Discussion of “Integration of Linear Equations of Motion”

1976 ◽  
Vol 102 (6) ◽  
pp. 1273-1274
Author(s):  
Anthony J. Medland
Keyword(s):  
Equations Of Motion ◽  
Linear Equations ◽  
Linear Equations Of Motion

scholarly journals INVESTIGATION OF THE DYNAMICS OF AN OVERHEAD CRANE LIFTING PROCESS IN A VERTICAL PLANE

Transport ◽  
2005 ◽  
Vol 20 (5) ◽  
pp. 176-180 ◽  
Author(s):  
Marijonas Bogdevičius ◽  
Aleksandr Vika
Keyword(s):  
Dynamic Behaviour ◽  
Equations Of Motion ◽  
Asynchronous Motor ◽  
Linear Equations ◽  
Vertical Plane ◽  
Overhead Crane ◽  
Dynamic Forces ◽  
Planet Gear ◽  
Linear Equations Of Motion ◽  
Non Linear Equations

The paper analyses the dynamic behaviour of supporting structure of an overhead crane during the operation of a hoisting mechanism. The crane is expected to operate with a hook and to carry 50 kN of weight. The electric hoist consists of an asynchronous motor with a magnetic brake, a two‐level planet gear, a load drum and an upper block. Non‐linear equations of motion of a crane hoisting mechanism are derived. Real dynamic forces and their influence on the hoisting crane behaviour are obtained. Numerical results of the crane are derived considering two hoisting regimes during the operation of the hoisting.

Formulation of Multiple Belt System and its Dynamic Analysis

1993 ◽  
Author(s):  
Takuzo Iwatsubo ◽  
Shiro Arii ◽  
Kei Hasegawa ◽  
Koki Shiohata
Keyword(s):  
Computer Program ◽  
Dynamic Analysis ◽  
Dynamic Characteristics ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Transient Responses ◽  
Fundamental Idea ◽  
Linear Equations Of Motion ◽  
Simulation Results ◽  
Belt System

Abstract This paper presents a method for analyzing the dynamic characteristics of driving systems consisting of multiple belts and pulleys. First, the algorithm which derives the linear equations of motion of arbitrary multi-coupled belt systems is shown. Secondly, by using the algorithm, the computer program which formulates the equations of motion and calculates the transient responses of the belt system is presented. The fundamental idea of the algorithm is as follows: Complicated belt systems consisting of multiple belts and pulleys are regarded as combinations of simple belt systems consisting of a single belt and some pulleys. Therefore, the equations of motion of the belt systems can be derived by the superposition of the equations of motion of the simple belt systems. By means of this method, the responses of arbitrary multi-coupled belt systems can be calculated. Finally, to verify the usefulness of this method, the simulation results are compared with the experimental results.

Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link

1988 ◽  
Vol 110 (4) ◽  
pp. 416-421 ◽  
Author(s):  
Enrique Barbieri ◽  
U¨mit O¨zgu¨ner
Keyword(s):  
Equations Of Motion ◽  
Linear Equations ◽  
Quantitative Comparison ◽  
Mode Shapes ◽  
Dimensional Model ◽  
Finite Dimensional ◽  
Linear Equations Of Motion ◽  
Aluminum Beam

The linear equations of motion of a uniform flexible slewing link which were derived via Hamilton’s Extended Principle are considered. These equations account for the coupling between bending and rigid modes. Unconstrained and constrained mode expansions are investigated and a quantitative comparison is made between the frequency equations and associated mode shapes. A finite dimensional model is derived using the assumed modes method and the theoretical frequencies are verified with an experimental counterbalanced aluminum beam.

Calculations for anemometry with fine hot wires

1968 ◽  
Vol 32 (1) ◽  
pp. 9-19 ◽  
Author(s):  
W. W. Wood
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Close Agreement ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Measured Data ◽  
Hot Wire ◽  
Linear Equations Of Motion ◽  
Hot Wires ◽  
Non Linear Equations

The heat transfer appropriate to low Reynolds number hot-wire anemometry is calculated from the full non-linear equations of motion and of heat transfer by an iterative method starting with the Oseen solution and its heat flux analogue. The second and third iterates yield close agreement with measured data.

Detection of Cracks in Rotating Timoshenko Shafts Using Axial Impulses

1991 ◽  
Vol 113 (1) ◽  
pp. 74-78 ◽  
Author(s):  
K. R. Collins ◽  
R. H. Plaut ◽  
J. Wauer
Keyword(s):  
Piecewise Linear ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Effective Means ◽  
Linear Equations ◽  
Free Vibrations ◽  
Frequency Spectra ◽  
Time Histories ◽  
Rotating Shafts ◽  
Linear Equations Of Motion

A rotating Timoshenko shaft with a single transverse crack is considered. The crack opens and closes during motion and is represented by generalized forces and moments. The shaft has simply supported ends, and the six coupled, piecewise-linear equations of motion (including longitudinal, transverse, and torsional displacements) are integrated numerically after application of Galerkin’s method with two-term approximations for each of the six displacements. Time histories and frequency spectra are compared for shafts with no crack and with a crack for which the crack depth is one-fifth of the shaft diameter. Free vibrations and the responses to a single axial impulse and periodic axial impulses are analyzed. The last case appears to provide an effective means for detecting cracks in rotating shafts.

Inviscid Shear Flow Analysis of Corner Eddies Ahead of a Channel Flow Contraction

1985 ◽  
Vol 107 (2) ◽  
pp. 212-217
Author(s):  
R. N. Meroney
Keyword(s):  
Shear Flow ◽  
Velocity Distribution ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Flow Analysis ◽  
Inviscid Fluid ◽  
Flow Vorticity ◽  
Flow Geometry ◽  
Linear Shear ◽  
Linear Equations Of Motion

The steady rotational flow of an inviscid fluid in a two-dimensional channel toward a sink or a contraction is treated. The velocity distribution at upstream infinity is approximated by a linear combination of uniform flow, linear shear flow, and a cosine curve. The combinations were adjusted to simulate flows ranging from laminar to turbulent. Vorticity is assumed conserved on streamlines. The resulting linear equations of motion are solved exactly. The solution show the dependence of the corner eddy separation and reattachment on flow geometry and approach flow vorticity and velocity distribution typified by a shape factor.

Numerical Simulation of Flutter of Suspension Bridges

1997 ◽  
Vol 50 (11S) ◽  
pp. S174-S179 ◽  
Author(s):  
S. Preidikman ◽  
D. T. Mook
Keyword(s):  
Control Systems ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Suspension Bridges ◽  
Governing Equations ◽  
Nonlinear Springs ◽  
Linear Equations Of Motion ◽  
The Time Domain ◽  
Present Simulation ◽  
Post Onset

A method for simulating the spontaneous, wind-excited vibrations of suspension bridges is described. The approach is based on a numerical model that treats the bridge and flowing air as elements of a single dynamic system; and all of the governing equations are integrated numerically, simultaneously, and interactively. It is shown that the present simulation predicts the same onset of flutter as the analysis of Fung. Unlike Fung’s analysis, the present analysis provides the solution in the time domain, is not restricted to periodic motions or linear equations of motion, and provides post-onset behavior as long as the effective angles of attack are not large enough to produce stall. As a consequence, the present analysis can be a very effective tool for the design of flutter-suppressing control systems. Because the equations are solved numerically, nonlinear supports do not present a problem. In the present work, it is shown how the nonlinear springs lead to limit-cycle responses.

scholarly journals Dynamics and rigidity of a manipulator with three DOFs

2018 ◽  
Vol 226 ◽  
pp. 01020 ◽  
Author(s):  
Serikbay Kosbolov ◽  
Yerlan Yeleukulov ◽  
Alfiya Atalykova ◽  
Algazy Zhauyt ◽  
Gulsara Yestemessova ◽  
...  
Keyword(s):  
Potential Energy ◽  
Cross Section ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Kinematic Chain ◽  
System Of Linear Equations ◽  
Anthropometric Data ◽  
Elastic Potential Energy ◽  
System Equations ◽  
Linear Equations Of Motion

The problem of dynamic elastic four-link initial kinematic chain (IKC) of the load-bearing manipulator, which is the basis for various modifications are considered. Using the Lagrange operator for this system, equations of motion in matrix form are obtained. To determine the potential energy of an elastic four-link IKC manipulator, we use the formula for the elastic potential energy of a rectilinear homogeneous rod of length l. The cross-section of the rod is considered annular or circular. Solving the system of linear equations of motion on a computer using the ADAMS program, the results of the movement of links and cargo were obtained. Kinematics and dynamics are presented for a generic 3 DOFs Initial Kinematic Chain; with anthropometric data and the dynamics equations, simulations were performed to understand its behavior.

Sign in / Sign up

Export Citation Format

Share Document