Nonlinear Deformation of a Shear-Deformable Laminated Composite-Material Flexible Robot Arm

1992 ◽  
Vol 114 (1) ◽  
pp. 96-102 ◽  
Author(s):  
F. Gordaninejad ◽  
N. G. Chalhoub ◽  
A. Ghazavi ◽  
Q. Lin
Keyword(s):  
Shear Deformation ◽  
Geometric Nonlinearity ◽  
General Procedure ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Element Model ◽  
Rotary Inertia ◽  
Robot Arm ◽  
Flexible Robot ◽  
Nonlinear Dynamic Model

In this work a general procedure to derive a nonlinear dynamic model for a three-link revolute flexible robot arm constructed from laminated fiber-reinforced composite materials is presented. The effects of geometric nonlinearity as well as rotary inertia and shear deformation are included to study the dynamic response of robotic manipulators made of moderately thick beams under large deformations. Hamilton’s principle is used to derive the equations of motion. A displacement finite element model based on the Timoshenko beam theory is implemented to approximate the solution. The digital simulation studies examine the combined effects of geometric nonlinearity, rotary inertia, and shear deformation on the arm’s end effector displacements. Furthermore, the effects of angle of fiber orientation and material orthotropy on the end-of-the-arm displacements and maximum normal bending stresses, are assessed.

Nonlinear Dynamic Modelling of a Revolute-Prismatic Flexible Composite-Material Robot Arm

1991 ◽  
Vol 113 (4) ◽  
pp. 461-468 ◽  
Author(s):  
F. Gordaninejad ◽  
A. Azhdari ◽  
N. G. Chalhoub
Keyword(s):  
Shear Deformation ◽  
Nonlinear Dynamic ◽  
Fibrous Composite ◽  
Equations Of Motion ◽  
Dynamic Modelling ◽  
Beam Theory ◽  
Rotary Inertia ◽  
Robot Arm ◽  
Nonlinear Dynamic Model ◽  
End Effector

In this work, a nonlinear dynamic model is derived to study the motion of a planar robot arm consisting of one revolute and one prismatic joint. Both links of the arm are considered to be flexible and are assumed to be constructed from either isotropic conventional metallic materials or anisotropic laminated fibrous composite materials. The model is derived based on the Timoshenko beam theory in order to account for the rotary inertia and shear deformation. In addition, a nonlinear strain-displacement field is implemented to consider the large deformation of the arm. The deflections of the links are discretized by using a shear-deformable beam finite element. The governing equations of motion are derived from Hamilton’s principle. The digital simulation studies examine the combined effects of geometric nonlinearity, rotary inertia, and shear deformation on the arm’s end effector displacements. Furthermore, effects of the fiber’s angle and material orthotropy on the end effector displacements and maximum normal bending stress are studied.

scholarly journals Natural Frequency Characteristics of the Beam with Different Cross Sections Considering the Shear Deformation Induced Rotary Inertia

2020 ◽  
Vol 10 (15) ◽  
pp. 5245
Author(s):  
Chunfeng Wan ◽  
Huachen Jiang ◽  
Liyu Xie ◽  
Caiqian Yang ◽  
Youliang Ding ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Cross Sections ◽  
Timoshenko Beam ◽  
High Frequency ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Timoshenko Beam Theory ◽  
Rotary Inertia ◽  
Cross Sectional

Based on the classical Timoshenko beam theory, the rotary inertia caused by shear deformation is further considered and then the equation of motion of the Timoshenko beam theory is modified. The dynamic characteristics of this new model, named the modified Timoshenko beam, have been discussed, and the distortion of natural frequencies of Timoshenko beam is improved, especially at high-frequency bands. The effects of different cross-sectional types on natural frequencies of the modified Timoshenko beam are studied, and corresponding simulations have been conducted. The results demonstrate that the modified Timoshenko beam can successfully be applied to all beams of three given cross sections, i.e., rectangular, rectangular hollow, and circular cross sections, subjected to different boundary conditions. The consequence verifies the validity and necessity of the modification.

Effect of Slenderness Ratio on the Natural Frequencies of Pre-Twisted Cantilever Beams of Uniform Rectangular Cross-Section

1971 ◽  
Vol 13 (1) ◽  
pp. 51-59 ◽  
Author(s):  
B. Dawson ◽  
N. G. Ghosh ◽  
W. Carnegie
Keyword(s):  
Differential Equations ◽  
Shear Deformation ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Slenderness Ratio ◽  
Twist Angle ◽  
Equations Of Motion ◽  
Rotary Inertia ◽  
Cantilever Beams

This paper is concerned with the vibrational characteristics of pre-twisted cantilever beams of uniform rectangular cross-section allowing for shear deformation and rotary inertia. A method of solution of the differential equations of motion allowing for shear deformation and rotary inertia is presented which is an extension of the method introduced by Dawson (1)§ for the solution of the differential equations of motion of pre-twisted beams neglecting shear and rotary inertia effects. The natural frequencies for the first five modes of vibration are obtained for beams of various breadth to depth ratios and lengths ranging from 3 to 20 in and pre-twist angle in the range 0–90°. The results are compared with those obtained by an alternative method (2), where available, and also to experimental results.

About the Use of the Floating Frame in the Optimal Control of the Flexible Robot Arm

1992 ◽  
Vol 4 (4) ◽  
pp. 330-338 ◽  
Author(s):  
M. Bisiacco ◽  
◽  
R. Caracciolo ◽  
M. Giovagnoni ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Linear Model ◽  
Equations Of Motion ◽  
Flexible Manipulator ◽  
Robot Arm ◽  
Flexible Robot ◽  
Coupled Equations ◽  
Weakly Coupled ◽  
Tip Position ◽  
The Mathematical Model

The mathematical model of a single-link flexible manipulator is obtained by measuring transverse deflections in a rotating reference frame which is floating with respect to the link. The use of this particular frame, the rigidbody mode frame, enables one to obtain weakly coupled equations of motion. The size of the inertia coupling terms can be easily evaluated: these terms can be shown to be negligible thus leading to an essentially linear model. An example of optimal control of manipulator's tip position is numerically reproduced. The same controller is first applied to the mechanical model of the arm accounting for non-linear coupling and then to the linear model: the two responses are found to be very close to each other.

scholarly journals Nonlinear Free and Forced Vibration Behavior of Shear-Deformable Composite Beams with Shape Memory Alloy Fibers

2016 ◽  
Vol 2016 ◽  
pp. 1-16
Author(s):  
Ren Yongsheng ◽  
Du Chenggang ◽  
Shi Yuyan
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Shear Deformation ◽  
Forced Vibration ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Composite Beams ◽  
Vibration Behavior ◽  
Shear Deformable

The nonlinear free and forced vibration of the composite beams embedded with shape memory alloy (SMA) fibers are investigated based on first-order shear deformation beam theory and the von Kármán type nonlinear strain-displacement equation. A thermomechanical constitutive equation of SMA proposed by Brinson is used to calculate the recovery stress of the constrained SMA fibers. The equations of motion are derived by using Hamilton’s principle. The approximate solution is obtained for vibration analysis of the composite beams based on the Galerkin approach. The parametric study is carried out to display the effect of the actuation temperature, the volume fraction, the initial strain of SMA fibers, and the length-to-thickness ratio. The shear deformation is shown to have a significant contribution to nonlinear vibration behavior of the composite beams with SMA fibers.

A NEW NONLOCAL BEAM THEORY WITH THICKNESS STRETCHING EFFECT FOR NANOBEAMS

2013 ◽  
Vol 12 (04) ◽  
pp. 1350025 ◽  
Author(s):  
ABDELOUAHED TOUNSI ◽  
SOUMIA BENGUEDIAB ◽  
MOHAMMED SID AHMED HOUARI ◽  
ABDELWAHED SEMMAH
Keyword(s):  
Shear Deformation ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Dynamic Responses ◽  
Theoretical Development ◽  
Small Scale ◽  
Small Scale Effect ◽  
Nonlocal Beam

This paper presents a new nonlocal thickness-stretching sinusoidal shear deformation beam theory for the static and vibration of nanobeams. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and it accounts for both shear deformation and thickness stretching effects by a sinusoidal variation of all displacements through the thickness without using shear correction factor. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanobeam are derived using Hamilton's principle. The effects of nonlocal parameter, aspect ratio and the thickness stretching on the static and dynamic responses of the nanobeam are discussed. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the bending and dynamic behaviors of complex-nanobeam-system such as complex carbon nanotube system.

Application of Timoshenko Beam Theory to the Dynamics of Flexible Legged Locomotion

1988 ◽  
Vol 110 (1) ◽  
pp. 28-34
Author(s):  
E. M. Bakr ◽  
A. A. Shabana
Keyword(s):  
Shear Deformation ◽  
Timoshenko Beam ◽  
Shape Function ◽  
Reference Conditions ◽  
Beam Theory ◽  
Legged Locomotion ◽  
Rotary Inertia ◽  
Stiffness Matrices ◽  
Reference Motion ◽  
Invariant Matrices

A method for the dynamic analysis of flexible legged locomotion systems that accounts for the rotary inertia and shear deformation effects is presented. The motion of the flexible components in the legged vehicle is described using a set of inertia-variant Timoshenko beams that undergo large rotations. A shape function that accounts for the combined effect of rotary inertia and shear is employed to describe the deformation relative to a selected component reference and the rigid-body modes of the shape function are eliminated using a set of reference conditions. Kinetic and strain energies are derived for each Timoshenko beam, thus identifying the beam mass and stiffness matrices which account for the rotary inertia and shear deformation effects. A new set of time-invariant matrices that describe the nonlinear inertia coupling between the reference motion and elastic deformation and account for the rotary inertia and shear is developed and it is shown that the form of these matrices as well as the mass and stiffness matrices are significantly affected by the inclusion of rotary inertia and shear. Numerical experimentations indicate that shear and rotary inertia can have a significant effect on the dynamics of flexible legged locomotion.

The Effects of Shear Deformation and Rotary Inertia on the Lateral Frequencies of Cantilever Beams in Bending

1972 ◽  
Vol 94 (1) ◽  
pp. 267-278 ◽  
Author(s):  
W. Carnegie ◽  
J. Thomas
Keyword(s):  
Finite Difference ◽  
Shear Deformation ◽  
Matrix Equation ◽  
Equations Of Motion ◽  
Flexural Vibration ◽  
Experimental Results ◽  
Rotary Inertia ◽  
Cantilever Beams ◽  
Algebraic Equations ◽  
Good Agreement

This paper deals with the effect of shear deformation and rotary inertia on the frequencies of flexural vibration of pre-twisted and non-pre-twisted uniform and tapered cantilever beams. The equations of motion are derived and transformed into a set of linear simultaneous algebraic equations by using finite-difference solutions for the derivatives. The resulting eigenvalue matrix equation is solved for the frequency parameters by a QR transformation. The effects of various tapers, depth-to-length ratios and pre-twist angles on the frequencies of vibration are investigated for the first five modes. Results obtained are compared with those presented by other investigators where available and show good agreement. The experimental results presented also show good agreement with the corresponding theoretical values.

Effects of Shear Deformation and Rotary Inertia on the Nonlinear Dynamics of Rotating Curved Beams

1990 ◽  
Vol 112 (2) ◽  
pp. 183-193 ◽  
Author(s):  
Wei-Hsin Gau ◽  
A. A. Shabana
Keyword(s):  
Shear Deformation ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Body Motion ◽  
Rotary Inertia ◽  
Element Formulation ◽  
Timoshenko Beams ◽  
Curved Beams ◽  
Finite Rotations ◽  
Deformable Bodies

In this investigation a method for the dynamic analysis of initially curved Timoshenko beams that undergo finite rotations is presented. The combined effect of rotary inertia, shear deformation, and initial curvature is examined. The kinetic energy is first developed for the curved beam and the beam mass matrix is identified. It is shown that the form of the mass matrix as well as the nonlinear inertia terms that represent the coupling between the rigid body motion and the elastic deformation can be expressed in terms of a set of invariants that depend on the assumed displacement field, rotary inertia, shear deformation, and the initial beam curvature. A nonlinear finite element formulation is then developed for Timoshenko beams that undergo finite rotations. The nonlinear formulation presented in this paper is applied to multibody dynamics where mechanical systems consist of an interconnected set of rigid and deformable bodies, each of which may undergo finite rotations. The equations of motion are developed using Lagrange’s equation and nonlinear algebraic constraint equations that mathematically describe mechanical joints and specified trajectories are adjoined to the system differential equations using the vector of Lagrange multipliers.

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