Showing papers in "Shock and Vibration in 2006"

The Effect of Degree of Saturation of Sand on Detonation Phenomena Associated with Shallow-Buried and Ground-Laid Mines

Abstract: A new materials model for sand has been developed in order to include the effects of the degree of saturation and the deformation rate on the constitutive response of this material. The model is an extension of the original compaction materials model for sand in which these effects were neglected. The new materials model for sand is next used, within a non-linear-dynamics transient computational analysis, to study various phenomena associated with the explosion of shallow-buried and ground-laid mines. The computational results are compared with the corresponding experimental results obtained through the use of an instrumented horizontal mine-impulse pendulum, pressure transducers buried in sand and a post-detonation metrological study of the sand craters. The results obtained suggest that the modified compaction model for sand captures the essential features of the dynamic behavior of sand and accounts reasonably well for a variety of the experimental findings related to the detonation of shallow-buried or ground-laid mines.

Some recent developments in adaptive tuned vibration absorbers/neutralisers

Abstract: The vibration absorber has been used for vibration control purposes in many sectors of engineering from aerospace, to automotive to civil, for the past 100 years or so. A limitation of the device, however, is that it acts like a notch filter, only being effective over a narrow band of frequencies. Recent developments have overcome this limitation by making it possible to tune the device over a range of frequencies. This has been achieved by incorporating a variable stiffness element that can be adjusted in real-time. In this paper, some ways in which stiffness change can be achieved in practice are reviewed and some examples of prototype adaptive tuned vibration absorbers (ATVAs) are described. A simple control scheme to automatically tune an ATVA is also presented.

Accurate assessment of computed order tracking

Abstract: Spectral vibration analysis using the Fourier transform is the most common technique for evaluating the mechanical condition of machinery working in stationary regimen. However, machinery operating in transient modes, such as variable speed equipment, generates spectra with distinct frequency content at each time, and the standard approach is not directly applicable for diagnostic. The "order tracking" technique is a suitable tool for analyzing variable speed machines. We have studied the computed order tracking (COT), and a new computed procedure is proposed for solving the indeterminate results generated by the traditional method at constant speed. The effect on the accuracy of the assumptions inherent in the COT was assessed using data from various simulations. The use of these simulations allowed us to determine the effect on the overall true accuracy of the method of different user-defined factors: the signal and tachometric pulse sampling frequency, the method of amplitude interpolation, and the number of tachometric pulses per revolution. Tests on real data measured on the main transmissions of a mining shovel were carried out, and we concluded that the new method is appropriate for the condition monitoring of this type of machine.

Coupling sensing hardware with data interrogation software for structural health monitoring

Abstract: The process of implementing a damage detection strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM). The authors' approach is to address the SHM problem in the context of a statistical pattern recognition paradigm. In this paradigm, the process can be broken down into four parts: (1) Operational Evaluation, (2) Data Acquisition and Cleansing, (3) Feature Extraction and Data Compression, and (4) Statistical Model Development for Feature Discrimination. These processes must be implemented through hardware or software and, in general, some combination of these two approaches will be used. This paper will discuss each portion of the SHM process with particular emphasis on the coupling of a general purpose data interrogation software package for structural health monitoring with a modular wireless sensing and processing platform. More specifically, this paper will address the need to take an integrated hardware/software approach to developing SHM solutions.

Vibrational energy flow analysis of corrected flexural waves in Timoshenko beam - Part I: Theory of an energetic model

Abstract: In this paper, an energy flow model is developed to analyze transverse vibration including the effects of rotatory inertia as well as shear distortion, which are very important in the Timoshenko beam transversely vibrating in the medium-to-high frequency ranges. The energy governing equations for this energy flow model are newly derived by using classical displacement solutions of the flexural motion for the Timoshenko beam, in detail. The derived energy governing equations are in the general form incorporating not only the Euler-Bernoulli beam theory used for the conventional energy flow model but also the Rayleigh, shear, and Timoshenko beam theories. Finally, to verify the validity and accuracy of the derived model, numerical analyses for simple finite Timoshenko beams were performed. The results obtained by the derived energy flow model for simple finite Timoshenko beams are compared with those of the classical solutions for the Timoshenko beam, the energy flow solution, and the classical solution for the Euler-Bernoulli beam with various excitation frequencies and damping loss factors of the beam. In addition, the vibrational energy flow analyses of coupled Timoshenko beams are described in the other companion paper.

Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads

Abstract: The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.

Vibrational energy flow analysis of corrected flexural waves in Timoshenko beam - Part II: Application to coupled Timoshenko beams

Abstract: This paper presents the methodology for the energy flow analysis of coupled Timoshenko beam structures and various numerical applications to verify the developed methodology. To extend the application of the energy flow model for corrected flexural waves in the Timoshenko beam, which is developed in the other companion paper, to coupled structures, the wave transmission analyses of general coupled Timoshenko beam systems are performed. First, power transmission and reflection coefficients for all kinds of propagating waves in the general, coupled Timoshenko beam structures are derived by the wave transmission approach. In numerical applications, the energy flow solutions using the derived coefficients agree well with the classical solutions for various exciting frequencies, damping loss factors, and coupled Timoshenko beam structures. Additionally, the numerical results for the Timoshenko beam are compared with those for the Euler-Bernoulli beam.

Closed loop finite element modeling of piezoelectric smart structures

Abstract: The objective of this paper is to develop a general design and analysis scheme for actively controlled piezoelectric smart structures. The scheme involves dynamic modeling of a smart structure, designing control laws and closed-loop simulation in a finite element environment. Based on the structure responses determined by finite element method, a modern system identification technique known as Observer/Kalman filter Identification (OKID) technique is used to determine the system Markov parameters. The Eigensystem Realization Algorithm (ERA) is then employed to develop an explicit state space model of the equivalent linear system for control law design. The Linear Quadratic Gaussian (LQG) control law design technique is employed to design a control law. By using ANSYS parametric design language (APDL), the control law is incorporated into the ANSYS finite element model to perform closed loop simulations. Therefore, the control law performance can be evaluated in the context of a finite element environment. Finally, numerical examples have demonstrated the validity and efficiency of the proposed design scheme. Without any further modifications, the design scheme can be readily applied to other complex smart structures.

Chaos control in mechanical systems

Abstract: Chaos has an intrinsically richness related to its structure and, because of that, there are benefits for a natural system of adopting chaotic regimes with their wide range of potential behaviors. Under this condition, the system may quickly react to some new situation, changing conditions and their response. Therefore, chaos and many regulatory mechanisms control the dynamics of living systems, conferring a great flexibility to the system. Inspired by nature, the idea that chaotic behavior may be controlled by small perturbations of some physical parameter is making this kind of behavior to be desirable in different applications. Mechanical systems constitute a class of system where it is possible to exploit these ideas. Chaos control usually involves two steps. In the first, unstable periodic orbits (UPOs) that are embedded in the chaotic set are identified. After that, a control technique is employed in order to stabilize a desirable orbit. This contribution employs the close-return method to identify UPOs and a semi-continuous control method, which is built up on the OGY method, to stabilize some desirable UPO. As an application to a mechanical system, a nonlinear pendulum is considered and, based on parameters obtained from an experimental setup, analyses are carried out. Signals are generated by numerical integration of the mathematical model and two different situations are treated. Firstly, it is assumed that all state variables are available. After that, the analysis is done from scalar time series and therefore, it is important to evaluate the effect of state space reconstruction. Delay coordinates method and extended state observers are employed with this aim. Results show situations where these techniques may be used to control chaos in mechanical systems.

Vibration Analysis of Rotating Tapered Timoshenko Beams by a New Finite Element Model

Abstract: A new finite element model is developed and subsequently used for transverse vibrations of tapered Timoshenko beams with rectangular cross-section. The displacement functions of the finite element are derived from the coupled displacement field (the polynomial coefficients of transverse displacement and cross-sectional rotation are coupled through consideration of the differential equations of equilibrium) approach by considering the tapering functions of breadth and depth of the beam. This procedure reduces the number of nodal variables. The new model can also be used for uniform beams. The stiffness and mass matrices of the finite element model are expressed by using the energy equations. To confirm the accuracy, efficiency, and versatility of the new model, a semi-symbolic computer program in MATLAB® is developed. As illustrative examples, the bending natural frequencies of non-rotating/rotating uniform and tapered Timoshenko beams are obtained and compared with previously published results and the results obtained from the finite element models of solids created in ABAQUS. Excellent agreement is found between the results of new finite element model and the other results.

Nonlinear dynamics and chaos in systems with discontinuous support

Abstract: Non-smooth systems are abundant in nature being usually related to physical systems with dry friction, impact and backlash. These systems operate in different modes, and the transition from one mode to another can often be idealized as an instantaneous or discrete transition. Since the time scale of this transition is much smaller than the scale of the individual modes dynamics, its mathematical modeling can be lead as non-smooth. This contribution uses a smoothened switch model to analyze non-smooth systems. The procedure seems to be effective to deal with this kind of system, presenting advantages for the numerical implementation. As an application of the general formulation, a single-degree of freedom oscillator with discontinuous support is analyzed. System dynamical behavior shows a rich response, presenting dynamical jumps, bifurcations and chaos.

Transient dynamic response of delaminated composite rotating shallow shells subjected to impact

Abstract: In this paper a transient dynamic finite element analysis is presented to study the response of delaminated composite pretwisted rotating shallow shells subjected to low velocity normal impact. Lagrange's equation of motion is used to derive the dynamic equilibrium equation and moderate rotational speeds are considered wherein the Coriolis effect is negligible. An eight noded isoparametric plate bending element is employed in the finite element formulation incorporating rotary inertia and effects of transverse shear deformation based on Mindlin's theory. To satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front a multipoint constraint algorithm is incorporated which leads to unsymmetric stiffness matrices. The modified Hertzian contact law which accounts for permanent indentation is utilized to compute the contact force, and the time dependent equations are solved by Newmark's time integration algorithm. Parametric studies are performed in respect of location of delamination, angle of twist and rotational speed for centrally impacted graphite-epoxy composite cylindrical shells.

Sensitivity Analysis of Viscoelastic Structures

Abstract: In the context of control of sound and vibration of mechanical systems, the use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications. Numerical models based on finite element discretization have been frequently used in the analysis and design of complex structural systems incorporating viscoelastic materials. Such models must account for the typical dependence of the viscoelastic characteristics on operational and environmental parameters, such as frequency and temperature. In many applications, including optimal design and model updating, sensitivity analysis based on numerical models is a very usefull tool. In this paper, the formulation of first-order sensitivity analysis of complex frequency response functions is developed for plates treated with passive constraining damping layers, considering geometrical characteristics, such as the thicknesses of the multi-layer components, as design variables. Also, the sensitivity of the frequency response functions with respect to temperature is introduced. As an example, response derivatives are calculated for a three-layer sandwich plate and the results obtained are compared with first-order finite-difference approximations.

A novel engine mount with semi-active dry friction damping

Abstract: In this paper the authors present a semi-active engine mount with a controllable friction damper. The normal force of the friction contact is applied by an electromagnetic actuator and can be varied dynamically. The nonlinear current-force-relation of the actuator is linearized. To account for wear and assembly tolerances, an initialization method is developed, that is based on indirect measurement of the actuators inductance. The friction contact is made up of industrial friction pads and a friction rod of steel. The friction model used is suitable especially for small oscillations of the friction damper. The control policy imitates viscous damping forces that exert a minimum of harmonics. Damping is activated only when necessary. Finally the friction mount is compared to the original mount in a row of test rack experiments and also in the car.

An FFT-based spectral analysis method for linear discrete dynamic systems with non-proportional damping

Abstract: This paper proposes a fast Fourier transforms (FFT)-based spectral analysis method for the dynamic analysis of linear discrete dynamic systems which have non-proportional viscous damping and are subjected to non-zero initial conditions. To evaluate the proposed FFT-based spectral analysis method, the forced vibration of a three degree-of-freedom (DOF) system is considered as an illustrative problem. The accuracy of the proposed FFT-based spectral analysis method is evaluated by comparing the forced vibration responses obtained by the present FFT-based spectral analysis method with those obtained by using the well-known Runge-Kutta method and modal analysis method.

Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback

Abstract: Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.

Reliability and Optimization of Structural Systems

Abstract: As is well known, the classical Kriging-based probabilistic approaches such as the Active learning method combining Kriging and Monte Carlo Simulations MCS (named AK-MCS method) or the method combining Kriging and Importance Sampling IS (named AK-IS method) involve the construction of a surrogate Kriging metamodel based on the responses of a small design of experiments computed using the mechanical model. This approximate Kriging meta-model is then successively updated via an enrichment process by selecting new training points that are close to the limit state surface using a learning function. The essential issues in these approaches are that both the choice of a ‘best new point’ and the stopping criterion are defined from the perspective of individual responses, which may lead to some extra evaluations of unnecessary added training points. To overcome this shortcoming, a reliable and efficient probabilistic methodology based on an enhanced Kriging model (called Global Sensitivity Analysis-enhanced Surrogate GSAS modeling) was proposed by Hu and Mahadevan (2016). In this method, both the convergence criterion and the strategy of selecting new training points are defined from the perspective of reliability estimate instead of individual responses of MCS or IS points. A global sensitivity analysis is performed to select the optimal new training point and the convergence criterion is reached based on the desired accuracy of the reliability estimate. This method is applied in this paper in combination with the classical MCS or IS approach in order to reduce the number of calls of the mechanical model with respect to the corresponding classical AK-MCS and AK-IS approaches. It is used for the probabilistic analysis of the ultimate limit state of a strip footing resting on a spatially varying soil. The aim is the computation of the failure probability against soil punching. The mechanical model was based on numerical simulations using the finite difference code FLAC3D. The soil behavior was modeled using a conventional elastic-perfectly plastic model based on Mohr-Coulomb failure criterion. The soil cohesion c and angle of internal friction φ were modeled as two anisotropic non-Gaussian random fields. An anisotropic square exponential autocorrelation function was used for the two random fields. EOLE methodology was used to discretize these fields. All the other soil parameters are assumed to be deterministic. The numerical results obtained from the combination of GSAS with either MCS or IS are compared to those obtained from the AK-MCS and AK-IS approaches. A significant reduction in the number of calls to the mechanical model was observed in both cases where GSAS was introduced in the probabilistic model. It should be noted that the probabilistic models allow one to obtain not only the failure probability but also the reliability index and the corresponding design point. The critical realization obtained at the design point was shown to be symmetrical with respect to the central vertical axis of the foundation with the weaker soil properties near the footing, the stronger soil being far from the footing. A.-K. El Haj, A.-H. Soubra and T. Al-Bittar

Hydraulic power plant machine dynamic diagnosis

Abstract: A method how to perform an entire structural and hydraulic diagnosis of prototype Francis power machines is presented and discussed in this report. Machine diagnosis of Francis units consists on a proper evaluation of acquired mechanical, thermal and hydraulic data obtained in different operating conditions of several rotary and non rotary machine components. Many different physical quantities of a Francis machine such as pressure, strains, vibration related data, water flow, air flow, position of regulating devices and displacements are measured in a synchronized way so that a relation of cause an effect can be developed for each operating condition and help one to understand all phenomena that are involved with such kind of machine. This amount of data needs to be adequately post processed in order to allow correct interpretation of the machine dynamics and finally these data must be compared with the expected calculated data not only to fine tuning the calculation methods but also to accomplish fully understanding of the influence of the water passages on such machines. The way how the power plant owner has to operate its Francis machines, many times also determined by a central dispatcher, has a high influence on the fatigue life time of the machine components. The diagnostic method presented in this report helps one to understand the importance of adequate operation to allow a low maintenance cost for the entire power plant. The method how to acquire these quantities is discussed in details together with the importance of correct sensor balancing, calibration and adequate correlation with the physical quantities. Typical results of the dynamic machine behavior, with adequate interpretation, obtained in recent measurement campaigns of some important hydraulic turbines were presented. The paper highlights the investigation focus of the hydraulic machine behavior and how to tailor the measurement strategy to accomplish all goals. Finally some typical recommendations based on the experience obtained on previous diagnostic reports of Francis turbines are performed in order to allow a better and safe operation of these power plant units.

A Monolithic High-G SOI-MEMS Accelerometer for Measuring Projectile Launch and Flight Accelerations

Abstract: Analog Devices (ADI) has designed and fabricated a monolithic high-g acceleration sensor (ADXSTC3-HG) fabricated with the ADI silicon-on-insulator micro-electro-mechanical system (SOI-MEMS) process. The SOI-MEMS sensor structure has a thickness of 10 um, allowing for the design of inertial sensors with excellent cross-axis rejection. The high-g accelerometer discussed in this paper was designed to measure in-plane acceleration to 10,000 g while subjected to 100,000 g in the orthogonal axes. These requirements were intended to meet Army munition applications. The monolithic sensor was packaged in an 8-pin leadless chip carrier (LCC-8) and was successfully demonstrated by the US Army Research Laboratory (ARL) as part of an inertial measurement unit during an instrumented flight experiment of artillery projectiles launched at 15,000 g.

Vision influence on whole-body human vibration comfort levels

Abstract: The well being of people needs to be a priority in the modern world. In that respect, vibration cannot be one more cause of stress. Besides that, vibration comfort is very important, since high levels may cause health or even tasks' accomplishment problems. Several parameters may influence the levels of vibration a human being supports. Among them, one can mention the influence of gender, age, corporeal mass index (CMI), temperature, humor, anxiety, hearing, posture, vision, etc. The first three parameters mentioned were already investigated in previous studies undertaken by GRAVI (Group of Acoustics and Vibration) researchers. In this paper, the influence of vision is evaluated. The main objective with this series of tests performed is to try to quantify in a future the influence of each parameter in a global vibration comfort level. Conclusions are presented for the parameter investigated.

Natural frequencies and modal damping ratios identification of civil structures from ambient vibration data

Abstract: Damping is a mechanism that dissipates vibration energy in dynamic systems and plays a key role in dynamic response prediction, vibration control as well as in structural health monitoring during service. In this paper a time domain and a time-scale domain approaches are used for damping estimation of engineering structures, using ambient response data only. The use of tests under ambient vibration is increasingly popular today because they allow to measure the structural response in service. In this paper we consider two engineering structures excited by ambient forces. The first structure is the 310 m tall TV tower recently constructed in the city of Nanjing in China. The second example concerns the Jinma cable-stayed bridge that connects Guangzhou and Zhaoqing in China. It is a single tower, double row cable-stayed bridge supported by 112 stay cables. Ambient vibration of each cable is carried out using accelerometers. From output data only, the modal parameter are extracted using a subspace method and the wavelet transform method.

Reduction of Contact Forces in a Rotor-Stator-System in case of Rubbing through Active Auxiliary Bearing

Abstract: The present manuscript deals with the problem of rotor-stator rubbing. Due to performance increase in rotating machinery, rubbing processes happen more frequently. These are very complicated mechanisms that lead to high impact loads, vibrations and instability. The authors propose a control technique by using an active auxiliary bearing to overcome the problem of rubbing. The control concept enables a transition of the rotor towards a contact situation (with an auxiliary bearing) without rebounding and loss of contact. To investigate the practical feasibility of this approach, numerical simulation has been used to show that using this control concept the impulse (and contact force respectively) can be significantly decreased. Experiments to validate the theoretical findings are already in progress and will be published soon.

Comparison of estimation techniques for vibro-acoustic transfer path analysis

Abstract: Vibro-acoustic Transfer Path Analysis (TPA) is a tool to evaluate the contribution of different energy propagation paths between a source and a receiver, linked to each other by a number of connections. TPA is typically used to quantify and rank the relative importance of these paths in a given frequency band, determining the most significant one to the receiver. Basically, two quantities have to be determined for TPA: the operational forces at each transfer path and the Frequency Response Functions (FRF) of these paths. The FRF are obtained either experimentally or analytically, and the influence of the mechanical impedance of the source can be taken into account or not. The operational forces can be directly obtained from measurements using force transducers or indirectly estimated from auxiliary response measurements. Two methods to obtain the operational forces indirectly - the Complex Stiffness Method (CSM) and the Matrix Inversion Method (MIM) - associated with two possible configurations to determine the FRF - including and excluding the source impedance - are presented and discussed in this paper. The effect of weak and strong coupling among the paths is also commented considering the techniques previously presented. The main conclusion is that, with the source removed, CSM gives more accurate results. On the other hand, with the source present, MIM is preferable. In the latter case, CSM should be used only if there is a high impedance mismatch between the source and the receiver. Both methods are not affected by a higher or lower degree of coupling among the transfer paths.

Dynamic Stability of a Circular Pre-Stressed Elastic Orthotropic Plate Subjected to Shock Excitation

Abstract: The problem on low-velocity impact of an elastic body upon a pre-stressed circular orthotropic plate possessing cylindrical anisotropy is considered. The dynamic behavior of the plate is described by equations taking the rotary inertia and transverse shear deformations into account. Longitudinal compressing forces are uniformly distributed along the plate's median plane. Contact interaction is modeled by a linear spring, and a force arising in it is the linear approximation of Herts'z contact force. During the shock interaction of the impactor with the plate, the waves which are the surfaces of strong discontinuity are generated in the plate and begin to propagate. Behind the fronts of these waves, the solution is constructed in terms of ray series, which coefficients are the different order discontinuities in partial time-derivatives of the desired functions, and a variable is the time elapsed after the wave arrival at the plate's point under consideration. The ray series coefficients are determined from recurrent equations within accuracy of arbitrary constants, which are then determined from the conditions of dynamic contact interaction of the impactor with the target. The found arbitrary constants allow one to construct the solution both within and out of the contact region. The analysis of the solution obtained enables one to find out the new effect and to make the inference that under a certain critical magnitude of the compression force the orthotropic plate goes over into the critical state, what is characterized by 'locking' the shear wave within the contact region, resulting in plate damage within this zone as soon as the compression force exceeds its critical value.

Flight path reconstruction and parameter estimation using output-error method

Abstract: This work describes the application of the output-error method using the Levenberg-Marquardt optimization algorithm to the Flight Path Reconstruction (FPR) problem, which constitutes an important preliminary step towards the aircraft parameter identification. This method is also applied to obtain the aerodynamic and control derivatives of a regional jet aircraft from flight test data with measurement noise and bias. Experimental results are reported, employing a real jet aircraft, with flight test data acquired by smart probes, inertial sensors (gyrometers and accelerometers) and Global Positioning Systems (GPS) receivers.

Modelling and experimental investigation of an active damper

Abstract: This paper presents a validation methodology of the dynamic behavior of an active viscous damper. The damper has two flexible metallic bellows connected to a rigid reservoir filled with fluid. When one of the bellows is connected to a vibrating structure a periodic flow passes through a variable internal orifice and the damping effect is produced. The size of the orifice is adjusted by a controlled linear piezoelectric actuator that positions the conical core into a conical cavity. The device finite element structural model consists of the valve body and its conical core that are assumed rigid and the flexible bellows are represented by two pistons with elastic suspensions. The flow developed inside the damper is modeled considering the fluid-structure interation, using the Lagrangean-Eulerian formulation. To validate the proposed model a prototype was constructed and experimental tests and numerical simulations are accomplished in the time domain, applying harmonic excitations. The results are compared using curves that relate the damping coefficient with the orifice size and with the input velocity applied at the bellows face. However, for the proper control design and system operation, the direct use of the finite element model becomes unviable due to its high computational time. Then, a reduced second order discrete dynamic model for the damper was developed. The model parameters are identified by analysis in the frequency domain, using impulsive excitation force, for constant and variable orifice sizes. At low excitation frequencies, the damper prototype behaves like a single degree of freedom system which damping factor changes with the orifice size A fuzzy controller was designed and it generates the orifice reference size associated to the desired damping factor. The active system presented better performance when compared to the passive one.

Application of Evolutionary Computation in Automotive Powertrain Mount Tuning

Abstract: Engine mount tuning is a multi-disciplinary exercise since it affects Idle-shake, Road-shake and power-train noise response. Engine inertia is often used as a tuned absorber for controlling suspension resonance related road-shake issues. Last but not least, vehicle ride and handling may also be affected by mount tuning. In this work, Torque-Roll-Axis (TRA) decoupling of the rigid powertrain was used as a starting point for mount tuning. Nodal point of flexible powertrain bending was used to define the envelop for transmission mount locations. The frequency corresponding to the decoupled roll mode of the rigid powertrain was then adjusted for idle-shake and road-shake response management. A TRA decoupling procedure, cast as a multi-objective optimization problem, was applied to a body-on-frame sport-utility vehicle powertrain system. In addition to a standard gradient based optimization algorithm, available in commercial finite element software, an evolutionary computation paradigm known as Evolutionary Strategies (ES) was used to solve the optimization problem. The primary advantages of evolutionary computation over gradient based algorithms are as follows: i) They are less likely to get trapped in local minima and less dependent on initial values of the design parameters and therefore able to handle multi-modal optimization problems unlike gradient based algorithms, ii) They produce a population of viable solutions, unlike gradient based algorithms which yields a single solution. The second advantage is very attractive in a production environment since packaging and other multi-disciplinary constraints often require multiple quality solutions for the same problem. The process outlined in this work was verified by exercising a full-vehicle finite element model. The process produced a set of production feasible powertrain mount parameters for acceptable idle and road shake performance.

Design and test of a blast shield for boeing 737 overhead compartment

Abstract: This work demonstrates the feasibility of using a composite blast shield for hardening an overhead bin compartment of a commercial aircraft. If a small amount of explosive escapes detection and is brought onboard and stowed in an overhead bin compartment of a passenger aircraft, the current bins provide no protection against a blast inside the compartment. A blast from the overhead bin will certainly damage the fuselage and likely lead to catastrophic inflight structural failure. The feasibility of using an inner blast shield to harden the overhead bin compartment of a Boeing 737 aircraft to protect the fuselage skin in such a threat scenario has been demonstrated using field tests. The blast shield was constructed with composite material based on the unibody concept. The design was carried out using LS-DYNA finite element model simulations. Material panels were first designed to pass the FAA shock holing and fire tests. The finite element model included the full coupling of the overhead bin with the fuselage structure accounting for all the different structural connections. A large number of iterative simulations were carried out to optimize the fiber stacking sequence and shield thickness to minimize weight and achieve the design criterion. Three designs, the basic, thick, and thin shields, were field-tested using a frontal fuselage section of the Boeing 737-100 aircraft. The basic and thick shields protected the integrity of the fuselage skin with no skin crack. This work provides very encouraging results and useful data for optimization implementation of the blast shield design for hardening overhead compartments against the threat of small explosives.

Vibroacoustic Analysis of Cyclic Structures by Using Dof’s Size Reduction and Holographic Measurements

Abstract: We propose a method for the vibroacoustic analysis of structures having symmetry properties. This method is based on the reduction of the number of the degrees of freedom involved (size reduction) and the use of experimental data (confrontation numerical/experimental). We propose the extension of the method of the linear representations of finite symmetry groups to problems of coupling fluid-structure. This approach, while keeping the quality of the approximations, leads to a significant reduction of the number of degrees of freedom, with a maximal reduction for the so called repetitive structures. Finally, we present a practical case of modal analysis - in air and water - of a ship propeller formed by 3 stainless steel blades. The experimental results are obtained by using the whole-field, non-contact technique of electronic holography. Manufacturers are interested in forecasts concerning the dynamical behavior of structures, since improvements in the lifetime, security, comfort or global performance may be obtained by determining the unacceptable levels of vibration and protecting their products against them. In the particular case of hydraulic turbines, ribbed shells, aerospatial structures, such an analysis is considered as crucial since these structures are exposed to a significant number of sources of vibration, a fact which increases the risks of failure and nuisance. In this case, the models used must take into account the operating conditions, particularly the immersion of the structure into a dense fluid (air or water). The modal analysis of complex structures by Finite Element Methods (FEM) involves generally a large number of degrees of freedom (DOF). When the coupling with a fluid is considered, this already large number is increased even more by the addition of the DOF corresponding to the fluid domain. In order to perform an appropriate computational analysis, a reduction of the size of the resulting matrix (i.e., the reduction of the number of DOF) is needed. For linear structures presenting symmetry of repetitive type, the theory of finite symmetry groups furnishes tools (3) which allow such a reduction without a significant loss of precision: the amount of reduction is such that the quality of the approximation is not degraded. The present work is a step for the extension of this method to the dynamical analysis of a rotating cyclic elastic structure immersed into a dense fluid - which is the case of the mechanical structures mentioned above. We focus on the vibroacoustic analysis and the determination of the modal basis of the structure immersed in a fluid at rest. We examine the coupled fluid-structure system for the range of low frequencies, where a linear behavior is assumed. This situation corresponds to a significant number of industrial applications, as for example turbomachinery. To keep the paper concise, we do not present here the theory of symmetry groups, but merely focus on its application to the coupled fluid-structure situation and the significant reduction of the number of DOF which is obtained. We also present a practical example concerning the modal analysis of a ship propeller.

Reduced Model in H∞ Vibration Control Using Linear Matrix Inequalities

Abstract: Many practical problems in structural dynamics are modeled with a high number of degrees of freedom in order to properly describe the structure. A formulation to design robust controllers is the H∞ technique where the controller has the same order of the mathematical model and this becomes unpractical and infeasible for most practical problems where the number of degrees of freedom is not small. One way to overcome this difficulty is to employ a model reduction technique, and design a reduced order controller based on this reduced model. In this case, it is required that the reduced controller ensures a good performance also for the nominal model (reduced) and for the real model (non-reduced) of the structure. Since the reduced controller is designed based on a truncated dynamic model, the non-modeled vibration modes can be excited causing the spillover phenomena, which is a severe undesirable effect. This work investigates the behavior of a reduced order controller obtained based on a reduced model through the Guyan reduction. The H∞ robust control and Linear Matrix Inequalities (LMI) formulations are employed to the problem of controlling a flexible structure subjected to an external disturbance. Some simulations are performed using a cantilever beam modeled by the finite element method. The results show that the Guyan reduced order model can be used to design a controller to the non-reduced model with success.