Showing papers on "Inertia published in 1978"

Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. I. Equations of Motion

Abstract: This paper is divided into two parts. The authors’ purpose in Part I is to formulate a set of mathematically consistent governing differential equations of motion describing the nonplanar, nonlinear dynamics of an inextensional beam. The beam is assumed to undergo flexure about two principal axes and torsion. The equations are developed with the objective of retaining contributions due to nonlinear curvature as well as nonlinear inertia. A priori ordering assumptions are avoided as much as possible in the process. The equations are expanded to contain nonlinearities up to order three to facilitate comparison with analogous equations in the literature, and to render them amenable to the study of moderately large amplitude flexural-torsional oscillations by perturbation techniques. The utilization of the order-three equations in the analysis of nonlinear beam oscillations is the subject of Part II.

Fluid forces on oscillating cylinders

Abstract: The paper presents the results of an experimental and analytical investigation of the forced oscillations of a circular cylinder in uniform flow. The transverse force has been decomposed into two components and the appropriate force-transfer coefficients have been determined experimentally through the use of a Fourier averaging techinique. The results were then incorporated into the equation of motion to predict the dynamic responsee of elastically-mounted cylinders. The numerical predictions were found to be in good agreement with those obtained experimentally.

Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. II. Forced Motions

Abstract: The nonplanar, nonlinear, resonant forced oscillations of a fixed-free beam are analyzed by a perturbation technique with the objective of determining quantitative and qualitative information about the response. The analysis is based on the differential equations of motion developed in Part I of this paper which retain not only the nonlinear inertia but also nonlinear curvature effects. It is shown that the latter play a significant role in the nonlinear flexural response of the beam.

Simulator control loading inertia compensator

Abstract: Signals are developed representative of the mechanical inertia of a vehicle simulator linkage elements that drive control members utilized by a student operator. These signals are combined with signals representative of programmed vehicle operating data and signals representative of the student operator's mechanical input such that the mechanical inertia of the simulator linkage elements does not influence the signal which causes the actual operator control member to have an appropriate force/"feel".

Engineering Mechanics: Statics

Abstract: 1. General Principles. Mechanics. Fundamental Concepts. Units of Measurement. The International System of Units. Numerical Calculations. 2. Force Vectors. Scalars and Vectors. Vector Operations. Vector Addition of Forces. Addition of a System of Coplanar Forces. Cartesian Vectors. Addition and Subtraction of Cartesian Vectors. Position Vectors. Force Vector Directed Along a Line. Dot Product. 3. Equilibrium of a Particle. Condition for the Equilibrium of a Particle. The Free-Body Diagram. Coplanar Force Systems. Three-Dimensional Force Systems. 4. Force System Resultants. Moment of a Force--Scalar Formation. Cross Product. Moment of a Force--Vector Formulation. Principle of Moments. Moment of a Force About a Specified Axis. Moment of a Couple. Equivalent System. Resultants of a Force and Couple System. Further Reduction of a Force and Couple System. Reduction of a Simple Distributed Loading. 5. Equilibrium of a Rigid Body. Conditions for Rigid-Body Equilibrium. Equilibrium in Two Dimensions. Free-Body Diagrams. Equations of Equilibrium. Two- and Three-Force Members. Equilibrium in Three Dimensions. Free-Body Diagrams. Equations of Equilibrium. Constraints for a Rigid Body. 6. Structural Analysis. Simple Trusses. The Method of Joints. Zero-Force Members. The Method of Sections. Space Trusses. Frames and Machines. 7. Internal Forces. Internal Forces Developed in Structural Members. Shear and Moment Equations and Diagrams. Relations Between Distributed Load, Shear, and Moment. Cables. 8. Friction. Characteristics of Dry Friction. Problems Involving Dry Friction. Wedges. Frictional Forces on Screws. Frictional Forces on Flat Belts. Frictional Forces on Collar Bearings, Pivot Bearings, and Disks. Frictional Forces on Journal Bearings. Rolling Resistance. 9. Center of Gravity and Centroid. Center of Gravity and Center of Mass for a System of Particles. Center of Gravity, Center of Mass, and Centroid for a Body. Composite Bodies. Theorems of Pappus and Guldinus. Resultant of a General Distributed Force System. Fluid Pressure. 10. Moments of Inertia. Definitions of Moments of Inertia for Areas. Parallel-Axis Theorem for an Area. Radius of Gyration of an Area. Moments of Inertia for an Area by Integration. Moments of Inertia for Composite Areas. Product of Inertia for an Area. Moments of Inertia for an Area About Inclined Axes. Mohr's Circle for Moments of Inertia. Mass Moment of Inertia. 11. Virtual Work. Definition of Work and Virtual Work. Principle of Virtual Work for a Particle and a Rigid Body. Principle of Virtual Work for a System of Connected Rigid Bodies. Conservative Forces. Potential Energy. Potential Energy Criterion for Equilibrium. Stability of Equilibrium. Appendixes. A. Mathematical Expressions. B. Numerical and Computer Analysis. Answers. Index.

Engineering Mechanics: Statics and Dynamics

Abstract: 1. Introduction. Engineering and Mechanics. Learning Mechanics. Fundamental Concepts. Units. Newtonian Gravitation. 2. Vectors. Vector Operations and Definitions. Scalars and Vectors. Rules for Manipulating Vectors. Cartesian Components. Components in Two Dimensions. Components in Three Dimensions. Products of Vectors. Dot Products. Cross Products. Mixed Triple Products. 3. Forces. Types of Forces. Equilibrium and Free-Body Diagrams. Two-Dimensional Force Systems. Three-Dimensional Force Systems. 4. Systems of Forces and Moments. Two-Dimensional Description of the Moment. The Moment Vector. Moment of a Force About a Line. Couples. Equivalent Systems. Representing Systems by Equivalent Systems. 5. Objects in Equilibrium. The Equilibrium Equations. Two-Dimensional Applications. Statically Indeterminate Objects. Three-Dimensional Applications. Two-Force and Three-Force. 6. Structures in Equilibrium. Trusses. The Method of Joints. The Method of Sections. Space Trusses. Frames and Machines. 7. Centroids and Centers of Mass 316. Centroids. Centroids of Areas. Centroids of Composite Areas. Distributed Loads. Centroids of Volumes and Lines. The Pappus-Guldinus Theorems. Centers of Mass. Definition of the Center of Mass. Centers of Mass of Objects. Centers of Mass of Composite Objects. 8. Moments of Inertia. Areas. Definitions. Parallel-Axis Theorems. Rotated and Principal Axes. Masses. Simple Objects. Parallel-Axis Theorem. 9. Friction. Theory of Dry Friction. Applications. 10. Internal Forces and Moments. Beams. Axial Force, Shear Force, and Bending Moment. Shear Force and Bending Moment Diagrams. Relations Between Distributed Load, Shear Force, and Bending Moment. Cables. Loads Distributed Uniformly Along Straight Lines. Loads Distributed Uniformly Along Cables. Discrete Loads. Liquids and Gasses. Pressure and the Center of Pressure. Pressure in a Stationary Liquid. 11. Virtual Work and Potential Energy. Virtual Work. Potential Energy. Appendix A. Review of Mathematics. Algebra. Trigonometry. Derivatives. Integrals. Taylor Series. Vector Analysis. Appendix B. Properties of Areas and Lines. Areas. Lines. Properties of Volumes and Homogeneous Objects. Answers to Even-Numbered Problems. 12. Engineering and Mechanics. Engineering and Mechanics. Learning Mechanics. Fundamental Concepts. Units. Newtonian Gravitation. 13. Motion of a Point. Position, Velocity, and Acceleration. Straight-Line Motion. Curvilinear Motion. 14. Force, Mass, and Acceleration. Newton's Second Law. Equation of Motion for the Center of Mass. Inertial Reference Frames. Applications. Orbital Mechanics. Numerical Solutions. 15. Energy Methods. Work and Kinetic Energy. Principle of Work and Energy. Work and Power. Work Done by Particular Forces. Potential Energy. Conservation of Energy. Conservative Forces. Relationship between Force and Potential Energy. 16. Momentum Methods. Principle of Impulse and Momentum. Conservation of Linear Momentum. Impacts. Angular Momentum. Mass Flows. 17. Planar Kinematics of Rigid Bodies. Rigid Bodies and Types of Motion. Rotation about a Fixed Axis. General Motions: Velocities. General Motions: Accelerations. Sliding Contacts. Moving Reference Frames. 18. Planar Dynamics of Rigid Bodies. Preview of the Equations of Motion. Momentum Principles for a System of Particles. Derivation of the Equations of Motion. Applications. Numerical Solutions. Appendix: Moments of Inertia. 19. Energy and Momentum in Rigid-Body Dynamics. Principle of Work and Energy. Kinetic Energy. Work and Potential Energy. Power. Principles of Impulse and Momentum. Impacts. 20. Three-Dimensional Kinematics and Dynamics of Rigid Bodies. Kinematics. Euler's Equations. The Euler Angles. Appendix: Moments and Products of Inertia. 21. Vibrations 506 Conservative Systems. Damped Vibrations. Forced Vibrations. Appendix A. Review of Mathematics. Appendix B. Properties of Areas and Lines. Appendix C. Properties of Volumes and Homogeneous Objects. Appendix D. Spherical Coordinates. Appendix E. D'Alembert's Principle. Index.

Dynamic Tooth Loads and Stressing for High Contact Ratio Spur Gears

Abstract: A time history, closed form solution is presented for a dynamic model of spur gear systems for all practical contact ratios. The analysis determines the dynamic response of the gear system and the associated tooth loads and stressing. The dynamic model assumes the two gears act as a rigid inertia and the teeth act as a variable spring of a dynamic system excited by the meshing action of the teeth. Included in the analysis are the effects of the nonlinearity of the tooth pair stiffness during mesh, the tooth errors, and the tooth profile modifications. Besides reviewing the features, solution, and program of this analysis, preliminary results from applying the analysis are presented, which show that tooth profile modification, system inertia and damping, and system critical speeds can affect the dynamic gear tooth loads and stressing significantly.

Free Lateral Vibrations of Suspension Bridges

Abstract: A method is developed based on a linearized theory and the finite-element method. The method involves two distinct steps: (1)Specification of the potential and kinetic energies of the bridge, (2)use of finite element technique to: (a)discretize the structure into equivalent systems of finite elements; (b)select the displacement model most closely approximating the real case; (c)derive the element and assemblage stiffness and inertia properties; and finally (d)form the matrix equations of motion and the resulting eigenproblems. A numerical example is presented to illustrate the applicability of the analysis and to investigate the dynamic characteristics of laterally vibrating suspension bridges. This method eliminates the need to solve transcendental frequency equations, simplifies the determination of the energy stored in different members of the bridge, and represents a simple, fast, and accurate tool for calculating the natural frequencies and modes of lateral vibration by means of a digital computer.

The Parametric Response of a Horizontal Beam Carrying a Concentrated Mass Under Gravity

Abstract: This investigation treats the steady-state response of parametric vibration of a simply supported horizontal beam, carrying a concentrated mass under the influence of gravity. Nonlinear terms arising from moderately large curvatures, longitudinal inertia of the beam and concentrated mass, and rotatory inertia of the concentrated mass are included in the equation of motion. By using the one mode approximation and applying Galerkin’s method, the governing equation of motion is reduced to a nonlinear ordinary differential equation with periodic coefficient. The harmonic balance method is applied to solve the equation and the dynamic response is derived. The effects of the weight, the rotatory inertia, the location, and the vibratory amplitude of the concentrated mass on the natural frequency are also discussed.

Horizontal inertia-responsive shock absorber

Abstract: The shock absorber is designed to be horizontally mounted on a vehicle and incorporates a weight responsive to acceleration and deceleration forces developed by the vehicle itself. The arrangement is such that the weight will decrease the damping hydraulic fluid resistance under accelerating conditions and increase the hydraulic damping fluid resistance under decelerating conditions.

Force responsive device

Abstract: A device is disclosed which, in response to forces acting upon it, such as gravity, inertia, magnetic fields and the like, opens or closes electric circuits or otherwise generates signals which may be used to control predetermined functions.

Out-of-plane vibrations of a beam including non-linear inertia and non-linear curvature effects

Abstract: The harmonic, non-linear response and its stability, for a clamped-clamped/sliding beam subject to a planar excitation is investigated by a perturbation method taking into account the non-linear inertia and the non-linear curvature terms in the differential equations of motion. The influence of excitation and beam parameters in the planar and in the non-planar response of the beam is determined in detail and illustrated by several ‘response charts’.

Apparatus for roll-stabilizing a vehicle

Abstract: Apparatus for roll-stabilizing a vehicle broadly includes a compound physical pendulum operatively arranged to sense the lateral and angular acceleration of the vehicle attributable to an applied disturbance torque, and an inertia wheel arranged to be accelerated in the appropriate angular direction to exert a reaction torque on the vehicle to oppose the disturbance torque. The compound physical pendulum has a rigid dumbbell-shaped member mounted for frictionless pivotal movement between opposing discharge nozzles of a hydraulic amplifier. The hydraulic amplifier produces a differential control pressure in response to the acceleration forces acting on the pendulum, and this control pressure is used to operate a servovalve. The servovalve produces a drive pressure which is supplied to a hydraulic motor to accelerate the inertia wheel in the appropriate angular direction. The apparatus may further include static balance means for shifting a weight or fluid mass transversely of the vehicle to correct a static imbalance condition.

Virtual Mass of Coarse Granular Media

Abstract: An experimental study to determine the effect of unsteady flow on the hydraulic conductivity of coarse granular porous media is outlined. The acceleration effect was expressed in terms of two variables, i.e., acceleration coefficient, which is function of the well-known inertia coefficient, and the instantaneous flow acceleration. The inertia coefficient was found by comparing the resistance of both steady and unsteady flows through the same porous matrix. The results are given in two forms to show the effect of the unsteady flow on the hydraulic resistance, and to show the variation of the inertia coefficient with Reynolds number. The experimental results show that virtual mass effect does exist in coarse granular porous media, which is the usual construction material for rubble-mound breakwaters. Also, it was found that the acceleration effect becomes more important for large grain porous media, e.g., for particle sizes equal or larger than 40 mm.

Inertia drive head for optical scanning and readout

Abstract: The drawings illustrate the principles involved in an inertial shuttle device originally constructed to operate as an optical character recognition device and adapted to rapid photocomposition. The shuttle is a scanning device which is inherently a very uniform and smooth scanning velocity device and utilizes only a minute amount of driving power. This combination is achieved by means of energy conserving springs which reverse the head very rapidly at the end of each stroke with windage and friction losses made up by a lightweight, low inertia drive motor which itself is variable in power input by alteration of current intensity supplied to the motor.

Rubber viscous torsional dampers and method of making same

Abstract: Rubber viscous torsional dampers in which an annular inertia mass is coupled by elastic tuning spring, spacing and sealing rings to a radially outwardly extending circular body on a radially inner hub portion, have the elastic rings secured fixedly to axial surfaces of either or both the body and; the inertia mass by means of respective flat disks which are rigidly unyielding in plan and are permanently secured by vulcanized bonding to the rings, the disks being rigidly secured to the inertia mass and/or the body by structural adhesive.

Flexible disk--Read/write head interface

Abstract: The response of a rotating flexible magnetic disk interacting with a stationary read/write head is analyzed using a theory that accounts for the effects of bending forces, membrane forces of rotation, and inertia forces. The solution thus obtained is coupled with the solution to the Reynolds equation to determine the pressure profile and film thickness (flying height) between the head and disk.

A Procedure for Force-Balancing Planar Linkages Using Counterweights

Abstract: This paper presents a procedure for obtaining the conditions for a full force-balance of a planar linkage. It includes a check on whether a full force-balance is possible where the presence of prismatic joints or links that cannot be counter-weighted for some reason may preclude this. The procedure automatically uses the minimum number of counterweights and keeps the added inertia low. An example demonstrates the advantages of the procedure over those methods that require the derivation of the kinematic equations of motion for the linkage.

A Research on Inertia Charging Effect of Intake System in Multi-Cylinder Engines

Abstract: The paper describes a theoretical treatment that has been carried out to stud the dynamic behaviour of gas-flow in the intake manifold of a multi-cylinder internal combustion engine, whose performance is improved by inertia charging effect. The analysis is based on the characteristic method which is applicable to a one-dimensional flow. The configuration of intake manifold is made so complicated in order to utilize the inertia charging effect that the existence of a real one- dimensional flow can not be expected in the manifold. However, the results of calculation for the volumetric efficiency and pressure variations agree pretty well with the experimental ones. It seems that the characteristic method can be used to design the optimum intake manifold of a multi-cylinder engines. Furthermore, some items concerning the dimensions of engine and manifold are described in order to utilize the inertia charging effect positively.

Aeromechanical stability of helicopters with a bearingless main rotor. Part 1: Equations of motion

Abstract: Equations of motion for a coupled rotor-body system were derived for the purpose of studying air and ground resonance characteristics of helicopters that have bearingless main rotors. For the fuselage, only four rigid body degrees of freedom are considered; longitudinal and lateral translations, pitch, and roll. The rotor is assumed to consist of three or more rigid blades. Each blade is joined to the hub by means of a flexible beam segment (flexbeam or strap). Pitch change is accomplished by twisting the flexbeam with the pitch-control system, the characteristics of which are variable. Thus, the analysis is capable of implicitly treating aeroelastic couplings generated by the flexbeam elastic deflections, the pitch-control system, and the angular offsets of the blade and flexbeam. The linearized equations are written in the nonrotating system retaining only the cyclic rotor modes; thus, they comprise a system of homogeneous ordinary differential equations with constant coefficients. All contributions to the linearized perturbation equations from inertia, gravity, quasi-steady aerodynamics, and the flexbeam equilibrium deflections are retained exactly.