Rotary Springs Research Articles

Resonance and cancellation phenomena in partially clamped simply supported beam bridges under moving trains

Since the development of new railway lines of high speed, the dynamic response of bridges belonging to them constitutes a subject interest for researchers and engineers, in particular at resonance. In the present work, an analytical approach is developed to analyze the dynamic response of a single ballasted track railway bridges supported by identical rotational springs and subjected to the circulation of moving loads at constant speeds. Although the introduction of rotary springs at the ends of the deck enhances the choice of the appropriate analysis model, where most of the contributions reported in this field do not consider this effect. The central idea of the proposed model is based on analyzing the continuity effect of the ballasted track (rails and ballast) on the dynamic response of railway bridges, with taking into account an axial force that models the effect of prestressing, longitudinal ballast-bridge interface, axial displacement, force braking. The equation of motion of the system is derived by using the Hamilton’s principle, two dynamic case studies of a simply supported and simply supported partially clamped Euler-Bernoulli beam are presented. The results revealed that the compression force presents an additional stiffness which affects the critical velocity and that the continuity of the track modeled by rotational springs at the beam’s end, as it increases the dynamic response decreases. Also, a dynamic analysis for the conditions for maximum response and cancellation in free vibration are derived and interpreted particularly the effect of the geometric scheme of train axles. Equating the condition for resonance of maximum free response and cancellation, cancelled resonance are obtained.

Reproduction of Intrinsic Localized Modes by Prototype Experiments of Nonlinear Magnetic Rotary Springs

Reproduction of Intrinsic Localized Modes by Prototype Experiments of Nonlinear Magnetic Rotary Springs

An improved spinal injury parameter model for underbody impulsive loading scenarios.

Underbody blast events such as aircraft ejection, mine blast, and helicopter crashes pose a serious threat to occupants. These impulsive excitations exert substantial axial loads on the thoracolumbar spine causing severe injuries. The Dynamic Response Index (DRI), which is commonly used as the injury parameter for underbody loading scenarios, suffers from inherent disadvantages and has been reported to underpredict the chances of injury. The main reasons are the inability of the DRI model to account for bending loads and posture of the spine. Thus, a novel lumped full spine model capable of modelling the spine in different posture along the sagittal plane is formulated. The unavailable data for the model were obtained using inverse parameter identification approach by eigenfrequency matching. Each vertebra has three degrees of freedom: axial, shear, and rotary motion to model the flexion of the spine. A new injury parameter is proposed based on the sum of compressions caused due to axial and rotary springs at each vertebral level, to account for wedge compression and burst fractures. The results indicate that the model was able to predict the motions of vertebrae under different postures of the spine according to trends in literature.

Principles of Lossless Adjustable One-Ports

This paper explores the possibility of constructing two-terminal mechanical devices (one-ports) which are lossless and adjustable. To be lossless, the device must be passive (i.e., not requiring a power supply) and nondissipative. To be adjustable, a parameter of the device should be freely variable in real time as a control input. For the simplest lossless one-ports, the spring and inerter, the question is whether the stiffness and inertance may be varied freely in a lossless manner. We will show that the typical laws which have been proposed for adjustable springs and inerters are necessarily active, and that it is not straightforward to modify them to achieve losslessness, or indeed, passivity. By means of a physical construction using a lever with moveable fulcrum, we will derive device laws for adjustable springs and inerters which satisfy a formal definition of losslessness. We further provide a construction method which does not require a power supply for physically realizable translational and rotary springs and inerters. The analogous questions for lossless adjustable electrical devices are examined.

On the prevention or facilitation of buckling of beams

The present paper considers the use of linear or rotary transverse springs to: (i) prevent the buckling of beams by raising the critical buckling load and thus allow a larger axial tension; (ii) provoke the buckling of beams, by lowering the critical buckling load, facilitating the demolition of a structure. The prevention or facilitation of buckling depends on the positioning of the linear and/or rotary springs to oppose or favour bending, for example: at the tip of a (i) cantilever or clamped–free beam; at the middle of a (ii) clamped–clamped, (iii) pinned–pinned or (iv) clamped–pinned beam. In all eight of the four beam supports (i)–(iv) with either linear or rotary springs, the relation between the critical buckling load and the resilience of the spring is obtained.

Structural and Aeroelastic Modeling of General Planform Wings with Morphing Airfoils

By use of equivalent plate modeling, an efficient method has been developed to study the structural behavior and static aeroelastic response of general builtup wing structures composed of skins, spars, and ribs. The model includes transverse shear effects by treating the wing as a plate, following the first-order shear deformation theory. The equations of motion are derived using the Ritz method with Legendre polynomials as trial functions. To model arbitrary wing planforms, the wing is composed of two plates, connected by distributed translatory and rotary springs of very high stiffness. The structural model has been validated for a set of examples by comparing the results with the ones obtained from MSC/NASTRAN. A distributed actuation scheme allows the modification of wing twist and camber for maneuver control of the vehicle. The model has been applied to study the roll performance of a flapless smart wing with morphing airfoils

A hybrid approach to the transient collapse analysis of thin walled frameworks I

A compound beam element for the transient hybrid finite element analysis have been developed. The new element is a combination of an elastic beam and nonlinear rotary springs whose behaviour in the elastic/plastic and deep collapse range is controlled by inputted moment-rotation curves. The element formulation is based on the rigid convected co-ordinate procedure similar to the one used by the Belytschko-Schwer (B-S) beam element [1]. The element mass and stiffness matrices have been derived and the stiffness matrix dependency on the spring behaviour explained. Semidiscretized equations of motion are discretized in time by the central difference method.

A hybrid approach to the transient collapse analysis of thin walled frameworks II

A new improved compound beam element (CBE2) for the transient hybrid finite element analysis is presented. The element is a combination of an elastic beam and two non-linear rotary springs whose behaviour in the elastic/plastic and deep collapse range is controlled by inputted moment-rotation curves and a load interaction curve. The formulation is based on the rigid convected coordinate procedure similar to the one used by the Belytschko-Schwer (B-S) beam element. The element stiffness matrix has been derived and its dependency on the spring behaviour explained. Two series of experiments were performed on two simple structures providing the data for the element performance evaluation. The tests performed were designed so that structural components collapse under biaxial bending and torsion. The tests results have shown, not only that CBE2 is more accurate than CBE1 but also that it does not suffer from the stability problems present in the formulation of CBE1 [1].

Influence of various types of elastic foundation on the divergence and flutter of Ziegler's model structure

Ziegler's model structure (consisting of two rigid massless bars connected by a frictionless joint, with two rotational springs under follower force) is utilized in order to illustrate the influence of various types of elastic foundation on the buckling loads. In particular, continuous rotary or translational (Winkler) foundations are studied, whereas in the case of discrete foundation two translational springs are introduced in addition to the rotary springs.

Vibration and acoustic radiation of elastically supported rectangular plates

A Green function solution is developed for the steady-state vibrations of an elastically supported rectangular plate coupled to a semi-infinite acoustic medium. Rotational motion at the plate boundaries is controlled by continuous distributions of rotary springs. The solution takes the form of that for a simply supported rectangular plate. The coefficients are determined from systems of simultaneous algebraic equations that include the coupling due to non-homogeneous boundary conditions and the acoustic surface impedance. The solution is also extended to cover the case of an arbitrary load distribution and an expression is derived for the power balance in the coupled plate-fluid system. Results of a numerical evaluation of the modal coupling factors due to fluid loading are compared with low frequency approximations. Effects of the support conditions on the low frequency sound radiation from a plate are illustrated by an example.