated numerically. Results show that the proposed shaping technique can effectively eliminate residual vibrations in rest-to-rest maneuvers of damped single-degree-of-freedom systems.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

Towards a Technique for Nonlinear Modal Analysis

2012 ◽  
Author(s):  
Simon A. Neild ◽  
Andrea Cammarano ◽  
David J. Wagg
Keyword(s):  
Normal Form ◽  
Modal Analysis ◽  
Equations Of Motion ◽  
Transformation Process ◽  
Second Order ◽  
Identity Transformation ◽  
Modal Testing ◽  
System Response ◽  
Weakly Nonlinear ◽  
Nonlinear Modal Analysis

In this paper we discuss a theoretical technique for decomposing multi-degree-of-freedom weakly nonlinear systems into a simpler form — an approach which has parallels with the well know method for linear modal analysis. The key outcome is that the system resonances, both linear and nonlinear are revealed by the transformation process. For each resonance, parameters can be obtained which characterise the backbone curves, and higher harmonic components of the response. The underlying mathematical technique is based on a near identity normal form transformation. This is an established technique for analysing weakly nonlinear vibrating systems, but in this approach we use a variation of the method for systems of equations written in second-order form. This is a much more natural approach for structural dynamics where the governing equations of motion are written in this form as standard practice. In fact the first step in the method is to carry out a linear modal transformation using linear modes as would typically done for a linear system. The near identity transform is then applied as a second step in the process and one which identifies the nonlinear resonances in the system being considered. For an example system with cubic nonlinearities, we show how the resulting transformed equations can be used to obtain a time independent representation of the system response. We will discuss how the analysis can be carried out with applied forcing, and how the approximations about response frequencies, made during the near-identity transformation, affect the accuracy of the technique. In fact we show that the second-order normal form approach can actually improve the predictions of sub- and super-harmonic responses. Finally we comment on how this theoretical technique could be used as part of a modal testing approach in future work.

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

The Dynamic Behaviour of Passively Compensated, Hydrostatic Journal Bearings with Various Numbers of Recesses

1976 ◽  
Vol 18 (6) ◽  
pp. 292-302 ◽  
Author(s):  
P. B. Davies
Keyword(s):  
Dynamic Behaviour ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Steady State Solution ◽  
Flow Equation ◽  
External Excitation ◽  
Signal Flow Graphs ◽  
Flow Compensation ◽  
Circular Functions ◽  
Flow Graphs

A previously established small-perturbation analysis is developed to express the unsteady-state continuity-of-flow equation for an isolated recess in a passively compensated, multirecess, hydrostatic journal bearing in terms of generalized co-ordinates. The concise form of this equation enables motion of the shaft about the concentric position to be described by equations which are derived in closed form for bearings with orifice, capillary or constant flow compensation and any number of recesses. These equations of motion, and hence the expressions for the receptances which describe the response of a bearing to external excitation, are shown to be of exactly the same form for all bearings of the type considered. Furthermore, the damping ratio and natural frequency in any particular case are determined by a single dynamic constant which is shown to be equal to a linear combination of circular functions and a limited number of coefficients which may be found explicitly by routine use of signal flow graphs. The results of the analysis, which is exact within the stated assumptions, are compared with those of other workers and the steady-state solution of the equations of motion is shown to give an expression for static stiffness which is useful for design purposes. Numerical values of the dynamic constant for bearings with between 3 and 20 recesses are given graphically.

A Strategy to Accelerate the Numerical Integration in the Dynamic Simulation of Multibody Systems

1997 ◽  
Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Stiff Systems ◽  
Step Size ◽  
Step Method ◽  
Integral Of Motion ◽  
Time Step ◽  
Time Step Size ◽  
Variable Time ◽  
Numerical Integrator

Abstract This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1991 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Models ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Different Levels

Abstract This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.

Influence of Material Damping on In-Plane Modal Parameters for Rotating Disks

2012 ◽  
Author(s):  
Hamid R. Hamidzadeh ◽  
Ehsan Sarfaraz
Keyword(s):  
Elastic Moduli ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Stability ◽  
Rotating Disks ◽  
Governing Equations ◽  
Annular Disk ◽  
Stress Theory ◽  
Hysteretic Damping ◽  
Circumferential Wave

The linear in-plane free vibration of a thin, homogeneous, viscoelastic, rotating annular disk is investigated. In the development of an analytical solution, two dimensional elastodynamic theory is employed and the viscoelastic material for the medium is allowed by assuming complex elastic moduli. The general governing equations of motion are derived by implementing plane stress theory. Natural frequencies are computed for several modes at specific radius ratios with fixed-free boundary conditions and modal loss factors for different damping ratios are determined. The computed results were compared to previously established results. It was observed that the effects of rotational speed and hysteretic damping ratio on natural frequency and elastic stability of the rotating disks were related to the mode of vibration and type of circumferential wave occurring.

Multi-Parameter Optimization of Damped Linear Continuous Systems

1972 ◽  
Vol 94 (1) ◽  
pp. 1-7 ◽  
Author(s):  
O. B. Dale ◽  
R. Cohen
Keyword(s):  
Optimal Parameter ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
System Response ◽  
Continuous Systems ◽  
Frequency Interval ◽  
State Variables ◽  
Initial Value ◽  
Unknown Parameters ◽  
One Dimensional

A method is presented for obtaining and optimizing the frequency response of one-dimensional damped linear continuous systems. The systems considered are assumed to contain unknown constant parameters in the boundary conditions and equations of motion which the designer can vary to obtain a minimum resonant response in some selected frequency interval. The unknown parameters need not be strictly dissipative nor unconstrained. No analytic solutions, either exact or approximate, are required for the system response and only initial value numerical integrations of the state and adjoint differential equations are required to obtain the optimal parameter set. The combinations of state variables comprising the response and the response locations are arbitrary.

A Sequential Integration Method

1988 ◽  
Vol 110 (4) ◽  
pp. 382-388
Author(s):  
Liang-Wey Chang ◽  
James F. Hamilton
Keyword(s):  
Integration Method ◽  
Equations Of Motion ◽  
Slow Motion ◽  
Explicit Integration ◽  
Time Step ◽  
Lumped Model ◽  
Guaranteed Stability ◽  
Fast Motion ◽  
The Stability ◽  
Secular Terms

This paper presents a method for simulating systems with two inertially coupled motions, i.e., a slow motion and a fast motion. The equations of motion are separated into two sets of coupled nonlinear ordinary differential equations. For each time step, the two sets of equations are integrated sequentially rather than simultaneously. Explicit integration methods are used for integrating the slow motion since the stability of the integration is not a problem and the explicit methods are very convenient for nonlinear equations. For the fast motion, the equations are linear and the implicit integrations can be used with guaranteed stability. The size of time step only needs to be chosen to provide accuracy of the solution for the modes that are excited. The interaction between the two types of motion must be treated such that secular terms do not appear due to the sequential integration method. A lumped model of a flexible pendulum will be presented in this paper to illustrate the application of the method. Numerical results for both simultaneous and sequential integration are presented for comparison.

scholarly journals Seismic Assessment of 10-Story Building Using Tuned Mass Damper

2020 ◽  
Author(s):  
Mohammad Aghajani Delavar
Keyword(s):  
Frequency Tuning ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Tuned Mass Dampers ◽  
Earthquake Excitation ◽  
Optimum Parameters ◽  
Seismic Records ◽  
Structural Responses ◽  
Lateral Displacements ◽  
Shear Building

In this paper, optimum parameters of Tuned Mass Dampers (TMD) are considered to control the responses of 10-story shear building under harmonic loading and 22 set of seismic records of FEMA-P695. The criterion used to obtain the optimum parameters is to select mass ratio, the frequency (tuning) and damping ratio that would result in smallest lateral displacements. State-space equations of motion are presented to compute the structural responses by developing a MATLAB file. A 10-story shear building is presented as a case study to assess the effects of TMDs on the multi-story structures. The results indicate that using TMD can reduce structural responses up to the average 20% under earthquake excitation and up to 90% under harmonic loadings. TMDs are not always effective under any type of ground motion; therefore, being aware of the given location is significant to design TMDs properly.

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