Showing papers in "Shock and Vibration in 2004"
TL;DR: In this paper, a non-iterative frequency-domain parameter estimation method is proposed based on a weighted least-squares approach and uses multiple-input-multiple-output frequency response functions as primary data.
Abstract: Recently, a new non-iterative frequency-domain parameter estimation method was proposed. It is based on a (weighted) least-squares approach and uses multiple-input-multiple-output frequency response functions as primary data. This so-called "PolyMAX" or polyreference least-squares complex frequency-domain method can be implemented in a very similar way as the industry standard polyreference (time-domain) least-squares complex exponential method: in a first step a stabilisation diagram is constructed containing frequency, damping and participation information. Next, the mode shapes are found in a second least- squares step, based on the user selection of stable poles. One of the specific advantages of the technique lies in the very stable identification of the system poles and participation factors as a function of the specified system order, leading to easy-to-interpret stabilisation diagrams. This implies a potential for automating the method and to apply it to "difficult" estimation cases such as high-order and/or highly damped systems with large modal overlap. Some real-life automotive and aerospace case studies are discussed. PolyMAX is compared with classical methods concerning stability, accuracy of the estimated modal parameters and quality of the frequency response function synthesis.
667 citations
TL;DR: In this paper, an empirical method for particle damping design based on extensive experiments on three structural objects - steel beam, bond arm and bond head stand -was developed to provide guidelines for practical applications.
Abstract: Particle damping is an effective vibration suppression method. The purpose of this paper is to develop an empirical method for particle damping design based on extensive experiments on three structural objects - steel beam, bond arm and bond head stand. The relationships among several key parameters of structure/particles are obtained. Then the procedures with the use of particle damping are proposed to provide guidelines for practical applications. It is believed that the results presented in this paper would be helpful to effectively implement the particle damping for various structural systems for the purpose of vibration suppression.
50 citations
TL;DR: In this paper, the authors proposed a method for vibration suppression of flexible structures based on friction damping in semi-active joints, where conventional rigid connections of a large truss structure are replaced by semiactive friction joints.
Abstract: The present approach for vibration suppression of flexible structures is based on friction damping in semi-active joints. At optimal locations conventional rigid connections of a large truss structure are replaced by semi-active friction joints. Two different concepts for the control of the normal forces in the friction interfaces are implemented. In the first approach each semi-active joint has its own local feedback controller, whereas the second concept uses a global, clipped-optimal controller. Simulation results of a 10-bay truss structure show the potential of the proposed semi-active concept.
47 citations
TL;DR: In this paper, the authors evaluated the shock absorbing characteristics and vibration transmissibility of honeycomb paperboards with different thickness by a series of experimental studies on the drop shock machine and vibration table.
Abstract: Honeycomb paperboard is a kind of environmental-friendly package cushioning material with honeycomb sandwich structure, and may be employed to protect products from shock or vibration damage during distribution. This paper deals with the characterization of properties of honeycomb paperboard relevant to its application for protective packaging in transportation, such as dynamic cushion curves and vibration transmissibility. The main feature of the paper is the evaluation on the shock absorbing characteristics and vibration transmissibility of honeycomb paperboards with different thickness by a series of experimental studies on the drop shock machine and vibration table. By using the fitting polynomial of the curve, the experiential formulas and characteristic coefficients of dynamic cushion curves of honeycomb paperboards with different thickness have been obtained. From the vibration tests with slow sine sweep, the peak frequencies and vibration transmissibility are measured and used to estimate the damping ratios. All the works provide basic data and curves relevant to its application for protective packaging in transportation.
47 citations
TL;DR: In this paper, the transmissibility concept was generalized to multi-degree-of-freedom systems with multiple random excitations, and the definition of a transmissability matrix, relating two sets of responses when the structure is subjected to excitation at a given set of coordinates, was proposed.
Abstract: The transmissibility concept may be generalized to multi-degree-of-freedom systems with multiple random excitations. This generalization involves the definition of a transmissibility matrix, relating two sets of responses when the structure is subjected to excitation at a given set of coordinates. Applying such a concept to an experimental example is the easiest way to validate this method.
45 citations
TL;DR: In this paper, the authors investigated the seismic response of liquid storage tanks isolated by elastomeric bearings and sliding system under real earthquake ground motions, where the continuous liquid mass of the tank is modeled as lumped masses known as sloshing mass, impulsive mass and rigid mass.
Abstract: Seismic response of liquid storage tanks isolated by elastomeric bearings and sliding system is investigated under real earthquake ground motions. The continuous liquid mass of the tank is modeled as lumped masses known as sloshing mass, impulsive mass and rigid mass. The coupled differential equations of motion of the system are derived and solved in the incremental form using Newmark's step-by-step method with iterations. The seismic response of isolated tank is studied to investigate the comparative effectiveness of various isolation systems. A parametric study is also carried out to study the effect of important system parameters on the effectiveness of seismic isolation for liquid storage tanks. The various important parameters considered are: (i) aspect ratio of the tank and (ii) the time period of the isolation systems. It was observed that both elastomeric and sliding systems are found to be effective in reducing the earthquake forces of the liquid storage tanks. However, the elastomeric bearing with lead core is found to perform better in comparison to other systems. Further, an approximate model is proposed for evaluation of seismic response of base-isolated liquid storage tanks. A comparison of the seismic response evaluated by the proposed approximate method and an exact approach is made under different isolation systems and system parameters. It was observed that the proposed approximate analysis provides satisfactory response estimates of the base-isolated liquid storage tanks under earthquake excitation.
39 citations
TL;DR: In this paper, the authors analyze the possibility of assembling together different substructures' models and highlight the important role of rotational DoFs, underlying the difficulty of assembling theoretical and experimental models, for which, usually, the rotational DOFs are not available.
Abstract: Substructures coupling is still an important tool in several applications of modal analysis, especially structural modification and structures assembling. The subject is particularly relevant in virtual prototyping of complex systems and responds to actual industrial needs. This paper analyzes the possibility of assembling together different substructures' models. The important role of rotational DoFs is highlighted, underlying the difficulty of assembling theoretical and experimental models, for which, usually, the rotational DoFs are not available. Expansion techniques can be used to provide this information as well as appropriate modelling of joints. With this information FRF models, modal models and FE models can be appropriately combined together and solutions for several cases of practical interest are presented. The analyzed procedures are tested on purpose-built benchmarks, showing limits and capabilities of each of them.
33 citations
TL;DR: The paper is devoted to the problem of discriminating between operational and natural modes of structures excited by generic inputs and two new techniques are introduced and their capabilities are checked with numerical and experimental data from a paper machine.
Abstract: The paper is devoted to the problem of discriminating between operational and natural modes of structures excited by generic inputs. This case often occurs when the system under analysis holds rotating parts and is contemporary excited by ambient noise; in this case the output-only techniques may fail being easily trapped in a misinterpretation of the system eigenvalues. A survey of the methods available in literature is given, together with the explanation of their failures. To solve this problem, two new techniques are introduced and their capabilities are checked with numerical and experimental data from a paper machine.
28 citations
TL;DR: In this article, classical and advanced theories for free vibrational response of homogeneous and multilayered simply supported plates are compared. And the effect of the Zig-Zag form of the displacement distribution in z as well as of the Interlaminar Continuity of transverse shear and normal stresses at the layer interface were evaluated.
Abstract: This paper assesses classical and advanced theories for free vibrational response of homogeneous and multilayered simply supported plates. Closed form solutions are given for thick and thin geometries. Single layer and multilayered plates made of metallic, composite and piezo-electric materials, are considered. Classical theories based on Kirchhoff and Reissner-Mindlin assumptions are compared with refined theories obtained by enhancing the order of the expansion of the displacement fields in the thickness direction z. The effect of the Zig-Zag form of the displacement distribution in z as well as of the Interlaminar Continuity of transverse shear and normal stresses at the layer interface were evaluated. A number of conclusions have been drawn. These conclusions could be used as desk-bed in order to choose the most valuable theories for a given problem.
27 citations
TL;DR: In this paper, an alternative method based upon coupling techniques is developed, in which rotational receptances are estimated without the need of applying a moment excitation, which is accomplished by introducing a rotational inertia modification when rotating the T-block.
Abstract: The dynamic response of a structure can be described by both its translational and rotational receptances. The latter ones are frequently not considered because of the difficulties in applying a pure moment excitation or in measuring rotations. However, in general, this implies a reduction up to 75% of the complete model. On the other hand, if a modification includes a rotational inertia, the rotational receptances of the unmodified system are needed. In one method, more commonly found in the literature, a so called T-block is attached to the structure. Then, a force, applied to an arm of the T-block, generates a moment together with a force at the connection point. The T-block also allows for angular displacement measurements. Nevertheless, the results are often not quite satisfactory. In this work, an alternative method based upon coupling techniques is developed, in which rotational receptances are estimated without the need of applying a moment excitation. This is accomplished by introducing a rotational inertia modification when rotating the T-block. The force is then applied in its centroid. Several numerical and experimental examples are discussed so that the methodology can be clearly described. The advantages and limitations are identified within the practical application of the method.
27 citations
TL;DR: In this paper, the authors analyzed some aspects related to bifurcation phenomenon in a shape memory oscillator where the restitution force is described by a polynomial constitutive model.
Abstract: The remarkable properties of shape memory alloys have been motivating the interest in applications in different areas varying from biomedical to aerospace hardware. The dynamical response of systems composed by shape memory actuators presents nonlinear characteristics and a very rich behavior, showing periodic, quasi-periodic and chaotic responses. This contribution analyses some aspects related to bifurcation phenomenon in a shape memory oscillator where the restitution force is described by a polynomial constitutive model. The term bifurcation is used to describe qualitative changes that occur in the orbit structure of a system, as a consequence of parameter changes, being related to chaos. Numerical simulations show that the response of the shape memory oscillator presents period doubling cascades, direct and reverse, and crises.
TL;DR: In this article, the wave propagation in and the vibration of cylindrical grid structures are analyzed, where each cell is modelled as an assembly of curved beam elements, formulated according to a mixed interpolation method.
Abstract: The wave propagation in and the vibration of cylindrical grid structures are analyzed. The grids are composed of a sequence of identical elementary cells repeating along the axial and the circumferential direction to form a two-dimensional periodic structure. Two-dimensional periodic structures are characterized by wave propagation patterns that are strongly frequency dependent and highly directional. Their wave propagation characteristics are determined through the analysis of the dynamic properties of the unit cell. Each cell here is modelled as an assembly of curved beam elements, formulated according to a mixed interpolation method. The combined application of this Finite Element formulation and the theory of two-dimensional periodic structures is used to generate the phase constant surfaces, which define, for the considered cell lay-out, the directions of wave propagation at assigned frequencies. In particular, the directions and frequencies corresponding to wave attenuation are evaluated for cells of different size and geometry, in order to identify topologies with attractive wave attenuation and vibration confinement characteristics. The predictions from the analysis of the phase constant surfaces are verified by estimating the forced harmonic response of complete cylindrical grids, obtained through the assembly of the unit cells. The considered analysis provides invaluable guidelines for the investigation of the dynamic properties and for the design of grid stiffened cylindrical shells with unique vibration confinement characteristics.
Abstract: A critical analysis of the available methods for the assessment of structural concrete bridges through the observation of their dynamic response is carried out A mathematical model for the evaluation of the natural frequencies shift due to bridge damage is applied to the case of an existing reinforced concrete bridge The numerical results, along with the general structure of the mathematical problem, allow discussing some limitation and drawbacks of the dynamic methods Namely the need for a reference set of the bridges dynamic properties before the onset of damage and the effect of the ambient temperature variation may lead, in many cases, to unreliable estimates of the structural condition of the investigated bridges
TL;DR: In this article, a sliding contact between the overhead line (OHL) and the collector strips mounted on the pantograph head is used to ensure the contact pressure for the electrical contact.
Abstract: Trains current collection for traction motors is obtained by means of a sliding contact between the overhead line (OHL) and the collector strips mounted on the pantograph head. The normal force by which the collector presses against the contact wire ensures the contact pressure for the electrical contact. As the train speed increases, the variation of contact force between pantograph and catenary increases, and the pantograph-OHL dynamic interaction becomes greater. This condition causes excessive mechanical wear and contact wire uplift (for high values of contact forces), and leads to high percentage of contact loss, arcing and electrically related wear.
TL;DR: In this article, an analytical procedure is given to study the free vibration characteristics of laminated nonhomogeneous orthotropic thin circular cylindrical shells resting on elastic foundation, accounting for Karman type geometric nonlinearity.
Abstract: In this paper an analytical procedure is given to study the free vibration characteristics of laminated non-homogeneous orthotropic thin circular cylindrical shells resting on elastic foundation, accounting for Karman type geometric non-linearity. At first, the basic relations and modified Donnell type stability equations, considering finite deformations, have been obtained for laminated thin orthotropic circular cylindrical shells, the Young's moduli of which varies piecewise continuously in the thickness direction. Applying Galerkin method to the latter equations, a non-linear time dependent differential equation is obtained for the displacement amplitude. The frequency is obtained from this equation as a function of the shell displacement amplitude. Finally, the effect of elastic foundation, non-linearity, non-homogeneity, the number and ordering of layers on the frequency is found for different mode numbers. These results are given in the form of tables and figures. The present analysis is validated by comparing results with those in the literature.
TL;DR: In this article, the authors compare the dynamic behavior of a wheelset on a full scale roller and on a scaled roller rig to be applied in the case of the test bench developed for experimental analysis.
Abstract: This paper addresses the comparison of dynamic behavior of a wheelset on roller and on rails. The development of equations of kinematics and motion allow to put in evidence the intrinsic differences between the dynamic behavior on rail and on roller. The stylized conical profile approximation of the wheel allows to focus the attention on the differences in creepages definition and in contact point shift due to the roller curvature. The treatise is addressed to a full scale roller and can be extended in the case of scaled roller rig to be applied in the case of the test bench developed for experimental analysis. In the present paper numerical simulation and examples are used to proof the analytical results.
TL;DR: In this article, the vibration characteristics of stiffened plates with cutouts subjected to uni-axial in-plane uniform edge loading at the plate boundaries are investigated using the finite element method.
Abstract: Vibration characteristics of stiffened plates with cutouts subjected to uni-axial in-plane uniform edge loading at the plate boundaries are investigated using the finite element method. The characteristic equations for the natural frequencies, buckling loads and their corresponding mode shapes are obtained from the equation of motion. The vibration frequencies and buckling load parameters for various modes of stiffened plates with cutouts have been determined for simply supported and clamped edge boundary conditions. In the structure modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. Numerical results are presented for a range of hole to plate width ratios of 0 to 0.8. The correlations of the natural frequencies and buckling parameters obtained by the present approach with those available in the literature are found to show good agreement.
TL;DR: In this article, an analysis of the handling and stability of two-wheeled vehicles depends on structural flexibility, and the authors deal with laboratory experimentation carried out to identify the vehicle's structural modes of vibration and obtain information about the influence of structural modes on weave and wobble modes.
Abstract: An analysis of the handling and stability of two-wheeled vehicles depends on structural flexibility. This paper deals with laboratory experimentation carried out to identify the vehicle's structural modes of vibration. The tests were carried out in stationary conditions considering several combinations of constraints. Although the testing conditions did not correspond completely to actual road conditions, information about the influence of structural modes on weave and wobble modes was obtained. An analysis of the Frequency Response Functions obtained from several kinds of tests made it possible to establish the best testing conditions to obtain the desired information. Experimental results regarding a super-sport motorcycle and a maxi-scooter are presented and discussed in this paper.
TL;DR: In this article, a closed-form solution in form of infinite series was developed for the radiation of sound from a spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity, while positioned within an acoustic quarterspace.
Abstract: Radiation of sound from a spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity, while positioned within an acoustic quarterspace is analyzed in an exact manner. The formulation utilizes the appropriate wave field expansions along with the translational addition theorem for spherical wave functions in combination with the classical method of images to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which the spherical source, vibrating in the pulsating (n = 0) and translational oscillating (n =1) modes, is positioned near the rigid boundary of a water-filled quarterspace. Subsequently, the basic acoustic field quantities such as the modal acoustic radiation impedance load and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system.
TL;DR: In this article, a new method is presented for synthesizing the dynamic responses of a complex structure based upon the frequency response functions of the substructures, which is shown to be superior to traditional methods for several reasons: (i) it can be applied to a generic class of systems.
Abstract: A new method is presented for synthesizing the dynamic responses of a complex structure based upon the frequency response functions of the substructures. This method is shown to be superior to traditional methods for several reasons: (i) It can be applied to a generic class of systems. (ii) The analyst is spared the responsibilities of eliminating the coupling forces and rearranging the equations of motion. (iii) The coupling forces and the responses of the total system can be obtained simultaneously and efficiently.
TL;DR: In this paper, the authors investigated the application of the analysis of transmission of waves in elastic media in order to predict the dynamic response to pyroshocks, which are high frequency transients due to pyrotechnic devices used in aerospace engineering to deploy solar arrays and antennae, separate subsystems from the spacecraft or separate the spacecraft itself from the base stage booster.
Abstract: Pyroshocks are high frequency transients due to pyrotechnic devices used in aerospace engineering in order to deploy solar arrays and antennae, separate subsystems from the spacecraft or separate the spacecraft itself from the base stage booster; their prediction is usually complex and very time consuming. The aim of this article is to investigate on the application of the analysis of transmission of waves in elastic media in order to predict the dynamic response to pyroshocks. The work is completed by numerical examples, related to components of common use in the aerospace engineering field, showing the comparison between results obtained by using both MSC-NASTRAN and this novel application of wave propagation analysis. Launch vehicles make use of explosive charges to separate structural subsystems (such as a satellite) from the launcher, deploy appendices, activate or deactivate subsystems (such as valves of the propulsion subsystem). These devices have the drawback of giving rise to high accelerations (called pyroshocks) and extremely short transients with a very broad-band frequency spectrum that may be highly dangerous for flight equipments such as electronic devices. The evaluation of the dynamic response to pyroshocks is a hard task: in this case classical techniques based on the Finite Element Method (FEM) are not efficient, since at high frequency a huge number of elements is required
TL;DR: In this paper, the effects of generalized damping distributions on vibrating linear systems were studied in terms of modal analysis, defining and discussing the orthogonality properties of their eigenfunctions.
Abstract: This paper deals with the effects of generalized damping distributions on vibrating linear systems. The attention is focused on continuous linear systems with distributed and possibly non-proportional viscous damping, which are studied in terms of modal analysis, defining and discussing the orthogonality properties of their eigenfunctions.
TL;DR: In this paper, a new fluid mount design is proposed to reduce the fluid mount notch frequency tuning cycle time, and the notch frequency can be easily modified without the need for any redesigns.
Abstract: Passive fluid mounts are commonly used in the automotive and aerospace applications to isolate the cabin from the engine noise and vibration. Due to manufacturing and material variabilities, no two identical fluid mount designs act the same. So, fluid mounts are tuned one by one before it is shipped out to customers. In some cases, for a batch of fluid mounts manufactured at the same time, one is tuned and the rest is set to the same settings. In some cases they are shipped as is with its notch frequency not being in its most optimum location. Since none of the passive fluid mount parameters are controllable, the only way to tune the mount is to redesign the mount by changing fluid, changing inertia track length or diameter, or changing rubber stiffness. This trial and error manufacturing process is very costly. To reduce the fluid mount notch frequency tuning cycle time, a new fluid mount design is proposed. In this new fluid mount design, the notch frequency can be easily modified without the need for any redesigns. In this paper, the new design concept, and its mathematical model and simulation results will be presented.
TL;DR: In this article, the root flexibility of a turbine blade is idealized by a continuum model unlike the discrete model approach of a combination of translational and rotational elastic springs, as used by other researchers, and the cross-section properties of the fir tree root of the blade considered as an example are expressed by assigning proper order polynomial functions similar to cross-sectional properties of a tapered blade.
Abstract: The purpose of this paper is to extend a previously published beam model of a turbine blade including the centrifugal force field and root flexibility effects on a finite element model and to demonstrate the performance, accuracy and efficiency of the extended model for computing the natural frequencies. Therefore, only the modifications due to rotation and elastic root are presented in great detail. Considering the shear center effect on the transverse displacements, the geometric stiffness matrix due to the centrifugal force is developed from the geometric strain energy expression based on the large deflections and the increase of torsional stiffness because of the axial stress. In this work, the root flexibility of the blade is idealized by a continuum model unlike the discrete model approach of a combination of translational and rotational elastic springs, as used by other researchers. The cross-section properties of the fir-tree root of the blade considered as an example are expressed by assigning proper order polynomial functions similar to cross-sectional properties of a tapered blade. The correctness of the present extended finite element model is confirmed by the experimental and calculated results available in the literature. Comparisons of the present model results with those in the literature indicate excellent agreement.
TL;DR: In this paper, a refined numerical analysis of the dynamic behavior of roller chain drives is performed considering the roller assembly as a three-layer structure with mechanical clearance between each two of the mechanical components.
Abstract: A refined numerical analysis of the dynamic behavior of roller chain drives is performed considering the roller assembly as a three-layer structure with mechanical clearance between each two of the mechanical components. Instead of using analytical method, explicit finite element technique is utilized for modeling and simulating the dynamic behavior of chain drives. The complete standard geometry of sprockets and all components of chain links are used in the developed model with minor geometry simplification. A primary goal is to achieve a more complete understanding of the dynamic behavior of chain drives especially in the transient vibration response of the engaging rollers, which is crucial for noise emission calculation. The simulated velocity response of the engaging rollers and roller-sprocket contact forces achieved using the full model are compared with what found by the simple model which has been adopted in analytical study of chain roller dynamics.
TL;DR: By defining virtual antiresonances, this extension of the model updating method allows the use of previously identified modal data, and can be evaluated from a truncated modal expansion, and do not correspond to any physical system.
Abstract: This paper considers an extension of the model updating method that minimizes the antiresonance error, besides the natural frequency error. By defining virtual antiresonances, this extension allows the use of previously identified modal data. Virtual antiresonances can be evaluated from a truncated modal expansion, and do not correspond to any physical system. The method is applied to the Finite Element model updating of the GARTEUR benchmark, used within an European project on updating. Results are compared with those previously obtained by estimating actual antiresonances after computing low and high frequency residuals, and with results obtained by using the correlation (MAC) between identified and analytical mode shapes.
TL;DR: In this paper, a genetic algorithm based approach is proposed to achieve an optimal distribution of stiffening ribs and damping material for vehicle noise and vibration reduction, which takes into account both the vibroacoustic performance and the weight and cost reduction.
Abstract: Vehicle noise and vibration levels are basic parameters in passenger comfort. Both static and dynamic stiffness of sheet metal parts is commonly increased by means of stiffening ribs. Vibrations are also reduced by adding a layer of damping material on the floor, the roof, the firewall and other parts of the vehicle. In common practice the panels to be treated are ribbed according to criteria based on the designer's experience, rather than on well defined design procedures and are uniformly covered by a layer of damping material. However, these are not efficient design solutions, especially with regard to the effectiveness of vibration reduction and to weight containment. In this paper a novel approach to achieve an optimal distribution of stiffening ribs and damping material will be presented. The proposed method is based on a Genetic Algorithm (G.A.) procedure which takes into account both the vibroacoustic performance and the weight and cost reduction. A simple case study will be illustrated to demonstrate the capabilities of the developed procedure.
TL;DR: In this paper, the damped vibration of a laminated cantilever beam with a single closing delamination was investigated in the time domain using a dynamic contact algorithm developed by the authors, which is based on the Newmark method and also incorporates a Newton-Raphson based procedure for resolving the equation of motion.
Abstract: Certain results are presented in this paper on damped vibration of a laminated cantilever beam with a single closing delamination. In order to investigate this task the finite element method has been applied in the current study. For modelling the beam higher order shear deformation beam finite elements have been used. The vibration of the beam is investigated in the time domain using a dynamic contact algorithm developed by the authors. The algorithm is based on the Newmark method and also incorporates a Newton-Raphson based procedure for resolving the equation of motion. The time series obtained from solving the equation of motion have been subsequently analysed in the frequency domain by using FFT (Fast Fourier Transform). The vibration responses of the beam due to various harmonic and impulse excitations, at different delamination locations, and for different delamination lengths, as well as changes in the dissipation of damping energy due to the delamination, have all been considered in the paper.
TL;DR: In this article, a theoretical method based on the Transfer Matrix Formulation and Wavelet Transforms is developed in order to evaluate the influence of periodicity, variable geometry and material properties on the wave propagation characteristics of axis-symmetric shells.
Abstract: A theoretical method based on the Transfer Matrix Formulation and Wavelet Transforms is developed in order to effec- tively investigate the influence of periodicity, variable geometry and material properties on the wave propagation characteristics of axis-symmetric shells. Several experiments have been conducted to verify the numerical predictions and to demonstrate that the Wavelet Transform is a very powerful tool to uniquely identify and compare the energy distribution both in the time and frequency domain. Thin shells are modeled as two-dimensional wave-guides, where the propagation of the longitudinal waves is coupled with the flexural (radial) waves. Variations of the wall thickness, medium radius and element length of the shell can effectively filter out/stop undesirable bands of frequencies from the longitudinal and/or the transverse wave characteristics. The principal parameter that influences the width and location of the stop bands is the ratio between the cross sections at the two ends of the shell element. Sophisticated exponential profiles and simpler linear taper are implemented and compared. Functionally graded materials(FGM) are also investigated as an alternative way to influence the parameters of the stop bands. Combinations of the FGM and geometric taper give the flexibility needed for some very demanding applications. Different types of periodic taper configurations have complementary effects on the wave characteristics. Combinations of these complex geometries (bi-periodic tapered cells) are presented and shown to produce the most effectual energy redistribution.
TL;DR: In this paper, an analysis and a discussion about the robustness of the technique with respect to the errors than can affect estimation of the values of the system parameters is presented, and an analysis of the error model is presented.
Abstract: Open-loop control techniques, such as command input preshaping, are quite sensible to modelling errors and noise. In the paper, an analysis and a discussion about the robustness of the technique with respect to the errors than can affect estimation of the values of the system parameters is presented.