Estimating the oscillation frequency of a payload mass on quadcopter in non-autonomous flight

2021 ◽  
pp. 107754632110466
Author(s):  
Renan S Geronel ◽  
Earl H Dowell ◽  
Douglas D Bueno
Keyword(s):  
Time Domain ◽  
Aerial Photography ◽  
Oscillation Frequency ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Environmental Surveillance ◽  
Autonomous Flight ◽  
Aerial Vehicle ◽  
Payload Mass ◽  
The Time Domain

Unmanned aerial vehicles (UAVs) have been employed in several engineering applications, such as aerial photography, environmental surveillance, delivery tasks, and others. Most of these applications have attracted increasing attention due to their ability to carry different payloads, which can change the dynamic of flight. The present article investigates the dynamics of a quadcopter with a payload mass including the stiffness of the attachment to the aerial vehicle. An approach to obtain non-dimensional equations of motion is introduced, and as a consequence, it is possible to determine the frequency of vibration of the payload mass during the flight. The results are presented for non-autonomous flight, and they establish a simple equation to estimate the oscillation frequency depending on the relation between the quadcopter and the payload masses, also considering the stiffness of attachment, without requiring a solution to the equation of motion in the time domain.

Time Domain Simulations on a Single Point Moored Submerged Sphere of Variable Radius

2005 ◽  
Author(s):  
Joa˜o M. B. P. Cruz ◽  
Anto´nio J. N. A. Sarmento
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Physical Phenomenon ◽  
Single Point ◽  
Vertical Direction ◽  
Equation Of Motion ◽  
Hydrodynamic Coefficients ◽  
Energy Converter ◽  
Submerged Sphere ◽  
The Time Domain

This paper presents a different approach to the work developed by Cruz and Sarmento (2005), where the same problem was studied in the frequency domain. It concerns the same sphere, connected to the seabed by a tension line (single point moored), that oscillates with respect to the vertical direction in the plane of wave propagation. The pulsating nature of the sphere is the basic physical phenomenon that allows the use of this model as a simulation of a floating wave energy converter. The hydrodynamic coefficients and diffraction forces presented in Linton (1991) and Lopes and Sarmento (2002) for a submerged sphere are used. The equation of motion in the angular direction is solved in the time domain without any assumption about its output, allowing comparisons with the previously obtained results.

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.

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.

scholarly journals Vibration of a Laminated Beam with a Delamination Including Contact Effects

2004 ◽  
Vol 11 (3-4) ◽  
pp. 157-171 ◽  
Author(s):  
W. Ostachowicz ◽  
A. Żak
Keyword(s):  
Time Domain ◽  
Dynamic Contact ◽  
Equation Of Motion ◽  
Newmark Method ◽  
The Finite Element Method ◽  
Laminated Beam ◽  
Contact Algorithm ◽  
Vibration Responses ◽  
Newton Raphson ◽  
The Time Domain

Certain results are presented in this paper on damped vibration of a laminated cantilever beam with a single closing delamination. In order to investigate this task the finite element method has been applied in the current study. For modelling the beam higher order shear deformation beam finite elements have been used. The vibration of the beam is investigated in the time domain using a dynamic contact algorithm developed by the authors. The algorithm is based on the Newmark method and also incorporates a Newton-Raphson based procedure for resolving the equation of motion. The time series obtained from solving the equation of motion have been subsequently analysed in the frequency domain by using FFT (Fast Fourier Transform). The vibration responses of the beam due to various harmonic and impulse excitations, at different delamination locations, and for different delamination lengths, as well as changes in the dissipation of damping energy due to the delamination, have all been considered in the paper.

A standard finite‐difference scheme for the time‐domain computation of anelastic wavefields

Geophysics ◽  
1994 ◽  
Vol 59 (2) ◽  
pp. 290-296 ◽  
Author(s):  
E. S. Krebes ◽  
Gerardo Quiroga‐Goode
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Time Domain ◽  
Finite Difference Scheme ◽  
Initial Conditions ◽  
Homogeneous Medium ◽  
Standard Technique ◽  
Equation Of Motion ◽  
Central Difference ◽  
The Time Domain

We show that the finite‐differencing technique based on the consecutive application of the central difference operator to spatial derivatives, a standard well‐known technique that has been commonly used in the seismological literature for solving the elastic equation of motion, can also be used to obtain a stable time‐domain, finite‐difference scheme for solving the anelastic equation of motion. We compare the results of the scheme for a heterogeneous medium with those of the time‐domain finite‐difference scheme previously developed by Emmerich and Korn and find that they agree very closely. We show, analytically, that in the case of a homogeneous medium, the two schemes give identical numerical results for certain zero initial conditions. The scheme based on the standard technique uses more computer time and memory than the scheme of Emmerich and Korn. However, from a theoretical viewpoint, it is easier to analyze, as it is developed solely with a familiar standard method.

A COMPARISON OF DIFFERENT SOLUTION ALGORITHMS FOR THE NUMERICAL ANALYSIS OF VEHICLE–BRIDGE INTERACTION

2014 ◽  
Vol 14 (02) ◽  
pp. 1350065 ◽  
Author(s):  
K. LIU ◽  
N. ZHANG ◽  
H. XIA ◽  
G. DE ROECK
Keyword(s):  
Numerical Analysis ◽  
Time Domain ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Good Choice ◽  
Contact Forces ◽  
Time Dependent ◽  
Time Step ◽  
Solution Algorithms ◽  
Coupled Equation

The interaction between a bridge and a train moving on the bridge is a coupled dynamic problem. The equations of motion of the bridge and the vehicle are coupled by the time dependent contact forces. At each time step, the motion of the bridge influences the forces transferred to the vehicle and this, in turn, changes the forces acting on the bridge. In this paper, a comparison of three different time domain solution algorithms for the coupled equation of motion of the train–bridge system is presented. Guidelines are given for a good choice of the time step.

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.

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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