scholarly journals Approximate Formulation of the Rigid Body Motions of an Elastic Rectangle Under Sliding Boundary Conditions

2021 ◽  
Vol 15 (2) ◽  
pp. 82-90
Author(s):  
Onur Şahin ◽  
Barış Erbaş ◽  
Brent Wilson
Keyword(s):  
Boundary Conditions ◽  
Rigid Body ◽  
Separation Of Variables ◽  
Low Frequency ◽  
Plane Motion ◽  
Body Motion ◽  
Perturbation Scheme ◽  
Biharmonic Equations ◽  
Approximate Formulation ◽  
Rigid Body Motions

Abstract Low-frequency analysis of in-plane motion of an elastic rectangle subject to end loadings together with sliding boundary conditions is considered. A perturbation scheme is employed to analyze the dynamic response of the elastic rectangle revealing nonhomogeneous boundary-value problems for harmonic and biharmonic equations corresponding to leading and next order expansions, respectively. The solution of the biharmonic equation obtained by the separation of variables, a consequence of sliding boundary conditions, gives an asymptotic correction to the rigid body motion of the rectangle. The derived explicit approximate formulae are tested for different kinds of end loadings together with numerical examples demonstrating the comparison against the exact solutions.

Eigenanalysis of the Rigid Body Motion Effect on Elastic Systems

1983 ◽  
Vol 105 (4) ◽  
pp. 461-466 ◽  
Author(s):  
A. Maher ◽  
A. L. Schlack
Keyword(s):  
Eigenvalue Problem ◽  
Rigid Body ◽  
Free Vibration Analysis ◽  
Plane Motion ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Computer Calculations ◽  
Motion Effect ◽  
Ritz Procedure ◽  
The Difference

In this paper, the influence of rigid body motion on the behavior of a vibrating elastic system is treated by the development of a difference eigenvalue problem. The maximum possible changes in eigenfrequencies due to removal of constraints are obtained by the employment of the bound approach [1, 2]. As an application to a structural system the Rayleigh-Ritz procedure is employed for constructing the difference eigenvalue problem. Discussion of the use of the method for various types of engineering problems is outlined. An example of a free vibration analysis of a simply supported beam in plane motion with a nonuniform mass and elasticity distribution is solved. A comparison between computer calculations and previously published results is presented.

On Higher Order Point-Line and the Associated Rigid Body Motions

2006 ◽  
Vol 129 (2) ◽  
pp. 166-172 ◽  
Author(s):  
Yi Zhang ◽  
Kwun-Lon Ting
Keyword(s):  
Rigid Body ◽  
Higher Order ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Dual Quaternion ◽  
Displacement Operator ◽  
Screw Motion ◽  
Rigid Body Motions ◽  
Point Line

This paper presents a study on the higher-order motion of point-lines embedded on rigid bodies. The mathematic treatment of the paper is based on dual quaternion algebra and differential geometry of line trajectories, which facilitate a concise and unified description of the material in this paper. Due to the unified treatment, the results are directly applicable to line motion as well. The transformation of a point-line between positions is expressed as a unit dual quaternion referred to as the point-line displacement operator depicting a pure translation along the point-line followed by a screw displacement about their common normal. The derivatives of the point-line displacement operator characterize the point-line motion to various orders with a set of characteristic numbers. A set of associated rigid body motions is obtained by applying an instantaneous rotation about the point-line. It shows that the ISA trihedrons of the associated rigid motions can be simply depicted with a set of ∞2 cylindroids. It also presents for a rigid body motion, the locus of lines and point-lines with common rotation or translation characteristics about the line axes. Lines embedded in a rigid body with uniform screw motion are presented. For a general rigid body motion, one may find lines generating up to the third order uniform screw motion about these lines.

A Hybrid Method for Fan Simulations in Full Vehicle Thermal Analyses

2020 ◽  
Author(s):  
Zhilei Wu ◽  
Michael Blatnik ◽  
Eamonn Kress ◽  
Lester Deleon
Keyword(s):  
Boundary Conditions ◽  
Rigid Body ◽  
Mass Flow Rate ◽  
Flow Rate ◽  
Transient Simulation ◽  
Body Motion ◽  
Thermal Flow ◽  
Full Vehicle ◽  
Steady Simulation ◽  
Thermal Wake

Abstract In full vehicle thermal flow analyses, the most often used procedure to simulate fluid motions driven by the cooling fan is the Moving Reference Frame (MRF) method. In the MRF approach, the fan is fixed in space and the fan rotation is modeled using grid fluxes. This method is widely used because it provides a fast and effective means of simulating fans. However, the MRF method does not always accurately predict the thermal wake and the mass flow rate through the fan, which causes errors in predicted temperatures on the parts downstream of the fan. Another method for fan simulation is the Rigid Body Motion (RBM) method in which the fan rotates in time. The RBM method models the fan motions directly, thus it can accurately predict the mass flow rate and thermal wake. However, an RBM simulation is transient and needs a time-average to obtain statistically steady-state results. The RBM method requires a significant amount of CPU resources and simulation time, which prevents it from being widely used in industry. In the current work, a Hybrid Rigid Body Motion (HRBM) method is developed and validated. The HRBM method splits the full vehicle thermal simulation into two simulations, and then couples them at the interface. The first simulation is transient, utilizes the RBM method for the fan, and only models the fan regions. The second simulation is steady, which models the full vehicle except the fan regions. The solution from the transient simulation is time-averaged on the exchange interface and used as boundary conditions for the steady simulation. Conversely, the solution for the steady simulation is used as boundary conditions for the transient simulation at the exchange interface. Due to the slight differences resulting from time-averaging, there is a mismatch in the physical quantities at the exchange interface. This causes stability issues which prevent the coupled simulations from converging. Special techniques have been used in this work to stabilize the solution at the interface, which ensured the convergence of the coupled simulations. The HRBM method greatly improves the accuracy of the full vehicle thermal flow simulation compared to using the MRF method. The thermal wake that results from using HRBM to model the fan is very similar to that produced by RBM, but HRBM utilizes ∼20–30% of the simulation resources required by RBM to achieve convergence.

scholarly journals Acceleration Signal Processing Method of Impact Response of Floating Shock Platform Based on Rigid Body Motion Model

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Wenqi Zhang ◽  
Xiongliang Yao ◽  
Zhikai Wang ◽  
Jin Chen ◽  
Heng Yang
Keyword(s):  
Signal Processing ◽  
Rigid Body ◽  
High Frequency ◽  
Response Spectrum ◽  
Low Frequency ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Shock Acceleration ◽  
Motion Model ◽  
Acceleration Signal

Floating shock platform is generally used to test the antishock performance of large shipboard equipment. Shock acceleration signal will produce zero-shift phenomenon in the test measurement process, which will affect the subsequent shock response spectrum analysis. In this paper, a method of shock acceleration signal processing based on rigid body motion revision model is established. The rigid body motion revision model adopts the theory of ship’s seakeeping based on the hypothesis of KrylovFroude, in which the shock wave load of underwater explosion adopts the empirical formula. The bubble pulsation load adopts the GeersHunter spherical bubble model. The empirical mode decomposition method is used to eliminate the trend term of the low-frequency part of the acceleration signal, and the frequency filtering technology is used to eliminate the noise of the high frequency part. The response estimated by the rigid body motion model is used to modify the measured signal. The modified signal is analyzed by shock response spectrum to get the round design spectrum. The validity of the signal is determined by the Pauta criterion. Finally, the shock environment statistics of the whole platform is given. This method can eliminate the low-frequency trend term and high frequency noise and has good robustness. It can be applied to many kinds of signals. This method can provide technical support for antishock performance of shipboard equipment and also applied to other shock signal processing fields.

A Computationally Efficient Planar Rigid Body Velocity Measure

2009 ◽  
Author(s):  
Luis E. Criales ◽  
Joseph M. Schimmels
Keyword(s):  
Rigid Body ◽  
Rigid Bodies ◽  
Body Motion ◽  
Computationally Efficient ◽  
Straight Line ◽  
Body Velocity ◽  
Velocity Measure ◽  
Rigid Body Motions ◽  
Line Path ◽  
Planar Motions

A planar rigid body velocity measure based on the instantaneous velocity of all particles that constitute a rigid body is developed. This measure compares the motion of each particle to an “ideal”, but usually unobtainable, motion. This ideal motion is one that would carry each particle from its current position to its desired position on a straight-line path. Although the ideal motion is not a valid rigid body motion, this does not preclude its use as a reference standard in evaluating valid rigid body motions. The optimal instantaneous planar motions for general rigid bodies in translation and rotation are characterized. Results for an example planar positioning problem are presented.

Use of experimental dynamic substructuring to predict the low frequency structural dynamics under different boundary conditions

2017 ◽  
Vol 23 (11) ◽  
pp. 1444-1455
Author(s):  
Walter D’Ambrogio ◽  
Annalisa Fregolent
Keyword(s):  
Boundary Conditions ◽  
Rigid Body ◽  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Low Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Different Boundary Conditions ◽  
Rigid Body Modes

Flexible structural components can be attached to the rest of the structure using different types of joints. For instance, this is the case of solar panels or array antennas for space applications that are joined to the body of the satellite. To predict the dynamic behaviour of such structures under different boundary conditions, such as additional constraints or appended structures, it is possible to start from the frequency response functions in free-free conditions. In this situation, any structure exhibits rigid body modes at zero frequency. To experimentally simulate free-free boundary conditions, flexible supports such as soft springs are typically used: with such arrangement, rigid body modes occur at low non-zero frequencies. Since a flexible structure exhibits the first flexible modes at very low frequencies, rigid body modes and flexible modes become coupled: therefore, experimental frequency response function measurements provide incorrect information about the low frequency dynamics of the free-free structure. To overcome this problem, substructure decoupling can be used, that allows us to identify the dynamics of a substructure (i.e. the free-free structure) after measuring the frequency response functions on the complete structure (i.e. the structure plus the supports) and from a dynamic model of the residual substructure (i.e. the supporting structure). Subsequently, the effect of additional boundary conditions can be predicted using a frequency response function condensation technique. The procedure is tested on a reduced scale model of a space solar panel.

scholarly journals A Matrix Information-Geometric Method for Change-Point Detection of Rigid Body Motion

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 531
Author(s):  
Xiaomin Duan ◽  
Huafei Sun ◽  
Xinyu Zhao
Keyword(s):  
Rigid Body ◽  
Change Point ◽  
Order Approximation ◽  
Local Maximum ◽  
Change Point Detection ◽  
Body Motion ◽  
Geometric Method ◽  
Change Points ◽  
Gradient Descent Algorithm ◽  
Rigid Body Motions

A matrix information-geometric method was developed to detect the change-points of rigid body motions. Note that the set of all rigid body motions is the special Euclidean group S E ( 3 ) , so the Riemannian mean based on the Lie group structures of S E ( 3 ) reflects the characteristics of change-points. Once a change-point occurs, the distance between the current point and the Riemannian mean of its neighbor points should be a local maximum. A gradient descent algorithm is proposed to calculate the Riemannian mean. Using the Baker–Campbell–Hausdorff formula, the first-order approximation of the Riemannian mean is taken as the initial value of the iterative procedure. The performance of our method was evaluated by numerical examples and manipulator experiments.

Optimal rigid body motions, part 1: Approximate formulation

1991 ◽  
Vol 70 (1) ◽  
pp. 57-78 ◽  
Author(s):  
R. S. Chowdhry ◽  
J. Z. Ben-Asher ◽  
E. M. Cliff
Keyword(s):  
Rigid Body ◽  
Approximate Formulation ◽  
Rigid Body Motions

Dynamic Response of Composite Pressure Vessels to Inertia Loads

1991 ◽  
Vol 113 (1) ◽  
pp. 86-91
Author(s):  
J. C. Prucz ◽  
J. D’Acquisto ◽  
J. E. Smith
Keyword(s):  
Rigid Body ◽  
Combustion Engine ◽  
Pressure Vessels ◽  
Body Motion ◽  
Connecting Rod ◽  
Filament Wound ◽  
Potential Benefits ◽  
Rigid Body Motions ◽  
Crank Mechanism ◽  
Selection Of

A new analytical model has been developed in order to investigate the potential benefits of using fiber-reinforced composites in pressure vessels that undergo rigid-body motions. The model consists of a quasi-static lamination analysis of a cylindrical, filament-wound, pressure vessel, combined with an elastodynamic analysis that accounts for the coupling effects between its rigid-body motion and its elastic deformations. The particular type of motion investigated in this paper is that of an oil-pressurized, tubular connecting rod in a slider-crank mechanism of an internal combustion engine. A comprehensive parametric study has been focused on the maximum wall stresses induced in such a rod by the combined effect of internal pressure and inertia loads associated with its motion. The numerical results illustrate potential ways to reduce these stresses by appropriate selection of material systems, lay-up configurations and geometric parameters.

Solutions for Transient Heat Conduction With Solid Body Motion and Convective Boundary Conditions

2007 ◽  
Author(s):  
Robert L. McMasters ◽  
James V. Beck
Keyword(s):  
Boundary Conditions ◽  
Solid Body ◽  
Green's Functions ◽  
Green’S Functions ◽  
Separation Of Variables ◽  
Body Movement ◽  
Convective Boundary Condition ◽  
Body Motion ◽  
Convective Boundary Conditions ◽  
Convective Boundary

The analytical solution for the problem of transient thermal conduction with solid body movement is developed for a parallelepiped with convective boundary conditions. An effective transformation scheme is used to eliminate the flow terms. The solution uses Green’s functions containing convolution-type integrals, which involve integration over a dummy time, referred to as “cotime.” Two types of Green’s functions are used: one for short cotimes comes from the Laplace transform and the other for long cotimes from the method of separation of variables. A primary advantage of this method is that it incorporates internal verification of the numerical results by varying the partition time between the short and long components. In some cases, the long time solution requires a zeroth term in the summation, which does not occur when solid body motion is not present. The existence of this zeroth term depends upon the magnitude of the heat transfer coefficient associated with the convective boundary condition. An example is given for a two-dimensional case involving both prescribed temperature and convective boundary conditions. Comprehensive tables are also provided for the nine possible combinations of boundary conditions in each dimension.

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