Dynamics of Flexible Manipulator Arms: Alternative Derivation, Verification, and Characteristics for Control

1993 ◽  
Vol 115 (3) ◽  
pp. 394-404 ◽  
Author(s):  
B.-S. Yuan ◽  
W. J. Book ◽  
J. D. Huggins
Keyword(s):  
Mass Matrix ◽  
Equations Of Motion ◽  
Structural Complexity ◽  
Hydraulic Cylinder ◽  
Geometric Constraints ◽  
Flexible Manipulator ◽  
Mode Shapes ◽  
Actuator Dynamics ◽  
Transformation Matrices ◽  
Uniform Cross Section

This work seeks to provide an effective way for developing the dynamics of a multi-link flexible manipulator consisting of rotary joints connecting two links. Kinematics of both the rotary joint motion and the link deformation are described by 4×4 transformation matrices as proposed in previous works (Book, 1984). The link deflection is assumed small so that the link transformation can be composed of summations of assumed link shapes. To determine the appropriate choice of component mode shapes, two essential techniques employed here are experimental and finite element methods. The resulting equations of motion allow the complete nonlinear model to be recursively derived from the Jacobian matrix and the mass properties via symbolic manipulation. Two prototype models of flexible manipulators are used to verify the dynamics with frequency and time responses. This paper contributes several new results: (1) the velocity terms (Coriolis and centrifugal forces) are related to variations in the mass matrix, (2) the skew symmetry of certain useful terms are shown, (3) the system is theoretically demonstrated to be stable with joint P.D. controllers in addition to an experimental approach, (4) practical and effective incorporation of actuator dynamics (hydraulic cylinder) and structural complexity (non-uniform cross section) is achieved through selection of mode shapes, (5) geometric constraints are incorporated through simplified coordinate transformations and (6) the results are verified on two physical cases.

Critical Speed Analysis of Multi-Cylider Engines As Spatial Elastic Linkage Systems

1996 ◽  
Author(s):  
Sirihari Kurnool ◽  
Cemil Bagei
Keyword(s):  
Critical Speed ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Lumped Mass ◽  
Constant Frequency ◽  
Elastic Mechanism ◽  
Finite Line ◽  
Crankshaft Rotation

Abstract A multi-cylinder engine is a cluster of slider-crank linkages. Presently used conventional pure torsional shaft models predict results far from the results predicted considering actual three-dimensional linkage and crankshaft geometries. Pure torsional model doesn’t sense the variation in frequency with the variation in engine geometry. It predicts one constant frequency value for each mode; it does not permit the use of flexible bearings. Article offers a finite element method for performing frequency and critical speed analysis of multi-cylinder engines considering three-dimensional geometries of the linkage loops, crankshaft, and the crankshaft throws, as a spatial elastic mechanism system. Any number of cylinders in any angular orientations with respect to each other may be considered. A three-dimensional flexural finite-line element with isoparametric joint freedom irregularity is developed and used to formulate the eigenvalue equations of motion for the system. Consistent mass matrix as well as lumped mass matrix methods can be used. The element can be restrained to perform coupled torsional and flexural or pure torsional frequency analysis of geared rotor model of engines and shafts on many rigid or flexible bearings. Geared connections can also be considered flexible. A generalized computer program is made available for industrial use. It determines frequencies, mode shapes and critical speed bands of an engine for complete crankshaft rotation for as many modes as desired. The frequency and critical speed analysis of a four-cylinder MGB automobile engine with in-plane crank throws, with and without bearing flexibilities, is performed and the results are compared with those obtained using the conventional pure torsional shaft model. Geared tandem ship drive system is studied to test the reliability of the developments.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

Experimental and Numerical Modal Analysis of Composite Laminated Shells

2019 ◽  
Vol 161 (A1) ◽  
Keyword(s):  
Heat Dissipation ◽  
Mass Matrix ◽  
Experimental Studies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Lumped Mass ◽  
Auxiliary Equipment ◽  
Mass Model ◽  
Laminated Shells

The presence of cut outs at different positions of laminated shell component in marine and aeronautical structures facilitate heat dissipation, undertaking maintenance, fitting auxiliary equipment, access ports for mechanical and electrical systems, damage inspection and also influences the dynamic behaviour of the structures. The aim of the present study is to establish a comprehensive perspective of dynamic behavior of laminated deep shells (length to radius of curvature ratio less than one) with cut-out by experiments and numerical simulation. The glass epoxy laminated composite shell has been prepared in the laboratory by resin infusion. The experimental free vibration analysis is carried out on laminated shells with and without cut-out. The mass matrix is developed by considering rotary inertia in a lumped mass model in the numerical modeling. The results obtained from numerical and experimental studies are compared for verification and the consistency between mode shapes is established by applying modal assurance criteria.

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.

Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory

2018 ◽  
Author(s):  
Igor Orynyak ◽  
Yaroslav Dubyk
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Middle Surface ◽  
Axial Direction ◽  
Mode Shapes ◽  
Natural Mode ◽  
Transverse Deflection ◽  
Approximate Formulas

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

On the Properties of a Dynamic Model of Flexible Robot Manipulators

1998 ◽  
Vol 120 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Marco A. Arteaga
Keyword(s):  
Dynamic Model ◽  
Structural Properties ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Control Design ◽  
Flexible Manipulator ◽  
Robot Dynamics ◽  
Flexible Link ◽  
Flexible Robot

Control design of flexible robot manipulators can take advantage of the structural properties of the model used to describe the robot dynamics. Many of these properties are physical characteristics of mechanical systems whereas others arise from the method employed to model the flexible manipulator. In this paper, the modeling of flexible-link robot manipulators on the basis of the Lagrange’s equations of motion combined with the assumed modes method is briefly discussed. Several notable properties of the dynamic model are presented and their impact on control design is underlined.

Free Vibration Analysis of a Carbon Nanotube Reinforced Composite Beam

2014 ◽  
Vol 592-594 ◽  
pp. 2041-2045 ◽  
Author(s):  
B. Naresh ◽  
A. Ananda Babu ◽  
P. Edwin Sudhagar ◽  
A. Anisa Thaslim ◽  
R. Vasudevan
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Composite Beam ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Element Formulation ◽  
Reinforced Composite ◽  
Vibration Responses

In this study, free vibration responses of a carbon nanotube reinforced composite beam are investigated. The governing differential equations of motion of a carbon nanotube (CNT) reinforced composite beam are presented in finite element formulation. The validity of the developed formulation is demonstrated by comparing the natural frequencies evaluated using present FEM with those of available literature. Various parametric studies are also performed to investigate the effect of aspect ratio and percentage of CNT content and boundary conditions on natural frequencies and mode shapes of a carbon nanotube reinforced composite beam. It is shown that the addition of carbon nanotube in fiber reinforced composite beam increases the stiffness of the structure and consequently increases the natural frequencies and alter the mode shapes.

Hydroelastic Vibration of Rectangular Plates

1996 ◽  
Vol 63 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Moon K. Kwak
Keyword(s):  
Boundary Conditions ◽  
Approximate Formula ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Ritz Method ◽  
Plate Boundary ◽  
Rigid Wall ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Virtual Mass

This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

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

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