Vibrations of beams with a breathing crack and large amplitude displacements

2015 ◽  
Vol 230 (1) ◽  
pp. 34-54 ◽  
Author(s):  
Gonçalo Neves Carneiro ◽  
Pedro Ribeiro
Keyword(s):  
Time Domain ◽  
Equations Of Motion ◽  
Shape Functions ◽  
Breathing Crack ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Time Histories ◽  
Linear Effects ◽  
Fourier Spectra ◽  
The Time Domain

The vibrations of beams with a breathing crack are investigated taking into account geometrical non-linear effects. The crack is modeled via a function that reduces the stiffness, as proposed by Christides and Barr (One-dimensional theory of cracked Bernoulli–Euler beams. Int J Mech Sci 1984). The bilinear behavior due to the crack closing and opening is considered. The equations of motion are obtained via a p-version finite element method, with shape functions recently proposed, which are adequate for problems with abrupt localised variations. To analyse the dynamics of cracked beams, the equations of motion are solved in the time domain, via Newmark's method, and the ensuing displacements, velocities and accelerations are examined. For that purpose, time histories, projections of trajectories on phase planes, and Fourier spectra are obtained. It is verified that the breathing crack introduce asymmetries in the response, and that velocities and accelerations can be more affected than displacements by the breathing crack.

Finite Element Modelling of Rotating Tires in the Time Domain

2002 ◽  
Vol 30 (1) ◽  
pp. 19-33 ◽  
Author(s):  
O. A. Olatunbosun ◽  
A. M. Burke
Keyword(s):  
Finite Element ◽  
Dynamic Behavior ◽  
Time Domain ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
Element Analysis ◽  
Successful Model ◽  
Linear Effects ◽  
Tire Rotation ◽  
The Time Domain

Abstract Finite element analysis presents an opportunity for a detailed study of the dynamic behavior of a rotating tire under real operating conditions providing a better understanding of the influence of tire construction and material detail on tire dynamic behavior in such areas as ride, handling and noise and vibration transmission. Modelling issues that need to be considered include non-linear effects due to tire inflation and hub loading, tire/road contact and time domain solution of the equations of motion. In this paper techniques and strategies for tire rotation modelling are presented and discussed as a guide to the creation of a successful model.

On the Dynamic Analysis of Roller Chain Drives: Part II — Case Study

1992 ◽  
Author(s):  
Nicholas M. Veikos ◽  
Ferdinand Freudenstein
Keyword(s):  
Dynamic Analysis ◽  
Time Domain ◽  
Equations Of Motion ◽  
Axial Stiffness ◽  
Roller Chain ◽  
Computer Aided ◽  
Computational Aspects ◽  
The Time Domain ◽  
Chain Drives

Abstract Part I of this paper (5) summarized the previous work and has described the theoretical and computational aspects of a computer-aided procedure which has been developed by the authors for the dynamic analysis of roller chain drives. Lagrange’s equations of motion have been derived by assuming the roller chain to behave as a series of masses lumped at the roller centers and connected by bars of constant axial stiffness. The equations of motion are solved in the time domain until steady state conditions are achieved.

scholarly journals Generalized eigenfunction method for floating bodies

2011 ◽  
Vol 667 ◽  
pp. 544-554 ◽  
Author(s):  
COLM J. FITZGERALD ◽  
MICHAEL H. MEYLAN
Keyword(s):  
Time Domain ◽  
Water Waves ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Two Dimensions ◽  
Floating Body ◽  
Floating Bodies ◽  
Abstract Wave Equation ◽  
Generalized Eigenfunction ◽  
The Time Domain

We consider the time domain problem of a floating body in two dimensions, constrained to move in heave and pitch only, subject to the linear equations of water waves. We show that using the acceleration potential, we can write the equations of motion as an abstract wave equation. From this we derive a generalized eigenfunction solution in which the time domain problem is solved using the frequency-domain solutions. We present numerical results for two simple cases and compare our results with an alternative time domain method.

Wrap‐around removal from one‐dimensional synthetic seismograms

Geophysics ◽  
1989 ◽  
Vol 54 (7) ◽  
pp. 911-915 ◽  
Author(s):  
Hans Thybo
Keyword(s):  
Frequency Domain ◽  
Computational Methods ◽  
Time Domain ◽  
Synthetic Seismograms ◽  
Seismic Exploration ◽  
One Dimensional ◽  
Borehole Logs ◽  
The Time Domain ◽  
Layered Models

One‐dimensional (1-D) synthetic seismograms are important tools in seismic exploration. They play an important role in the correlation of recorded seismograms with borehole logs and also permit the estimation of delay‐type attenuation in finely layered models. Existing computational methods for computing 1-D seismograms can be grouped according to whether the calculations are performed in the time domain or in the frequency domain.

Study on ship operation performance in actual seaways using time-domain free-running simulation

2020 ◽  
pp. 147509022094410
Author(s):  
Jae-Hoon Lee ◽  
Yonghwan Kim
Keyword(s):  
Time Domain ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Operational Performance ◽  
Environmental Load ◽  
Operation Performance ◽  
Route Maintenance ◽  
Free Running ◽  
The Time Domain

This study considers the evaluation of ship operational performance in real sea states using a time-domain approach. The current seakeeping-maneuvering coupling approach consists of two modules. First, in the seakeeping module, the time-domain three-dimensional Rankine panel method is applied to compute wave-induced forces and resultant ship motion. To validate this module, the computational results for wave drift force are compared with the existing experimental data for various forward speeds and regular wave conditions. Second, in the maneuvering module, the equations of motion with 4 degrees of freedom that are based on the Maneuvering Modeling Group are solved to simulate the ship navigation. The computed seakeeping and maneuvering values are immediately transferred between the two modules in the time domain, and so they are directly integrated. By applying this coupling method, a free-running simulation for a ship navigating along a given route is performed. The trajectory tracking method based on a proportional–derivative-based rudder control is adopted for straight course-keeping. Not only the speed loss but also the attitude for route maintenance is evaluated for various environmental load conditions. The simulation results are validated by a comparison with those of the existing free-running model test. Based on comparisons, environmental load effects and resultant quantities on operational performance are discussed.

Ship Motion Computations Using a High Froude Number Time Domain Strip Theory

2006 ◽  
Vol 50 (01) ◽  
pp. 15-30
Author(s):  
D. S. Holloway ◽  
M. R. Davis
Keyword(s):  
Froude Number ◽  
Time Domain ◽  
High Speed ◽  
Equations Of Motion ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Viscous Effects ◽  
Strip Theory ◽  
Large Amplitude Motions ◽  
The Time Domain

High-speed strip theories are discussed, and a time domain formulation making use of a fixed reference frame for the two-dimensional fluid motion is described in detail. This, and classical (low-speed) strip theory, are compared with the experimental results of Wellicome et al. (1995) up to a Froude number of 0.8, as well as with our own test data for a semi-SWATH, demonstrating the marked improvement of the predictions of the former at high speeds, while the need to account for modest viscous effects at these speeds is also argued. A significant contribution to time domain computations is a method of stabilizing the integration of the ship's equations of motion, which are inherently unstable due to feedback from implicit added mass components of the hydrodynamic force. The time domain high-speed theory is recommended as a practical alternative to three-dimensional methods. It also facilitates the investigation of large-amplitude motions with stern or bow emergence and forms a simulation base for the investigation of ride control systems and local or global loads.

An Improved Time Domain Simulation for Dynamic Milling at Small Radial Immersions and Large Depths of Cut

2001 ◽  
Author(s):  
Marc L. Campomanes ◽  
Yusuf Altintas
Keyword(s):  
Surface Finish ◽  
Time Domain ◽  
Dynamic Models ◽  
Three Dimensional ◽  
Domain Model ◽  
Time Domain Simulation ◽  
Chatter Stability ◽  
Linear Effects ◽  
Deep Cuts ◽  
The Time Domain

Abstract This paper presents an improved time domain model for milling, which can simulate vibratory cutting conditions at very small radial widths of cut and large depths of cut. The improved kinematics model allows simulation of very small radial immersions. The varying dynamics modeled along the cutting depth allows milling with very flexible cutters and/or flexible workpieces at very deep cuts to be simulated. The model can predict forces, surface finish, and chatter stability, accurately accounting for non-linear effects that are difficult to model analytically. The discretized cutter and workpiece kinematics and dynamic models are used to represent the exact trochoidal motion of the cutter, and to investigate the effects of forced vibrations and changing radial immersion due to deflection and vibrations on chatter stability. Three dimensional surface finish profiles are predicted and are compared to measured results. Stability lobes generated from the time domain simulation are also shown for various cases.

Motion Studies of a Vessel with Water on Deck

1981 ◽  
Vol 18 (01) ◽  
pp. 38-50
Author(s):  
Jeff Dillingham
Keyword(s):  
Time Domain ◽  
Equations Of Motion ◽  
Random Choice ◽  
Nonlinear Hyperbolic System ◽  
Random Choice Method ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
Energy Dissipators ◽  
Motion Studies ◽  
The Time Domain

The seakeeping characteristics of a small fishing vessel are investigated. The type of vessel under consideration has a large flat deck which may, under severe considerations, remain partially or totally awash. We consider the effect of such deck water on the vessel motions. The vessel is considered as a two-degree-of-freedom system and the equations of motion in sway and roll are formulated in the time domain using an impulse response technique. Formulation of the problem of describing the flow of the deck water leads to a nonlinear hyperbolic system of equations. An approximate solution to these equations is obtained numerically using the random-choice method, also known as Glimm's method. From this solution the static and dynamic forces exerted on the vessel by the deck water are computed. These forces are then added to the external wave exciting forces to obtain a complete time-domain solution for the motion of the vessel and the deck water. We examine the effect of several simple changes in ship geometry. In most cases the deck water is found to act as a rather effective roll-damping mechanism. This is a result of the frequent appearance of hydraulic jumps which act as energy dissipators. The greatest reduction in roll was achieved by adding a small amount of camber to the deck. Variations in scupper geometry did not have very great effects on the rolling motion.

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