scholarly journals NON-RIGID KINEMATIC EXCITATION FOR MULTIPLY-SUPPORTED SYSTEM WITH HOMOGENEOUS DAMPING

2018 ◽  
Vol 14 (4) ◽  
pp. 152-157
Author(s):  
Alexander G. Tyapin
Keyword(s):  
Mass Matrix ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Internal Damping ◽  
Static Response ◽  
Kinematic Excitation ◽  
Hand Part ◽  
Internal Forces ◽  
The Right ◽  
Damping Model

This paper continues the discussion of linear equations of motion. The author considers non-rigid kinematic excitation for multiply-supported system leading to the deformations in quasi-static response. It turns out that in the equation of motion written down for relative displacements (relative displacements are defined as absolute displacements minus quasi-static response) the contribution of the internal damping to the load in some cases may be zero (like it was for rigid kinematical excitation). For this effect the system under consideration must have homogeneous damping. It is the often case, though not always. Zero contribution of the internal damping to the load is different in origin for rigid and non-rigid kinematic excitation: in the former case nodal loads in the quasi-static response are zero for each element; in the latter case nodal loads in elements are non-zero, but in each node they are balanced giving zero resulting nodal loads. Thus, damping in the quasi-static response does not impact relative motion, but impacts the resulting internal forces. The implementation of the Rayleigh damping model for the right-hand part of the equation leads to the error (like for rigid kinematic excitation), as damping in the Rayleigh model is not really “internal”: due to the participation of mass matrix it works on rigid displacements, which is impossible for internal damping

scholarly journals RIGID AND NON-RIGID KINEMATIC EXCITATION FOR MULTIPLY-SUPPORTED SYSTEM: ONCE MORE ABOUT THE CONTRIBUTION OF DAMPING TO THE DYNAMIC LOADS IN SEISMIC ANALYSIS

2018 ◽  
Vol 14 (1) ◽  
pp. 164-170
Author(s):  
Alexander G. Tyapin
Keyword(s):  
Seismic Analysis ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Rigid Motion ◽  
Dynamic Loads ◽  
Rigid Support ◽  
Right Hand ◽  
Hand Part ◽  
The Right ◽  
Support Motion

Development of linear equations of motion for seismic analysis is discussed in the paper. The paper continues the discussion: the author does not agree with colleagues putting damping matrix into the right-hand part of the equation of motion describing dynamic loads. This disagreement refers to the most popular case of “rigid” motion of multiple supports. In this paper the author follows the logic of general “non-rigid” support motion and points out a step in the equation development when the transition to “rigid” support motion (as a particular case of “non-rigid” motion) is spoiled by the opponents. In the author’s opinion, the mistake is in the implementation of the Rayleigh damping model for the right-hand part of the equation. This is in the contradiction with physical logic, as damping in the Rayleigh model is not really “internal”: due to the participation of mass matrix it works on rigid displacements, which is impossible for internal damping.

Investigation of manipulator dynamics with a viscous damping model

2007 ◽  
Vol 221 (5) ◽  
pp. 513-517
Author(s):  
P Herman
Keyword(s):  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Viscous Damping ◽  
First Order ◽  
Manipulator Dynamics ◽  
Interesting Insight ◽  
Damping Model ◽  
Insight Into

In this article, some remarks concerning dynamics investigation of a manipulator described using first-order equations of motion with a viscous damping model is conducted. The viscous damping model arises from the Rayleigh dissipation potential and decomposition of the manipulator mass matrix. As a result, it takes into account both kinematic and mechanical parameters of the system. Moreover, the use of first-order equations of motion leads to obtaining some interesting insight into the manipulator dynamics. The proposed approach was tested on a three-degrees-of-freedom, three-dimensional Yasukawa-like robot.

LATERAL VIBRATIONS OF BEAMS ON AN ELASTIC BASE AT CHANGING THE SUPPORTING CONDITIONS

2020 ◽  
Vol 91 (5) ◽  
pp. 70-76
Author(s):  
E.V. LEONTIEV ◽  
◽  
Keyword(s):  
Dynamic Behavior ◽  
Elastic Foundation ◽  
Dynamic Problem ◽  
Static Problem ◽  
Elastic Base ◽  
Design Model ◽  
Lateral Vibrations ◽  
Internal Forces ◽  
Vibration Loads ◽  
The Right

The paper considers the system "beam - elastic foundation", in which a beam with free edges was at first on a solid elastic foundation, but when a defect suddenly forms in the foundation under the right side of the beam, part of foundation was removed from design model. As a result of calculations performed by the method of initial parameters, the displacements and internal forces for the static problem are determined. The dynamic problem of determining the forces and displacements was solved, taking into account the three vibration loads F (t) = F sinγt applied at arbitrary points d when the conditions for supporting the right side of the beam on an elastic foundation were changed, the values of the dynamics coefficients were determined. Conditions are formulated that must be taken into account when analyzing the dynamic behavior of a structure under the influence of vibration loads in the case of a change in the conditions of bearing on an elastic foundation.

NEUTRINO OSCILLATION AND LEPTON MASS MATRIX

1994 ◽  
Vol 09 (01) ◽  
pp. 41-50 ◽  
Author(s):  
KEN-ITI MATUMOTO ◽  
DAIJIRO SUEMATSU
Keyword(s):  
Solar Neutrino ◽  
Phase Structure ◽  
Quark Mass ◽  
Mass Matrix ◽  
Lepton Sector ◽  
Solar Neutrino Problem ◽  
Quark Sector ◽  
Mass Matrices ◽  
Suppression Mechanism ◽  
The Right

We apply the empirical quark mass matrices to the lepton sector and study the solar neutrino problem and the atmospheric vμ deficit problem simultaneously. We show that their consistent explanation is possible on the basis of these matrices. The lepton sector mass matrices need the phase structure which is different from the ones of the quark sector. However, even if the phase structure of the mass matrices is identical in both sectors, an interesting suppression mechanism of sin 2 2θ12 which is related to the solar neutrino problem can be induced from the right-handed neutrino Majorana mass matrix. We discuss such a possibility through the concrete examples.

UNCONSTRAINED HIGHER SPINS IN FOUR DIMENSIONS

2011 ◽  
Vol 08 (03) ◽  
pp. 511-556 ◽  
Author(s):  
GIUSEPPE BANDELLONI
Keyword(s):  
Equations Of Motion ◽  
Symmetric Tensor ◽  
Tensor Fields ◽  
Geometrical Meaning ◽  
Four Dimensions ◽  
Spin Field ◽  
Angular Momenta ◽  
Higher Spin ◽  
Spin Fields ◽  
The Right

The relativistic symmetric tensor fields are, in four dimensions, the right candidates to describe Higher Spin Fields. Their highest spin content is isolated with the aid of covariant conditions, discussed within a group theory framework, in which auxiliary fields remove the lower intrinsic angular momenta sectors. These conditions are embedded within a Lagrangian Quantum Field theory which describes an Higher Spin Field interacting with a Classical background. The model is invariant under a (B.R.S.) symmetric unconstrained tensor extension of the reparametrization symmetry, which include the Fang–Fronsdal algebra in a well defined limit. However, the symmetry setting reveals that the compensator field, which restore the Fang–Fronsdal symmetry of the free equations of motion, is in the existing in the framework and has a relevant geometrical meaning. The Ward identities coming from this symmetry are discussed. Our constraints give the result that the space of the invariant observables is restricted to the ones constructed with the Highest Spin Field content. The quantum extension of the symmetry reveals that no new anomaly is present. The role of the compensator field in this result is fundamental.

Optimization of Dynamic Forces in the Design of Mechanical Hands

1989 ◽  
Author(s):  
M. A. Nahon ◽  
J. Angeles
Keyword(s):  
Equations Of Motion ◽  
Inequality Constraints ◽  
Kinematic Chain ◽  
Programming Approach ◽  
Quadratic Optimization Problem ◽  
System A ◽  
Redundantly Actuated ◽  
Internal Forces ◽  
Constrained Quadratic Optimization ◽  
Mechanical Hands

Abstract Mechanical hands have become of greater interest in robotics due to the advantages they offer over conventional grippers in tasks requiring dextrous manipulation. However, mechanical hands also tend to be more complex in construction and require more sophisticated design analysis to determine the forces in the system. A mechanical hand can be described as a kinematic chain with time-varying topology which becomes redundantly actuated when an object is grasped. When this occurs, care must be exercised to avoid crushing the object or generating excessive forces within the mechanism. In the present work, this problem is formulated as a constrained quadratic optimization problem. The forces to be minimized form the objective, the dynamic equations of motion form the equality constraints and the finger-object contacts yield the inequality constraints. The quadratic-programming approach is shown to be advantageous due to its ability to minimize ‘internal forces’ A technique is proposed for smoothing the discontinuities in the force solution which occur when the toplogy changes.

Recursive Linearization of Multibody Dynamics and Application to Control Design

1990 ◽  
Author(s):  
Tsung-Chieh Lin ◽  
K. Harold Yae
Keyword(s):  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Control Design ◽  
Numerical Differentiation ◽  
Difficult Problem ◽  
Computational Method ◽  
Computational Error ◽  
Dynamics Modeling ◽  
Analytical Approximations

Abstract The non-linear equations of motion in multi-body dynamics pose a difficult problem in linear control design. It is therefore desirable to have linearization capability in conjunction with a general-purpose multibody dynamics modeling technique. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient. It has also turned out to be more accurate because the analytical perturbation requires matrix and vector operations by circumventing numerical differentiation and other associated numerical operations that may accumulate computational error.

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

2010 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Flexible Multibody System ◽  
Generalized Coordinates ◽  
Flexible Multibody ◽  
The Matrix

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

Simplified Procedure to Estimate the Wind Turbine Blade Aerodynamic Loadings Without Using CFD

2013 ◽  
Author(s):  
Fouad Mohammad ◽  
Emmanuel Ayorinde
Keyword(s):  
Wind Turbine ◽  
Turbine Blade ◽  
Equations Of Motion ◽  
Wind Turbine Blade ◽  
Aerodynamic Load ◽  
Horizontal Axis Wind Turbine ◽  
Cross Sectional ◽  
Flow Angle ◽  
Blade Length ◽  
The Right

The aerodynamic loadings that act on the blade of a horizontal axis wind turbine change as a function of time due to the instantaneous change of the wind speed, the wind direction and the blade position. The new contribution in this study is the introduction of a simplified non CFD based procedure for the calculation of all the aerodynamic loadings acting on a wind turbine blade. The premise of the current simplified model is that (a) the forces can be modeled by a set of point loads rather than distributed pressures, and (b) the magnitudes of these point loads can be estimated using the below load formulas, (c) an interpolation scheme needed to have all computed forces and moments as a function of the blade lengthwise x. Considering a 14m blade length and utilizing a time dependent set of parameters such as angle of attack, material and air density, wind and blade speed, flow angle, yaw, pitch angles, the centrifugal forces (along x-direction of the blade length), the cross-sectional forces (Fy and Fz) and the twisting moment of the blade (about the x-direction) were calculated for each of all the given time steps. After that the authors explain how to interpolate the calculated loadings (forces and twisting moment) and the right formulas to compute the aerodynamic load vector (the right side of the dynamic equations of motion).

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

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