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Showing papers on "Rotary inertia published in 2001"


Journal ArticleDOI
TL;DR: The Timoshenko beam theory includes the effects of shear deformation and rotary inertia on the vibrations of slender beams as discussed by the authors, which has been the subject of much previous research.
Abstract: The Timoshenko beam theory includes the effects of shear deformation and rotary inertia on the vibrations of slender beams. The theory contains a shear coefficient which has been the subject of much previous research. In this paper a new formula for the shear coefficient is derived. For a circular cross section, the resulting shear coefficient that is derived is in full agreement with the value most authors have considered best. Shear coefficients for a number of different cross sections are found.

509 citations


Journal ArticleDOI
TL;DR: In this article, an absolute nodal coordinate formulation is presented for the large rotation and deformation analysis of three dimensional beam elements, taking into account the effect of rotary inertia, torsion and shear, and ensuring continuity of the slopes as well as the rotation of the beam cross section at the nodal points.
Abstract: The description of a beam element by only the displacement of its centerline leads to some difficulties in the representation of the torsion and shear effects. For instance such a representation does not capture the rotation of the beam as a rigid body about its own axis. This problem was circumvented in the literature by using a local coordinate system in the incremental finite element method or by using the multibody floating frame of reference formulation. The use of such a local element coordinate system leads to a highly nonlinear expression for the inertia forces as the result of the large element rotation. In this investigation, an absolute nodal coordinate formulation is presented for the large rotation and deformation analysis of three dimensional beam elements. This formulation leads to a constant mass matrix, and as a result, the vectors of the centrifugal and Coriolis forces are identically equal to zero. The formulation presented in this paper takes into account the effect of rotary inertia, torsion and shear, and ensures continuity of the slopes as well as the rotation of the beam cross section at the nodal points. Using the proposed formulation curved beams can be systematically modeled.

401 citations


Journal ArticleDOI
TL;DR: In this paper, two beam elements that relax the assumptions of Euler-Bernoulli and Timoshenko beam theories are developed, which take into account the effect of rotary inertia, shear deformation and torsion, and yet they lead to a constant mass matrix.
Abstract: This part of these two companion papers demonstrates the computer implementation of the absolute nodal coordinate formulation for three-dimensional beam elements. Two beam elements that relax the assumptions of Euler-Bernoulli and Timoshenko beam theories are developed. These two elements take into account the effect of rotary inertia, shear deformation and torsion, and yet they lead to a constant mass matrix. As a consequence, the Coriolis and centrifugal forces are identically equal to zero. Both beam elements use the same interpolating polynomials and have the same number of nodal coordinates. However, one of the elements has two nodes, while the other has four nodes. The results obtained using the two elements are compared with the results obtained using existing incremental methods. Unlike existing large rotation vector formulations, the results of this paper show that no special numerical integration methods need to be used in order to satisfy the principle of work and energy when the absolute nodal coordinate formulation is used. These results show that this formulation can be used in manufacturing applications such as high speed forming and extrusion problems in which the element cross section dimensions significantly change.

279 citations


Journal ArticleDOI
TL;DR: In this article, an integrated piezoelectric sensor/actuator plate with a view to using it as a first step towards establishing an entire structural health monitoring system and to provide experimental verification of the proposed models.
Abstract: The objective of this study is to model the diagnostic transient waves in an integrated piezoelectric sensor/actuator plate with a view to using it as a first step towards establishing an entire structural health monitoring system and to provide experimental verification of the proposed models. PZT ceramic disks are surface mounted on an aluminum plate acting as both actuators and sensors to generate and collect A0 mode Lamb waves. Mindlin plate theory is adopted to model the propagating waves by taking both transverse shear and rotary inertia effects into account. Actuator and sensor models are both proposed. The interaction between an actuator and the host plate is modeled based on classical lamination theory. The converse piezoelectric effect of the actuator is treated as an equivalent bending moment applied to the host plate. The sensor acts as a capacitor that converts the sensed strain change into a voltage response. An analytical expression for the sensor output voltage in terms of the given input excitation signal is derived, and then experimental work is performed to verify the accuracy of the analytical model. Experimental results show that single-mode Lamb waves in the plate can be successfully generated and collected through the integrated PZT disks. The experiment also shows that the predicted sensor output for both amplitude and phase agrees well with experimentally collected data.

178 citations


Journal ArticleDOI
TL;DR: In this article, the stiffness and mass matrices of a rotating twisted and tapered beam element were derived and the effects of shear deformation and rotary inertia were also considered in deriving the elemental matrices.

143 citations


Journal ArticleDOI
TL;DR: In this paper, a linearized dynamic model for multi-link planar flexible manipulators is presented, where the elastic deformation of each link is modeled by using the assumed-mode method.

116 citations


Journal ArticleDOI
TL;DR: In this article, the authors report on modeling, numerical simulation, and experimental investigation of plates subjected to impulsive loading using the Chaboche and Bodner-Partom constitutive laws.

70 citations


Journal ArticleDOI
Usik Lee1, Joohong Kim1
TL;DR: In this article, a spectral finite element for the beam with active constrained layer damping (ACLD) is proposed, which is formulated from exact wave solutions of a set of fully coupled dynamic equations of motion.

64 citations


Proceedings ArticleDOI
11 Jun 2001
TL;DR: In this article, an integrated piezoelectric sensor/actuator plate with a view to using it as a first step towards establishing an entire structural health monitoring system and to provide experimental verification of the proposed models.
Abstract: The objective of this study is to model the diagnostic transient waves in an integrated piezoelectric sensor/actuator plate with a view to using it as a first step towards establishing an entire structural health monitoring system and to provide experimental verification of the proposed models. PZT ceramic disks are surface mounted on an aluminum plate acting as both actuators and sensors to generate and collect A0 mode Lamb waves. Mindlin plate theory is adopted to model the propagating waves by taking both transverse shear and rotary inertia effects into account. Actuator and sensor models are both proposed. The interaction between an actuator and the host plate is modeled based on classical lamination theory. The converse piezoelectric effect of the actuator is treated as an equivalent bending moment applied to the host plate. The sensor acts as a capacitor that converts the sensed strain change into a voltage response. An analytical expression for the sensor output voltage in terms of the given input excitation signal is derived, and then experimental work is performed to verify the accuracy of the analytical model. Experimental results show that single-mode Lamb waves in the plate can be successfully generated and collected through the integrated PZT disks. The experiment also shows that the predicted sensor output for both amplitude and phase agrees well with experimentally collected data.

61 citations


Journal ArticleDOI
TL;DR: In this paper, a non-linear transient analysis of the shear deformable laminated composite plates, subjected to step, ramp and sinusoidal loading is presented, where clamped, simply supported, free and their combinations (non-Levy type) of boundary conditions are considered.

49 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of shaft asymmetry was incorporated into an existing finite element procedure developed for rotors with symmetric shafts by taking into account rotary inertia and gyroscopic inertia.

Journal ArticleDOI
TL;DR: In this paper, the coupled governing differential equations and the general elastic boundary conditions for the coupled bending-bending forced vibration of a nonuniform pretwisted Timoshenko beam are derived by Hamilton's principle.

Journal ArticleDOI
TL;DR: In this article, a finite element computational procedure is presented for the determination of first-ply failure strengths of pretwisted rotating plates subjected to center point transverse load, where effects of transverse shear deformation and rotary inertia are included.
Abstract: In this paper a finite element computational procedure is presented for the determination of first-ply failure strengths of pretwisted rotating plates subjected to centre point transverse load. The finite element model is based on the tensor polynomial failure criterion that contains the maximum stress, maximum strain, Tsai-Hill, Tsai-Wu and Hoffman failure criteria as special cases. A nine-noded three-dimensional degenerated composite shell element is developed and used for the present finite element formulation. Effects of transverse shear deformation and rotary inertia are included. Lagrange's equation of motion is employed to derive the dynamic equilibrium equation considering moderate rotational speeds for which the Coriolis effect is negligible. Finally, the static equilibrium equation is formulated after discarding the time-dependent terms. Failure load computations for rotating cantilever plates with nonlinear pretwist are carried out to investigate the effects of angle of twist, rotational speed ...

Journal ArticleDOI
TL;DR: In this paper, the free vibration of anisotropic laminated composite, as well as isotropic open or closed, cylindrical shells submerged in and subjected simultaneously to an internal and external incompressible, inviscid fluid are discussed on the basis of a refined shell theory in which transverse shear deformation and rotary inertia effects are taken into account.

Journal ArticleDOI
TL;DR: In this article, a method for dynamic response analysis of spinning tapered Timoshenko beams utilizing the finite element method is developed, which includes the effects of Coriolis forces, shear deformation, rotary inertia, hub radius, taper ratios and angular setting of the beam.

Journal ArticleDOI
TL;DR: In this article, the dynamic instability analysis of a joined conical and cylindrical shell subjected to periodic in-plane load is investigated using C 0 two-noded shear flexible shell element.

Journal ArticleDOI
TL;DR: In this paper, the theory of a Cosserat point is used to formulate a numerical solution procedure for the dynamic three-dimensional motion of nonlinear curved rods by modeling the rod as a set of N connected Cossers, like finite elements.

Journal ArticleDOI
TL;DR: In this article, the derivation of the equations of motion of a spinning plate was revisited, focusing on the use of Hamilton's principle with linear Kirchhoff and nonlinear von Karman strain expressions.

Journal ArticleDOI
A. Nandi1, S. Neogy1
TL;DR: In this paper, a shaft is modelled using three-dimensional solid finite elements and the shear deformation and rotary inertia effects are automatically included through the threedimensional elasticity formulation.
Abstract: A shaft is modelled using three-dimensional solid finite elements. The shear-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warping of plane cross-sections and takes care of gyroscopic effect. Unlike a beam element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that the shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulation becomes much simpler in a rotating frame of reference that rotates about the centre-line of the bearings with an angular velocity equal to the shafts spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered sections and continuous or abrupt change in c...

Journal ArticleDOI
TL;DR: In this paper, the parametric resonance characteristics of laminated composite doubly curved panels subjected to various in-plane static and periodic compressive edge loadings, including partial and concentrated edge loading, were studied using finite element analysis.
Abstract: The parametric resonance characteristics of laminated composite doubly curved panels subjected to various in-plane static and periodic compressive edge loadings, including partial and concentrated edge loading are studied using finite element analysis. The first order shear deformation theory is used to model the doubly curved panels, consid- ering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to the Sander's first approxima- tion for doubly curved laminated shells, which can be reduced to Love's and Donnell's theories by means of tracers. The effects of number of layers, static load factor, side to thickness ratio, shallowness ratio, boundary conditions, degree of orthotropy, ply orienta- tions and various load parameters on the principal instability regions of doubly curved panels are studied in detail using Bolotin's method. Quantitative results are presented to show the effects of shell geometry, lamination details and load parameters on the stability boundaries. Results of plates and cylindrical shells are also presented as special cases and are compared with those available in the literature.

Journal ArticleDOI
TL;DR: In this article, the effects of static load factor, aspect ratio, radius-to-thickness ratio, shallowness ratio, boundary conditions and the load parameters on the principal instability regions of doubly curved panels are studied in detail using Bolotin's method.

Journal ArticleDOI
TL;DR: In this paper, a frequency domain analysis of a linear time-invariant (LTI) system with a single elastomeric isolator that is placed between a rigid body and a finite or infinite beam receiver is presented.

Journal ArticleDOI
TL;DR: In this article, the non-linear, moderately large amplitude flexural free vibrations of an arm clamped with a setting angle to a rigid rotating hub are studied. And the Lagrangian approach in conjunction with the assumed modes method, assuming constant hub rotation speed and constant blade setting angle, is used in a consistent manner to obtain the third order nonlinear uni-modal temporal problem.

Journal ArticleDOI
TL;DR: In this paper, the free vibration problem of unidirectional composite cylindrical helical springs is modelled theoretically as a continuous system considering the rotary inertia, shear and axial deformation effects.

Journal ArticleDOI
TL;DR: In this paper, two recently derived linear models for the transverse vibrations of a spinning plate are considered, one based on the assumption of linear (Kirchhoff) strains and the other based on non-linear (von Karman) strains.

Journal ArticleDOI
TL;DR: In this article, the first six resonance frequencies of unidirectional composite noncylindrical helical springs (barrel and hyperboloidal types) made of carbon-epoxy (T300/N5208) material are determined theoretically based on the transfer matrix method.
Abstract: The first six resonance frequencies of unidirectional composite noncylindrical helical springs (barrel and hyperboloidal types) made of carbon-epoxy (T300/N5208) material are determined theoretically based on the transfer matrix method. The rotary inertia, shear, and axial deformation effects are considered with the first-order shear deformation theory. The overall transfer matrix is obtained by integrating the 12 scalar ordinary differential equations with variable coefficients governing the free-vibration behavior of noncylindrical helical springs made of an anisotropic material. Numerical results are verified with the reported values for isotropic noncylindrical helices. A parametric study is performed to investigate the effects of the number of active coils (n = 5-10), the helix pitch angle ( f = 5° and 25°), the ratio of the minimum to maximum cylinder radii ( R min/ R max = 0.1 and 0.9), and the ratio of the maximum cylinder diameter to the wire diameter ( D max/ d = 5 and 15) on the free-vibration ...

Journal ArticleDOI
TL;DR: In this paper, closed-form solutions for dynamic analysis of extensional circular Timoshenko beams with general elastic boundary conditions are derived by taking the Laplace transform and some procedures, the system composed of three coupled governing differential equations and six coupled boundary conditions is uncoupled and reduced to a single equation in terms of the angle of rotation due to bending.

Journal ArticleDOI
TL;DR: In this paper, the free in-plane vibration of a shallow circular arch with uniform cross-section is investigated by taking into account axial extension, shear deformation and rotatory inertia effects.
Abstract: The free in-plane vibration of a shallow circular arch with uniform cross-section is investigated by taking into account axial extension, shear deformation and rotatory inertia effects. The exact solution of the governing differential equations is obtained by the initial value method. By employing the same solution procedure, the solutions are also given for the other cases, in which each effect is considered alone, as well as no effect. The frequency coefficients are obtained for the lowest five vibration modes of arches with five combinations of classical boundary conditions, and various slenderness ratios and opening angles. The results show that the shear deformation and rotatory inertia effects are also very important as well as the axial extension effect, even if a slender shallow arch is considered. The discrepancies among the results of the five cases decrease, when opening angle increases for a constant radius and slenderness ratio. The effects of the boundary conditions and the slenderness ratio of the arch are investigated. The discrepancies among the results of the cases become much more important in higher modes. The mode shapes of a shallow arch are obtained for each case.

Patent
27 Jul 2001
TL;DR: In this paper, an infinitely variable transmission (IVT) controller determines whether the operation mode of an IVT is a power recirculation mode or a CVT direct mode, and selects an inertial torque computing equation corresponding to the operation modes.
Abstract: An IVT controller determines whether the operation mode of an infinitely variable transmission (IVT) is a power recirculation mode or a CVT direct mode, and selects an inertial torque computing equation corresponding to the operation mode. The inertia torque accompanying a speed change of the IVT is computed using the computing equation. An engine controller adjusts the opening of an electronic control throttle, and adjusts the torque of the engine so that computed inertia torque is eliminated.

Journal ArticleDOI
TL;DR: In this paper, a numerical study was performed to investigate the common effects of the rotary inertia and shear deformation on the first six out-ofplane free vibration frequencies of symmetric cross-ply laminated circular bars with the help of the transfer matrix method.
Abstract: A numerical study is performed to investigate the common effects of the rotary inertia and shear deformation on the first six out-of-plane free vibration frequencies of symmetric cross-ply laminated circular bars with the help of the transfer matrix method. The distributed parameter model is employed in the free vibration analysis of the vibrating system. The overall transfer matrix is computed up to any desired accuracy using the effective numerical algorithm available in the literature. The first order shear deformation theory called as Timoshenko model is included in the analysis. For the opening angle α =90°, the effects of the rotary inertia and shear deformation are examined and presented in graphical forms considering boundary conditions (clamped–free, clamped–simple and clamped–clamped), and the slenderness ratios ( R / h =radius of the arch/thickness of the rectangular section=5–25). The effects of the ratio of the extensional modulus to the transverse modulus on the natural frequencies are also examined.