Showing papers on "Rotary inertia published in 1988"

Transient response of graphite/epoxy and Kevlar/epoxy laminates subjected to impact

Abstract: The influence of different parameters on the impact behavior of laminated composite plates is considered analytically. A Rayleigh-Ritz energy method was used to spatially discretize the time-varying boundary value problem and a set of coupled, ordinary differential equations in time were obtained based on the discretized system Lagrangian. The effects of shearing deformation, bending-twisting coupling, and nonlinear contact behavior were included in the model. The resulting equations were integrated using the implicit Newmark beta method without the effects of rotary inertia. The results indicate that the effective mass of the plate is often an important effect in the response to impact events. In general, the influence of the constitutive behavior dominates for very low velocity impact, whereas the target mass properties become more important as the impactor velocity increases. This importance of mass clearly shows that impactor kinetic energy is not sufficient to characterize the impactor as the impactor mass is shown to have a large influence on the resulting dynamic behavior. In addition to these parameters, the effects of preload and material properties are considered and discussed.

Low Frequency Flexural Wave Propagation in Laminated Composite Plates

Abstract: Shear deformation and rotary inertia are included in plate theory to determine the dispersion curves for flexural waves propagating in laminated composite plates. The results of a unidirectional laminate are compared with the elasticity solutions for flexural waves traveling in transversely isotropic plates to determine the shear correction factors in the low frequency, long wavelength range. The values of the shear correction factors for the unidirectional composite laminate are in good agreement with the theoretical values calculated from static cylindrical bending. An acousto-ultrasonic technique using narrowband excitation frequencies is used to obtain experimental data for flexural waves. By measuring the phase velocities for different excitation frequencies, dispersion curves are generated. There is excellent agreement between the experimentally determined values and the theoretical results for aluminum and unidirectional composite plates. For symmetric cross-ply and quasi-isotropic laminates, the data definitely have the characteristic of a dispersion curve for flexural waves, although the agreement between analytic and experimental results is not quite as good. The results of the present work indicate that the inclusion of shear deformation and rotary inertia in plate theory improves the prediction of dispersion curves for flexural waves propagating in composite laminates and suggest that the acousto-ultrasonic technique can be used to characterize composite plates with and without damage since each material and stacking sequence gives distinct dispersion curves.

Resolving membrane and shear locking phenomena in curved shear‐deformable axisymmetric shell elements

Abstract: A simple two-node axisymmetric shell element with shallowly curved meridian assumptions and the inclusion of shear deformation and rotary inertia is presented. The principal developments include: (a) consistent resolution of the membrane and shear related excessive stiffening (locking) via anisoparametric interpolations of the displacement variables; (b) further upgrading of strain energy by means of a shear relaxation (correction) parameter. The resulting element possesses an improved condition of the stiffness matrix, increased efficiency in explicit time integration and enhanced accuracy in coarse discretizations. Comprehensive vibration examples are carried out to assess the element performance. The numerical results demonstrate a wide applicability range with respect to element slenderness and curvature properties.

Determination of the Moments of Inertia of the Human Body and Its Limbs

Abstract: Experimental Determination of the Moments of Inertia of the Parts of the Body About Axes Through the Centre of Gravity and at Right Angles to the Longitudinal Axis, and About the Longitudinal Axis Itself.- Deduction of the Moments of Inertia About Any Axis Through the Centre of Gravity.- Deduction of the Moments of Inertia About Any Axis in Space.- Example of Application of the Moments of Inertia Thus Found: Determination of the Period of Oscillation of the Leg at Different Degrees of Flexion.- Summary.

Center of gravity and moments of inertia measurement device

Abstract: A device for calculating the center of gravity (CG) and moments of inertia of a vehicle. The vehicle is driven onto the device and the height of its center of gravity is determined by hanging weights on the device to displace the vehicle's CG from its position without the weights; the height of the CG is then calculated by a simple mathematical formula. The pitch moment of inertia is calculated by aligning its axis perpendicular to the axis of the pivots and allowing the vehicle to swing, then calculating the moment of inertia by another mathematical formula. The roll moment of inertia is calculated by rotating the vehicle 90 degrees, letting it swing, and then using a slighly different formula. The yaw moment of inertia is calculated by lowering the device to the ground and causing the vehicle to oscillate about a pivot point, then calculating the yaw moment of inertia by means of another mathematical formula.

Random vibration of laminated plates modeled within a high‐order shear deformation theory

Abstract: This article deals with the dynamic response of simply supported, symmetric cross‐ply laminates to stationary random load. The theory of laminated plates used here takes into account transverse shear flexibility, transverse normal stress, and rotary inertia effects for orthotropic and transversely isotropic laminates. Two cases of random pressure fields are considered in this analysis. In the first case, the random pressure field is modeled as a point load, random in time, with constant spectral density (ideal white noise), while in the second case, it is modeled as a turbulent boundary layer pressure fluctuation. The analysis presented herein, as well as the obtained response characteristics expressed in terms of mean squares, may be useful in the reliability computation of composite structures subjected to random pressure fields.

General dynamic shape functions and stiffness matrix of timoshenko beam and their application to structure-borne noise on ships

Abstract: The general dynamic shape functions and stiffness matrix of a Timoshenko beam are derived and used to establish the stiffness equations for an entire structural system. All the effects of rotary inertia of the mass, shear distortion, mass and structural dampings, axial force, elastic-spring and dashpot foundation are included in this formulation. These stiffness equations can then be easily modified to account for the influences from the concentrated dynamic properties. Both the low-and high-frequency dynamic responses are discussed generally, with special emphasis on the latter case. The problem of structure-borne noise on ships is also studied as an example for application.

Axisymmetric Free Vibration of Orthotropic Complete Spherical Shells

Abstract: This paper presents studies of the axisymmetric free vibration of moderately thick orthotropic complete spherical shells. The mathematical model is formulated in terms of the mid-surface meridian and radial displacements, and cross-section rotation of the meridians by the improved linear elastic shell theory with the effects of transverse shear strain and rotary inertia included. By the use of the Legendre polynomials, the exact solu tion from a set of three governing partial differential equations for the transversely iso tropic case and the series solution from the Ritz method for the polar orthotropic case are obtained. Natural frequencies and modes are found from the eigenproblems by using orthogonality and some special integrals with reasonable results.

Momentum compensated actuator with redundant drive motors

Abstract: This invention is a rotary actuator in which the angular momentum of a ratationally pointed structure is offset by the angular momentum of a compensating inertia. The compensating inertia structure is rotational driven relative to the pointed structure across a differential gear which assures the ratio of the rotational rate of the compensating inertia to the rotational rate of the pointed structure is a negative constant. The differential gear consist of a stationary gear fixed to the base vehicle, a platform gear axially coincident with the stationary gear but free to rotate relative to the stationary gear being fixed to the pointed structure. Planetary gears mesh with the stationary and planetary gears and are driven relative to the compensating inertia structure by planetary drive motors. The planetary drive motors are part of the rotating compensating insertia structure and are symmetrically positioned around the stationary gear axis driving the planetary gears around the periphery of the stationary gear and around the periphery of the platform gear. Because the diameter of the stationary gear is larger than the diameter of the platform gear assures the ratio of the rotational rate of the compensating inertia structure of the rotational rate of the pointed structure relative to the stationary gear axis is a negative constant. The magnitude of the rotational rate difference between the compensating inertia and pointed structure can be designed as large as desired by making the platform gear diameter approach the stationary gear diameter. Mechanical backlash is eliminated at rotational rate polarity changes by assigning one planetary drive motor polarity to one motor and the opposite polarity to a different planetary drive motor. Motor redundancy is achieved by having at least one planetary drive motor available in the event of a motor failure. Since the redundant planetary drive motors are part of the compensating inertia, they reduce the mass of inactive inertia structure required to achieve the desired compensating inertia magnitude.

Axisymmetric free vibration of orthotropic complete spherical shells

Abstract: This paper presents studies of the axisymmetric free vibration of moderately thick orthotropic complete spherical shells. The mathematical model is formulated in terms of the mid-surface meridian and radial displacements, and cross-section rotation of the meridians by the improved linear elastic shell theory with the effects of transverse shear strain and rotary inertia included. By the use of the Legendre polynomials, the exact solu tion from a set of three governing partial differential equations for the transversely iso tropic case and the series solution from the Ritz method for the polar orthotropic case are obtained. Natural frequencies and modes are found from the eigenproblems by using orthogonality and some special integrals with reasonable results.

Distributed Parameter Models of Flexible Robot Arms

Abstract: The modelling of a flexible robot arm is concerned with its rigid body motion as well as its oscillation due to the elasticity of the arm [1-4]. As the elastic deformation is distributed along the arm, it is obvious that this system is a distributed parameter system. Although a set of partial differential equations is presumed to be the best model for this system, it is limited to a relatively low frequency oscillation of a homogeneous, simply shaped arm. In the case of a more complicated flexible arm, the partial differential equation model is not necessarily advantageous, and another method such as the finite element method will be used. First, this paper presents the detailed development of the partial differential equations and boundary conditions for two models of a flexible robot arm. One is a rigorous model obtained through the use of Timoshenko beam theory, which takes into account the effect of transverse shear deformation and rotary inertia; the other is a simpler and more frequently used model ...

Device for balancing inertia forces and alternating torques

Abstract: A description is given of a device for balancing free inertia forces and of free alternating torques generated by gas and inertia forces about the longitudinal axis of reciprocating-piston crankshaft engines (1). The device has a pair of balance weights (9, 10) which are each held on balancing shafts (7, 8) offset relative to one another in relation to the axial direction of the cylinder, driven at twice the speed of the crankshaft (2) and rotating in opposite directions to one another. In order to achieve not only balancing of the free second-order inertia forces but also balancing of the alternating torques caused both by gas forces and inertia forces in, as far as possible, all operating ranges of the reciprocating-piston crankshaft machine, the directions of rotation of the balancing shafts (7, 8) should preferably be reversible as a function of the speed of the crankshaft (2).

Minimum weight design of rotorcraft blades with multiple frequency and stress constraints

Abstract: A method is developed for the minimum weight design of helicopter rotor blades having multiple coupled flap-lag natural frequency constraints, in addition to a constraint on the minimum blade autorotation value that will ensure sufficient rotary inertia for autorotation in the event of engine failure. Design variables encompass blade taper ratio, box beam dimensions, and the magnitudes of the nonstructural weights. Optimum designs have been obtained for both rectangular and tapered blades; attention is given to the optimum blade weight effect and the blade mass and stiffness distribution effects of adding constraints on higher frequencies and stresses.