The Forced Oscillations of Submerged Bodies

2003 ◽  
Vol 125 (4) ◽  
pp. 710-715
Author(s):  
Angel Sanz-Andre´s ◽  
Gonzalo Tevar ◽  
Francisco-Javier Rivas
Keyword(s):  
Rigid Body ◽  
Small Amplitude ◽  
Center Of Mass ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Central Point ◽  
Modal Testing ◽  
Forced Oscillations ◽  
Motion Equations ◽  
Marine Applications

The increasing use of very light structures in aerospace applications are given rise to the need of taking into account the effects of the surrounding media in the motion of a structure (as for instance, in modal testing of solar panels or antennae) as it is usually performed in the motion of bodies submerged in water in marine applications. New methods are in development aiming at to determine rigid-body properties (the center of mass position and inertia properties) from the results of oscillations tests (at low frequencies during modal testing, by exciting the rigid-body modes only) by using the equations of the rigid-body dynamics. As it is shown in this paper, the effect of the surrounding media significantly modifies the oscillation dynamics in the case of light structures and therefore this effect should be taken into account in the development of the above-mentioned methods. The aim of the paper is to show that, if a central point exists for the aerodynamic forces acting on the body, the motion equations for the small amplitude rotational and translational oscillations can be expressed in a form which is a generalization of the motion equations for a body in vacuum, thus allowing to obtain a physical idea of the motion and aerodynamic effects and also significantly simplifying the calculation of the solutions and the interpretation of the results. In the formulation developed here the translational oscillations and the rotational motion around the center of mass are decoupled, as is the case for the rigid-body motion in vacuum, whereas in the classical added mass formulation the six motion equations are coupled. Also in this paper the nonsteady motion of small amplitude of a rigid body submerged in an ideal, incompressible fluid is considered in order to define the conditions for the existence of the central point in the case of a three-dimensional body. The results here presented are also of interest in marine applications.

Application of Screw Theory to Rigid Body Dynamics

1992 ◽  
Vol 114 (2) ◽  
pp. 262-269 ◽  
Author(s):  
G. R. Pennock ◽  
B. A. Oncu
Keyword(s):  
Rigid Body ◽  
Euler Equation ◽  
Computer Aided Design ◽  
Graphical Representation ◽  
Screw Theory ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Dynamic State ◽  
Disk Rolling ◽  
Insight Into

This paper applies screw theory to the dynamic analysis of a rigid body in general spatial motion. Particular emphasis is placed upon the geometric interpretation of the velocity screw, the momentum screw, and the force screw which provide valuable physical insight into the dynamic behavior of the rigid body. The geometric relation between the velocity screw and the momentum screw is discussed in some detail. The paper shows that the dual angle between the two screws provides insight into the kinetics of the rigid body. The dynamic state of motion of the body is then described by a dual vector equation, referred to as the dual Euler equation. The paper shows that the geometric equivalent of the dual Euler equation is a spatial triangle which can be used as a graphical method of solution, or as a check, of the analytical formulation. The concepts introduced in this paper are illustrated by the well-known example of a thin, homogeneous, circular disk rolling without slipping on a flat horizontal surface. With the widespread use of computer graphics and computer-aided design, the geometric approach presented here will prove useful in the graphical representation of the dynamics of a rigid body.

The Null Dynamical Effect, and Some Frequency Spectra, of Resonant Inertial Pressure Waves in a Rapidly Rotating, Right Circular, Sectored Cylinder

1980 ◽  
Vol 47 (3) ◽  
pp. 475-481
Author(s):  
W. E. Scott
Keyword(s):  
Rigid Body ◽  
Small Amplitude ◽  
Incompressible Liquid ◽  
Reasonable Agreement ◽  
Center Of Mass ◽  
Experimental Results ◽  
Pressure Waves ◽  
Frequency Spectra ◽  
Gyroscopic Motion ◽  
Amplitude Growth

It is shown that inertial waves in the form of standing asymmetrical pressure waves can exist in an incompressible liquid in a rotating sectored cylinder in a rigid body (e.g., a top or a missile) executing a small amplitude gyroscopic motion about its center of mass. Some of the frequency spectra of these waves are presented along with the result that sectoring the cylinder into any number of equal sectors results in eliminating the destabilizing effect of these waves (i.e., the amplitude growth of the motion of the rigid container) when there is a “Stewartson” resonance between the frequency of one of the inertial modes and the frequency of the nutational component of the motion of the container. Experimental results are in reasonable agreement with the theory.

Introduction of New Concepts and Problem Solving in Engineering Dynamics

2007 ◽  
Author(s):  
Serge Abrate
Keyword(s):  
Problem Solving ◽  
Concept Maps ◽  
Center Of Mass ◽  
Rigid Body Dynamics ◽  
The Body ◽  
New Concepts ◽  
Body Dynamics ◽  
Basic Equations ◽  
And Mathematics ◽  
Work Done

A survey of a large number of well-known textbooks for an undergraduate dynamics class showed that often new concepts are introduced without a clear connection to previously discussed material. For example, the concepts of work done by a force, linear momentum, angular momentum, and power are often introduced without a clear direct connection to Newton’s law. Similarly, in rigid body dynamics, important concepts such as the center of mass and the moments of inertia of the body are often introduced with little or no background. This article shows how all the important concepts in dynamics flow directly and logically from Newton’s laws. This is done through simple direct derivations. Connections are made clear by concept maps that help students understand how these different concepts are related. In addition to introducing new concepts and deriving some of the basic equations, a dynamics class should also introduce students to problem solving help them develop a systematic approach. This article describes a five step approach that is recommended for both high context and low context problems. In that context we stress that problem solving is a process that involves the application of known concepts and mathematics.

Rigid Body Dynamics, Constraints, and Inverses

2005 ◽  
Vol 74 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Hooshang Hemami ◽  
Bostwick F. Wyman
Keyword(s):  
Rigid Body ◽  
State Space ◽  
Tracking Error ◽  
Feedback System ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Contact Forces ◽  
Constraint Forces ◽  
Inverse Systems ◽  
Body Dynamics

Rigid body dynamics are traditionally formulated by Lagrangian or Newton-Euler methods. A particular state space form using Euler angles and angular velocities expressed in the body coordinate system is employed here to address constrained rigid body dynamics. We study gliding and rolling, and we develop inverse systems for estimation of internal and contact forces of constraint. A primitive approximation of biped locomotion serves as a motivation for this work. A class of constraints is formulated in this state space. Rolling and gliding are common in contact sports, in interaction of humans and robots with their environment where one surface makes contact with another surface, and at skeletal joints in living systems. This formulation of constraints is important for control purposes. The estimation of applied and constraint forces and torques at the joints of natural and robotic systems is a challenge. Direct and indirect measurement methods involving a combination of kinematic data and computation are discussed. The basic methodology is developed for one single rigid body for simplicity, brevity, and precision. Computer simulations are presented to demonstrate the feasibility and effectiveness of the approaches presented. The methodology can be applied to a multilink model of bipedal systems where natural and/or artificial connectors and actuators are modeled. Estimation of the forces is accomplished by the inverse of the nonlinear plant designed by using a robust high gain feedback system. The inverse is shown to be stable, and bounds on the tracking error are developed. Lyapunov stability methods are used to establish global stability of the inverse system.

scholarly journals Cases of Integrability Which Correspond to the Motion of a Pendulum in the Three-dimensional Space

2021 ◽  
Vol 16 ◽  
pp. 73-84
Author(s):  
Maxim V. Shamolin
Keyword(s):  
Rigid Body ◽  
Force Fields ◽  
Characteristic Point ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
The Body ◽  
Spatial Motion ◽  
Free Rigid Body

We systematize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint, or the center of mass of the body moves rectilinearly and uniformly; this means that there exists a nonconservative couple of forces in the system

Design of a Compliant Jumping Robot With Passive Stabilizer

2020 ◽  
Author(s):  
Joshua Hooper ◽  
Martin Garcia ◽  
Paul Pena ◽  
Ayse Tekes
Keyword(s):  
Center Of Mass ◽  
Vertical Plane ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Main Body ◽  
Body Parts ◽  
Element Analysis ◽  
Flexure Hinges ◽  
Jumping Robot ◽  
The Impact

Abstract This study presents the design and development of a compliant multi-link hopping mechanism actuated by a single DC motor. Two main design goals are to have a single piece designed main body for the jumping robot and a passive stabilizer to allow consecutive jumps. Mechanism consists of monolithically designed large deflecting main body incorporating the gears and initially curved flexure hinge. Due to the limitations of the design goal, revolute motion between top and bottom legs on the main body are realized by a compliant link which replaces the need of ball bearings. Also, continuous energy store and release during jumping is ensured by the same flexure hinges. Passive self-righting cage is attached to the bottom of the main body to maintain upright position both in landing and takeoff. The cage allows the center of mass to stay in the vertical plane to prevent tilting. During landing, cage absorbs the impact and allows the main body to roll to its initial configuration so that the robot can complete jumping. Mechanism parts including the cage are 3D printed using PETG. Design optimization of the body parts including the rigid legs and flexure hinges are analyzed both experimentally and analytically. Finite element analysis is performed to calculate the equivalent stiffness and natural frequency of the jumping robot and simplified mathematical model is derived using rigid body dynamics.

Modelling lateral manoeuvres in fish

2012 ◽  
Vol 697 ◽  
pp. 1-34 ◽  
Author(s):  
K. Singh ◽  
T. J. Pedley
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Body Motion ◽  
Dynamic State ◽  
Parameter Study ◽  
Element Formulation ◽  
Turn Angle ◽  
Impulsive Input

AbstractWe propose a method to model manoeuvres in self-propelled flexible-bodied fish by modelling the hydrodynamics coupled to the body inertia. Flexible body motion is prescribed and the equations of motion are solved for the position of the centre of mass and rotation of the body. The governing equations are formulated by applying the conservation of linear and angular momentum. Two independent methods to model the fluid dynamics are pursued: Model 1 is an extension of elongated-body theory, modified for self-propulsion and flexible motion. Model 2 applies a numerical boundary-element formulation with the fish modelled as an infinitely thin rectangular body. The manoeuvring response to an impulsive input is first examined to understand the rigid-body characteristics of the fish. A flexible bend action is included to model C-bends of the type observed during escapes in fish. Models 1 and 2 are used to cross-verify the respective implementations as well as to develop physical insights into manoeuvring. A parameter study shows that fish of intermediate body depths are best adapted to rapid turns whereas the initial dynamic state of the fish is instrumental in affecting the sign as well as the magnitude of the turn angle, for a prescribed bend deflection. Computations for combined swimming and turning show that the initial rigid-body dynamics of the fish is much more effective than the induced effect of the prior shed wake in enhancing the turning response.

On Dynamically Equivalent Force Systems and Their Application to the Balancing of a Broom or the Stability of a Shoe Box

2004 ◽  
Author(s):  
Just L. Herder ◽  
Arend L. Schwab
Keyword(s):  
Rigid Body ◽  
Center Of Mass ◽  
The Body ◽  
Resultant Force ◽  
Dynamic Equivalence ◽  
Force Systems ◽  
The Stability ◽  
Metacentric Height ◽  
The Given

The stability of a rigid body on which two forces are in equilibrium can be assessed intuitively. In more complex cases this is no longer true. This paper presents a general method to assess the stability of complex force systems, based on the notion of dynamic equivalence. A resultant force is considered dynamically equivalent to a given system of forces acting on a rigid body if the contributions to the stability of the body of both force systems are equal. It is shown that the dynamically equivalent resultant force of two given constant forces applies at the intersection of its line of action and the circle put up by the application points of the given forces and the intersection of their lines of action. The determination of the combined center of mass can be considered as a special case of this theorem. Two examples are provided that illustrate the significance of the proposed method. The first example considers the suspension of a body, by springs only, that is statically balanced for rotation about a virtual stationary point. The second example treats the roll stability of a ship, where the metacentric height is determined in a natural way.

A variational principle for three-dimensional interactions between water waves and a floating rigid body with interior fluid motion

2019 ◽  
Vol 866 ◽  
pp. 630-659 ◽  
Author(s):  
Hamid Alemi Ardakani
Keyword(s):  
Variational Principle ◽  
Rigid Body ◽  
Water Waves ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Three Dimensions ◽  
Fluid Sloshing ◽  
Gravity Driven

A variational principle is given for the motion of a rigid body dynamically coupled to its interior fluid sloshing in three-dimensional rotating and translating coordinates. The fluid is assumed to be inviscid and incompressible. The Euler–Poincaré reduction framework of rigid body dynamics is adapted to derive the coupled partial differential equations for the angular momentum and linear momentum of the rigid body and for the motion of the interior fluid relative to the body coordinate system attached to the moving rigid body. The variational principle is extended to the problem of interactions between gravity-driven potential flow water waves and a freely floating rigid body dynamically coupled to its interior fluid motion in three dimensions.

Intrinsic Time Integration Procedures for Rigid Body Dynamics

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Olivier A. Bauchau ◽  
Hao Xin ◽  
Shiyu Dong ◽  
Zhiheng Li ◽  
Shilei Han
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Equations Of Motion ◽  
Time Integration ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Rotation Tensor ◽  
Intrinsic Nature ◽  
Intrinsic Form ◽  
Angular Velocities

The treatment of rotations in rigid body and Cosserat solids dynamics is challenging. In most cases, at some point in the formulation, a parameterization of rotation is introduced and the intrinsic nature of the equations of motions is lost. Typically, this step considerably complicates the form of the equations and increases the order of the nonlinearities. Clearly, it is desirable to bypass parameterization of rotation, leaving the equations of motion in their original, intrinsic form. This has prompted the development of rotationless and intrinsic formulations. This paper focuses on the latter approach. The most famous example of intrinsic formulation is probably Euler’s second law for the motion of a rigid body rotating about an inertial point. This equation involves angular velocities solely, with algebraic nonlinearities of the second-order at most. Unfortunately, this intrinsic equation also suffers serious drawbacks: the angular velocity of the body is computed, but not its orientation, the body is “unaware” of its inertial orientation. This paper presents an alternative approach to the problem by proposing discrete statements of the rotation kinematic compatibility equation, which provide solutions for both rotation tensor and angular velocity without relying on a parameterization of rotation. The formulation is also generalized using the motion formalism, leading to very simple discretized equations of motion.

Sign in / Sign up

Export Citation Format

Share Document