Showing papers on "Rotary inertia published in 1990"
TL;DR: In this paper, exact solutions for the free vibration of symmetrically laminated composite beams are presented for the first-order shear deformation and rotary inertia have been included in the analysis.
216 citations
TL;DR: In this paper, the wave transmission coefficients of structural joints are calculated for a generic plate/beam junction, which consists of an arbitrary number of plates which are either coupled through a beam or directly coupled along a line, and due allowance is made for offsets between the plate attachment lines and the shear axis of the beam.
151 citations
TL;DR: In this paper, the analysis is based on an expansion of the loads, displacements, and rotations in a double Fourier series which satisfies the end boundary conditions of simple support.
Abstract: The analysis is based on an expansion of the loads, displacements, and rotations in a double Fourier series which satisfies the end boundary conditions of simple support. By neglecting in-plane and rotary inertia the problem becomes a second-order ordinary differential equation in time for the Fourier coefficients of the radial deflection
106 citations
TL;DR: In this paper, the dynamic stability of laminated composite plates due to periodic inplane loads is investigated using the Galerkin finite element model, including the effects of transverse shear deformation and rotary inertia.
80 citations
TL;DR: In this article, an isoparametric finite element formulation based on a higher order displacement model for dynamic analysis of multilayer unsymmetric composite plates is presented, and the Newmark and Wilson-θ schemes are used for time integration of the discrete coupled second-order ordinary differential equation system of dynamic equilibrium.
60 citations
TL;DR: In this paper, the authors present design equations and techniques for the complete shaking force and shaking moment balancing of 26 types of four-five-and six-bar linkages with prismatic pairs due to both linear and rotary inertia, but external loads, by using the method which is a combination of mass redistribution and the addition of two kinds of the inertia counterweights.
40 citations
TL;DR: In this article, the authors analyzed errors due to instrument inertia for both step-jump and ramp-function programming in terms of an inertial response time β=KI/η, where K is the usual instrument constant for the particular rotational geometry, I the moment of inertia of the rotating part of the instrument, and η the viscosity of the sample.
Abstract: Instrument inertia can produce spurious effects in controlled‐stress rheometry whenever the imposed torque changes with time, as in step‐jump or ramp‐function programming of the torque. These errors are especially serious with samples of low to moderate viscosity, where spurious time‐dependent viscosities are found even with Newtonian samples. The usual way of dealing with this problem, that of slowing the speed change program sufficiently to eliminate errors caused by inertia, both lengthens the time of measurement and obscures any rapid thixotropic transformations. This paper analyzes errors due to instrument inertia for both step‐jump and ramp‐function programming in terms of an inertial response time β=KI/η, where K is the usual instrument constant for the particular rotational geometry, I the moment of inertia of the rotating part of the instrument, and η the viscosity of the sample. It then shows that ramp times of the order of 400β are needed to reduce inertial errors to acceptable levels. Finally,...
40 citations
TL;DR: In this paper, a statistical energy analysis approach is developed to evaluate the power transmission through the junction between two plates in an L-shaped configuration, where the solution includes the shear and rotary inertia effects (Mindlin bending) and the in-plane waves effects.
Abstract: In the analysis of the power transmission through junctions between thick plate structures, it is necessary to consider not only the transverse bending motion of the plates but also the in‐plane wave motion. That is, for these types of structures both the shear and rotary inertia effects and the in‐plane wave effects must be considered simultaneously in order to obtain a complete solution to the problem. In this paper, a statistical energy analysis approach is developed to evaluate the power transmission through the junction between two plates in an L‐shaped configuration, where the solution includes the shear and rotary inertia effects (Mindlin bending) and the in‐plane waves effects. Analytical results are presented for the absorption (or transmissibility) of the junction and the ratio between the incident bending wave power and the transmitted waves (bending and in‐plane) power. Results for pure (classical) bending are also presented for comparison with the Mindlin bending results.
31 citations
29 citations
TL;DR: In this paper, an analytical study was conducted to determine the stability and vibration characteristics of laminated cross-ply plates using the Levy approach, including the effects of shear deformation and rotary inertia.
23 citations
TL;DR: In this article, the flexural vibration characteristics of a uniform rotating bar with localized zones of damage are studied by using a finite element analysis, and the effects of shear deformation and rotary inertia have been taken into consideration.
TL;DR: In this paper, the minimum weight designs of helicopter rotor blades with constraints on multiple coupled flap-lag natural frequencies are studied, where the minimum value of the rotor autorotational inertia is defined to ensure sufficient rotary inertia to auto-otate in case of engine failure and on stresses to guard against structural failure due to blade centrifugal forces.
Abstract: Minimum weight designs of helicopter rotor blades with constraints on multiple coupled flap-lag natural frequencies are studied. Constraints are imposed on the minimum value of the blade autorotational inertia to ensure sufficient rotary inertia to autorotate in case of engine failure and on stresses to guard against structural failure due to blade centrifugal forces. Design variables include blade taper ratio, dimensions of the box beam located inside the airfoil and magnitudes of nonstructural weights. The program CAMRAD is used for the blade modal analysis; the program CONMIN is used for the optimization. A linear approximation involving Taylor series expansion is used to reduce the analysis effort. The procedure contains a sensitivity analysis consisting of analytical derivatives for objective function and constraints on autorotational inertia and stresses. Central finite difference derivatives are used for frequency constraints. Optimal designs are obtained for both rectangular and tapered blades. Using this method, it is possible to design a rotor blade with reduced weight, when compared to a baseline blade, while satisfying all the imposed design requirements.
TL;DR: In this paper, the dynamic stability of a Timoshenko beam with a thermal gradient lying on a variable Pasternak foundation and subjected to a pulsating axial force is studied.
TL;DR: A study of the natural vibration of a continuous Timoshenko curved beam on a Pasternak-type foundation is presented in this article, where the dynamic stiffness matrix of a curved member of constant section is derived and a two-span curved beam is given to illustrate the application of the proposed method and to show the effects of flexural and torsional rotary inertia, shear deformation, central angle of the arc, contact area between the beam and foundation, and the foundation constants on the natural frequencies of the beam.
TL;DR: In this paper, the MPF analysis of an L-shaped plate is performed for the case of point force excitation on one plate, with the two plates being identical in both size and thickness.
Abstract: The mobility power flow (MPF) approach is used in this paper to describe the flexural behavior of an L-shaped plate structure consisting of thick plates with rotary inertia and shear deformation effects included in the analysis. The introduction of the thick plate effects significantly increases the complexity of the structural mobility functions used in the definitions of the power flow terms; however, because of the substructuring that is used in the MPF approach, the complexity of the problem is significantly reduced as compared to solving for the global structure. Additionally, with the MPF approach the modal behavior is described. The MPF analysis of the L-shaped plate is performed for the case of point force excitation on one plate, with the two plates being identical in both size and thickness. The results of this analysis are compared to results from the finite-element analysis (FEA) and the statistical energy analysis (SEA) and show very good agreement in the low- and high-frequency regimes, respectively.
TL;DR: In this article, a parametric study carried out to investigate the vertical free vibrations of a ship hull is described, which takes into account all the effects of the rotary inertia of mass, shear distortion, thrust force, and various damping components.
Abstract: A parametric study carried out to investigate the vertical free vibrations of a ship hull is described. The analysis takes into account all the effects of the rotary inertia of mass, shear distortion, thrust force, shear lag and various damping components. The influence of these parameters on ship hull vibrations is explained. Special emphasis is placed upon a method for calculating the overall damping ratios.
TL;DR: In this article, a method based on the improved thick shell theory of Mirsky and Herrmann is presented for analyzing the free vibrations of noncircular thick cylindrical shells having circumferential thickness variation.
TL;DR: In this article, the axisymmetric dynamic response of an imperfectly bonded fluid-filled orthotropic cylindrical shell, excited by a plane longitudinal wave, is considered.
Patent•
05 Mar 1990
TL;DR: In this article, an apparatus for measuring moment of inertia incorporating a torsional pendulum and an analog electronic circuit is presented, which measures the period of oscillation, sets a scaling factor equal to the Torsional coefficient of the resilient member, and computes moment by multiplying the scaling factor by the square of the period.
Abstract: An apparatus for measuring moment of inertia incorporating a torsional pendulum and an analog electronic circuit. The circuit measures the period of oscillation, sets a scaling factor equal to the torsional coefficient of the resilient member, and computes moment of inertia by multiplying the scaling factor by the square of the period of oscillation. The moment of inertia is then displayed in metric units.
TL;DR: 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.
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 ...
TL;DR: In this paper, a method for the dynamic analysis of initially curved Timoshenko beams that undergo finite rotations is presented, where 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 are expressed in terms of a set of invariants that depend on the assumed displacement field, rotary inertia, shear deformation, and the initial beam curvature.
Abstract: A method for the dynamic analysis of initially curved Timoshenko beams that undergo finite rotations is presented. The kinetic energy is first developed for the curved beam and the beam mass matrix is identified. 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. 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
TL;DR: In this article, a computational method for dynamic analysis of flexible multi-body mechanisms is presented that extends lumped mass models to account for the influence of lumped rotary inertia.
Abstract: A computational method for dynamic analysis of flexible multi-body mechanisms is presented that extends lumped mass models to account for the influence of lumped rotary inertia. In order to account for the effect of lumped rotary inertia, a diagonal mass matrix is evaluated and the equations of motion are derived for a general diagonal mass matrix. The system equations of motion of a constrained mechanism are systematically assembled. Numerical results for a hollow pipe are compared to a finite element solution to demonstrate the accuracy of the approach. A wheeled vehicle example is presented to demonstrate the influence of lumped rotary inertia in a large-scale dynamic system.
TL;DR: In this paper, the authors deal with the nonaxisymmetric dynamic behavior of fluid-filled buried orthotropic cylindrical shells/pipes excited by plane longitudinal waves.
Abstract: This paper deals with the nonaxisymmetric dynamic behavior of fluid‐filled buried orthotropic cylindrical shells/pipes excited by plane longitudinal waves. A thick shell model including the effects of shear deformation and rotary inertia is taken. A perfect bond between the shell and the surrounding soil is assumed. The linear acoustic equation is used for wave propagation in the fluid inside the pipe. Results are presented for the axisymmetric as well as the flexural mode for different orthotropy parameters of the shell and also for different soil conditions around the pipe/shell. Results of the empty and fluid‐filled shells are compared. Effects of changes in the fluid density are also discussed. The presence of fluid inside the shell significantly alters the shell response. The effect of fluid, in general, is comparable to the effects of variation in the orthotropy parameters of the shell and also to the effects due to changes in the soil condition. In the flexural mode, deformations in the fluid‐fille...
TL;DR: In this paper, the constraint equations for deformable bodies are modified for use in the neighborhood of the singular configuration to yield the system inertia matrix which is nonsingular and also to take the actual generalized constraint forces into account.
TL;DR: In this article, the problem of controlling the spherical motion of a rotating solid when the torques delivered to the body by the controls do not contain an x-component and their axes are not the principal central axes of inertia of the body is investigated.
TL;DR: In this paper, an assumed displacement field that accounts for the coupling between the stretching and bending of a plate as the result of considering the effect of the rotary inertia is used to identify the configuration of the plate.
Abstract: The effect of the rotary inertia on the non-linear dynamics of plates that undergo a large reference displacement is examined in this paper. An assumed displacement field that accounts for the coupling between the stretching and bending of the plate as the result of considering the effect of the rotary inertia is used to identify the configuration of the plate. Furthermore, the coupling between the stretching and bending of the plate as the result of finite rotation is also considered in this investigation. Based on the assumed displacement field that accounts for the effect of the rotary inertia, a non-linear finite element formulation is developed for the large displacement analysis of plates. The element equations of motion are expressed in terms of a set of element invariants that depend on the assumed displacement field as well as the rotary inertia. The use of the formulation presented in this paper is demonstrated using numerical examples.
TL;DR: In this article, a tuning-fork type flexural-mode quartz crystal resonator is considered to have two cantilevers, and the equation of motion is solved under the boundary condition of a clamped-free end.
Abstract: A study was conducted with a view to finding theoretically and experimentally the relationship between the resonant frequency and its temperature dependence of the thickness of the resonator. As the analytical means, the energy method was used for deriving the equation of motion in which the thickness and rotary inertia and shear force were taken into account.
Since a tuning-fork type flexural-mode quartz crystal resonator is considered to have two cantilevers, the equation of motion was solved under the boundary condition of a clamped-free end. The frequency equation was derived as a function of the thickness zO' width xO and lenght yO.
Next, from this equation, the following relationships are derived: the frequency constant (f·yO) versus the dimensional ratio Rxy = xO/yO, the resonant frequency versus the dimensional ratio Rzy = zO/yO, the turnover temperature point Tp versus the dimensional ratio Rxy and the relationship between the first- and second-order frequency temperature coefficients and Tp versus the dimensional ratio Rzy. It is shown that the apex temperature Tp changes significantly for the thickness. Further, these results were compared with the experimental data and good agreement between them is shown. Hence, it is concluded that the present analysis results are useful for the design of new frequency resonators.
TL;DR: The rotary inertia and shear deformation effects are included in the model to study the dynamic response of robotic manipulators made of thick beams to derive a dynamic model for a revolute flexible robot arm constructed from laminated composite materials.
TL;DR: In this article, a method based on the variational procedure in conjunction with the finite difference technique is used to determine the natural frequencies and mode shapes, and the convergence characteristics of the present method is studied and the results are compared with existing solutions based on thin plate theory.
Abstract: A method based on the variational procedure in conjunction with the finite difference technique is used to determine the natural frequencies and mode shapes. The convergence characteristics of the present method is studied and the results are compared with existing solutions based on the classical thin plate theory