Active isolation of a flexible structure from base vibration

This paper presents a theoretical and experimental investigation into an active vibration isolation system. Electromagnetic actuators are installed in parallel with each of four passive mounts, which are placed between a flexible equipment structure and a base structure which is either flexible or rigid. Isolation of low-frequency vibration is studied, so that the passive mounts can be modelled as lumped parameter springs and dampers. Decentralized velocity feedback control is employed, where each actuator is operated independently by feeding back the absolute equipment velocity at the same location. Good control and robust stability have been obtained both theoretically and experimentally for the multichannel control systems. This is to be expected if the base structure is rigid, in which case the actuator and sensor are, in principle, collocated and the control system implements a skyhook damper. With a flexible base structure, however, collocation is lost due to the reactive actuator force acting on the base structure, but the control system is still found to be robustly stable and to perform well. Attenuations of 20 dB are obtained in the sum of squared velocities on the equipment structure at the rigid-body mounted resonance frequencies. In addition, attenuations of up to 15 dB are obtained at the resonance frequencies of both the low order flexible modes of the base structure and the equipment structure.     

Stability of a deploying/extruding beam in dense fluid

The equations of motion of a flexible slender cantilevered beam with uniform circular cross-section, extending axially in a horizontal plane at a known rate while immersed in an incompressible fluid are derived. An “axial added mass coefficient” is implemented in these equations in order to better approximate the mass of fluid which stays attached to the oscillating beam while moving in the axial direction. Realistic initial conditions are given to the system and numerical solutions are obtained. The dynamical behaviour of the system is observed for cases of constant extension rate and for a trapezoidal deployment rate profile.In the case of low constant extension rates, the system displays a phase of oscillation with increasing amplitude and decreasing frequency until the motion is strongly damped and later becomes statically unstable. For faster deployment rates, the beam has a short flutter phase at the beginning of the deployment, followed by a brief phase of damped oscillation until it exhibits static divergence. For fast enough deployment rates, the system is unstable from the beginning and never stabilizes. The effect the axial added mass coefficient has on the system is studied and it is found that it plays two roles in the stability of the system. The trapezoidal deployment rate profile is studied because it is deemed more representative of real-life applications. For long deployment times, the system behaves in a very similar manner to one with low constant extension rate, except that it does not become statically unstable. For shorter deployment times, the maximum amplitude of the tip displacement is usually attained after the beam has stopped extruding.     

Application of discrete-time variable structure control in the vibration reduction of a flexible structure

This paper studies the application of using the discrete-time variable structure control method to reduce the vibration of the flexible structure. The structure is subjected to arbitrary, unmeasurable disturbance forces. The concept of independent modal space control is adopted, and the system is studied by the discrete-time model. Here, discrete sensors and actuators are used. We choose the modal filters as the state estimator to obtain the modal co-ordinates and modal velocities for the modal space control. A discrete-time variable structure controller with a disturbance force observer is adopted due to its distinguished robustness property of insensitiveness to parameter uncertainties and external disturbances. The included disturbance force observer can observe the unknown disturbance modal forces, which are used in the discrete-time variable structure control law to cancel out the excitations. The upperbound limitations of the unknown disturbances in the variable structure control, therefore, are no longer needed. The switching surface, in the discrete-time variable structure control system, is designed in an optimal sense. That is, along the switching surface, the cost function of the states is minimized. The investigation of this research focuses on the optimal switching surface design and the control performances of the discrete-time variable structure controller. The performance of estimating the disturbance modal forces and the robustness property of the control law are also discussed.     

Genetic algorithm based active vibration control for a moving flexible smart beam driven by a pneumatic rod cylinder

A rod cylinder based pneumatic driving scheme is proposed to suppress the vibration of a flexible smart beam. Pulse code modulation (PCM) method is employed to control the motion of the cylinder's piston rod for simultaneous positioning and vibration suppression. Firstly, the system dynamics model is derived using Hamilton principle. Its standard state-space representation is obtained for characteristic analysis, controller design, and simulation. Secondly, a genetic algorithm (GA) is applied to optimize and tune the control gain parameters adaptively based on the specific performance index. Numerical simulations are performed on the pneumatic driving elastic beam system, using the established model and controller with tuned gains by GA optimization process. Finally, an experimental setup for the flexible beam driven by a pneumatic rod cylinder is constructed. Experiments for suppressing vibrations of the flexible beam are conducted. Theoretical analysis, numerical simulation and experimental results demonstrate that the proposed pneumatic drive scheme and the adopted control algorithms are feasible. The large amplitude vibration of the first bending mode can be suppressed effectively.     

Frictional vibration transmission from a laterally moving surface to a traveling beam

As the density of information stored in automated magnetic tape libraries continues to increase, greater requirements are placed on the precision of mechanical positioning in order to successfully read and write data bits. The location of the read/write head in the direction across the tape's width (termed the lateral direction) is actively controlled in order to maintain alignment between the head and data tracks, even in the presence of the tape's lateral vibration. However, during repositioning, vibration is undesirably transmitted from the laterally moving head structure to the axially moving tape because of frictional contact between the two adjacent surfaces. As an analog of that interaction, a model is developed here to describe frictional vibration transmission from a surface having prescribed lateral motion to a tensioned beam that travels and slides over it. For a transport speed that is high when compared to the lateral vibration velocity, Coulomb friction between the surface and the beam can be well-approximated by an equivalent form of viscous damping. The beam is divided into contiguous regions corresponding to free spans and the beam's portion that contacts the surface. A critical engagement length between the beam and the surface exists for which vibration transmission at a particular natural frequency can be substantially reduced, and for a given mode, that length depends weakly on the surface's position along the beam's span. By contouring the surface to have portions of differing radii of curvature, the extent of vibration transmission can be reduced over a broad range of frequency.     

Random vibration of a beam impacting stops

The random vibration of a beam impacting a spring-like stop is discussed. The mean square response and the frequency of impacts are obtained by an equivalent linearization. Reasonable agreement is obtained between these results and the results for an equivalent non-linear single-degree-of-freedom system.     

Suppression of random vibration in flexible structures using a hybrid vibration absorber

A design method is proposed to suppress stationary random vibration in flexible structures using a hybrid vibration absorber (HVA). While the traditional vibration absorber can damp down the vibration mainly at the pre-tuned mode of the primary structure, active damping is generated by the proposed HVA to damp down all resonant modes of interest of the vibrating structure and the spatial average mean square motion of the vibrating structure can be minimized. Only one absorber and one feedback signal are required to achieve global vibration suppression of a flexible structure under stationary random excitation. A special pole-placement controller is designed such that all vibration modes of the flexible structures become critically damped. It is proved analytically that the proposed HVA damps the vibration of the entire structure instead of just the attachment point of the absorber. The proposed optimized HVA is tested on a beam structure and it shows a superior performance on global suppression of broadband vibration in comparison to other published designs of passive and hybrid vibration absorbers.     

Measurement of viscoelastic properties from the vibration of a compliantly supported beam

A laboratory method is presented by which the viscoelastic properties of compliant materials are measured over a wide frequency range. The test setup utilizes a flexible beam clamped at one end and excited by a shaker at the free end. A small specimen of a compliant material is positioned to support the beam near its midpoint. The deformation from gravity is minimized since the specimen is not loaded by an attached mass. Forced vibration responses measured at two locations along the beam are used to derive a transfer function from which the dynamic properties of compliant materials are directly determined by use of a theoretical procedure investigating the effects of specimen stiffness on the propagation of flexural waves. Sensitivity of the measured properties to experimental uncertainties is investigated. Young's moduli and associated loss factors are determined for compliant materials ranging from low-density closed-cell foams to high-density damping materials. The method is validated by comparing the measured viscoelastic properties to those from an alternative dynamic test method.     

Forced vibration of a thin flexible cylinder in viscous flow

A thin, infinitely flexible cylinder in viscous axial flow is forced to vibrate by transverse motion of its upstream boundary condition and hydrodynamic forces due to arbitrary cross-flow components. This models a large-aspect-ratio cylindrical instrumentation package being towed in the ocean in which the “towpoint” has transverse motion and cross-currents exist. The governing momentum equation is derived as an extension to previous work by Ortloff and Ives [1], and the solution is studied. The response of the cylindrical structure to the two different forcing functions is quite different, although common physical elements exist. When the cylinder diameter is small relative to the wavelength of the forcing element, hydrodynamic forces dominate structural forces, and a unidirectional wave propagating downstream results. In the opposite limit, tension stiffness and velocity damping modify and complicate the response, but do not change the basic downstream-propagating induced wave.     

Efficient and flexible laser beam scanners constructed from volume holograms

We combine the scan flexibility of computer-generated holographic laser beam scanners with the high diffraction efficiency of volume phase holograms to produce a new type of “holo-scanner”. The scanner-hologram consists of numerous, small, volume hologram facets recorded in dichromated gelatin films and produces an arbitrary output pattern with greater than 90% light efficiency. Experimental results from discrete point, continuous line, and 3-D scanners are shown. Multi-wavelength scanners are also considered. This paper is based on the concepts presented in the preceding paper on “computer-interferometric holograms used for laser beam scanners”.     

Modal characteristics of a flexible beam with multiple distributed actuators

A flexible structure with surface-bonded piezoceramic patches is modelled using Timoshenko beam theory. Exact mode shapes and natural frequencies associated with the flexural motion are computed for various piezoceramic distributed actuator arrangements. The effects of patch placement and of shear on the modal characteristics are demonstrated using a cantilevered beam as an example. Perfect bonding of the piezoceramic to the beam substructure is assumed, and for the purposes of this paper only passive piezoceramic properties are considered. The modelling technique and results obtained in a closed form are intended to assist investigations into the modelling and control of active structures with surface-bonded piezoceramic actuators.     

Modal control of beam flexural vibration

An active control system was developed to control the flexural vibrations of a beam with a modal filtering with only one secondary actuator. Segmented piezoelectric actuators and sensors were used for driving and sensing the bending beam vibrations. The primary actuator was fed by a broadband random disturbance signal in order to excite the first five modes of the structure. However, only the second to fifth modes were controlled. The control algorithm was implemented on a DSP board and the input and output signals were filtered using high order low pass filters. These filters, implemented on the DSP board avoid the degrading effect on the control performances of the higher order modes and which are not controlled. The modal filtering was achieved by computing. To this end, it is based on a previous identification procedure. This latter models, in one step, the dynamics of the structure and also the transfer function of the electronic circuits of the controller. The identified filtered modes were then used to compute the gain matrix using a LQR technique (linear quadratic regulator). Simulations of the active control were carried out and practical implementation of the control algorithms was performed. Experimental and simulation results were then compared and discussed.     

Non-linear free vibration of a simply-supported beam by programming techniques

An account is given of a study of free vibrations of a simply-supported beam with non-linear material properties. The material is of the Ramberg-Osgood type. Non-linear programming technique was used to find the response of the system. The variation of frequency with amplitude has been obtained for different values of material properties. The results indicate that the beam behaves like a soft spring for the type of non-linearity introduced by the material. This method can be used for all modes directly without reference to the lower modes.     

Non-linear free vibration of a beam with time-dependent material properties

An account is given of a study of free vibrations of a simply supported beam with a central mass and undergoing creep deformation for the two cases (i) creep deformation is completely recoverable (without hysteresis) and (ii) creep deformation is partly recoverable (with hysteresis). The material is of the Ramberg-Osgood type. Numerical techniques were used to find the response of the system. The results indicate that the beam behaves like a soft spring and that amplitude and frequency decrease with time.     

The vibration characteristics of a beam with an axial force

Equations of motion are found for a non-uniform damped Timoshenko beam with a distributed axial force. Principal modes may be extracted by numerical means when the boundary conditions are specified, and the appropriate orthogonality conditions are given. The theory of linear forced vibration can thus be derived. It is an implicit requirement that all axial forces are conservative. That is to say, tangential, follower and partial follower axial forces (whether applied at an extremity or distributed along the beam) are excluded.     

Nonparaxial propagation of a cylindrical beam with Lanczos reduction

We discuss a numerical method based on Lanczos reduction of modeling nonparaxial propagation of a cylindrical symmetric beam. To illustrate the performance and demonstrate the significant difference between nonparaxial and paraxial beams, we consider Gaussian beam propagation in two different settings.     

Control of flexural waves on a beam using distributed vibration neutralisers

This paper is concerned with the use of distributed vibration neutralisers to control the transmission of flexural waves on a beam. Of particular interest is an array of beam-like neutralisers and a continuous plate-like neutraliser. General expressions for wave transmission and reflection metrics either side of the distributed neutralisers are derived. Based on transmission efficiency, the characteristics of multiple neutralisers are investigated in terms of the minimum transmission efficiency, the normalised bandwidth and the shape factor, allowing optimisation of their performance. Analytical results show that the band-stop property of the neutraliser array depends on various factors, including the neutraliser damping, mass, separation distance in the array and the moment arm of each neutraliser. Moreover, it is found that the particular attachment configuration of an uncoupled force-moment-type neutraliser can be used to improve their overall performance. It is also shown that in the limit of many neutralisers in the array, the performance tends to that of a continuous neutraliser.