Showing papers in "Shock and Vibration in 2008"

An Experimental Technique for the Evaluation of Strain Dependent Material Properties of Hard Coatings

Abstract: A novel vibration experiment consisting of a free-free boundary condition, an electromagnetic excitation source, a vacuum chamber, and a laser vibrometer based surface measurement system has been developed that permits high levels of excitation on highly damped specimens with a minimal amount of unwanted systematic error. While some of the aspects of this experiment are not unique, when combined with a processing technique that accounts for the nonlinearities present in the system, this experiment permits, accurate measurement of strain dependent stiffness and damping properties of hard coatings at high strain levels. This procedure has been demonstrated using a titanium beam that has been coated with a free-layer damping treatment of Magnesium Aluminate Spinel. The results indicate that Magnesium Aluminate Spinel has both nonlinear stiffness and damping properties. The stiffness asymptotes to a minimum value around 650 microstrain while the damping is a maximum around 100 microstrain. Additionally, the data contained herein cover a larger strain range for this material than previously reported.

Application of the modified compaction material model to the analysis of landmine detonation in soil with various degrees of water saturation

Abstract: A series of transient non-linear dynamics computational analyses of the explosion phenomena accompanying the detonation of a 100 g C4 mine buried in sand to different depths is carried out using the software package AUTODYN. The mechanical response of sand under high deformation-rate conditions has been represented using the modified compaction material model developed in our recent work (1). While the mechanical response of the other attendant materials (air, gaseous-detonation products and AISI 1006 mild steel) is accounted for using the material models available in literature. The results obtained (specifically, the temporal evolution of the sand overburden shape and pressure at various locations in air above the detonation site) were compared with their experimental counterparts for a (50wt%-sand/50wt.%-clay) soil obtained recently by Foedinger (2). The comparison revealed that the modified compaction material model for sand can account reasonably well for the magnitude, spatial distribution and the temporal evolution of the dynamic loads accompanying detonation of shallow-buried mines in soils with various clay and water contents.

Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System

Abstract: In this work we study the frequency and dynamic response of a damped Duffing system attached to a parametrically excited pendulum vibration absorber. The multiple scales method is applied to get the autoparametric resonance conditions and the results are compared with a similar application of a pendulum absorber for a linear primary system. The approximate frequency analysis reveals that the nonlinear dynamics of the externally excited system are suppressed by the pendulum absorber and, under this condition, the primary Duffing system yields a time response almost equivalent to that obtained for a linear primary system, although the absorber frequency response is drastically modified and affected by the cubic stiffness, thus modifying the jumps defined by the fixed points. In the absorber frequency response can be appreciated a good absorption capability for certain ranges of nonlinear stiffness and the internal coupling is maintained by the existing damping between the pendulum and the primary system. Moreover, the stability of the coupled system is also affected by some extra fixed points introduced by the cubic stiffness, which is illustrated with several amplitude-force responses. Some numerical simulations of the approximate frequency responses and dynamic behavior are performed to show the steady-state and transient responses.

Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations

Abstract: Most of the machines and engineering structures experience vibration and their design generally requires consideration for their dynamic behavior. Due to this, the study of vibration, as it deals with the vibratory behavior of bodies, is acquiring increasingly importance in several engineering applications, nuclear reactor technology and aeronautical field etc. Most of the work has been done in the field of elastic and non-elastic behavior of the bodies but a very little work is done in the field of visco-elastic bodies with varying thickness. The analysis presented here is to study the effect of taper constants on free vibration of a clamped visco-elastic rectangular plate with parabolically varying thickness. The two-dimensional thickness variation is taken as the Cartesian product of parabolic variations along the two concurrent edges of the plate. Using Rayleigh-Ritz method, frequency equation derives. Logarithmic decrement, time period and deflection for the first two modes of vibration are calculated for various values of taper constants and aspect ratio. With the advancement of space technology, development of more and more accurate designed structure are needed and hence modern technically better designs and their analysis methods are becoming more and more critical day by day. Depending upon the requirement, durability and reliability, the materials are being developed so that they can be used to give better strength and efficiency. Since these new developed materials are frequently used in the construction of equipments and structures, therefore advancement of the application of visco-elasticity is needed to permit rational design. Applications of such materials are due to reduction of weight and size, low expenses and enhancement in effectiveness and strength. Plates of variable thickness are often encountered in engineering applications and their use in machine design, nuclear reactor technology, naval structures and acoustical components is quite common. The consideration of visco-elastic behavior of the plate material together with the variation in thickness of the structural components not only ensure the reduction in the rate and size but also meets the desirability of high strength in various technological situations of aerospace industry, ocean engineering and electronic and optical equipments. Several authors (1-4) have studied the effect of taper constants in two directions for elastic plate but none of them considering visco-elastic plate. Sobotka (9) has considered free vibrations of uniform visco-elastic orthotropic rectangular plates. Bhatnagar and Gupta (6,7) have studied the effect of thermal gradient on vibration of visco- elastic circular and elliptic plate of variable thickness. Ratko (10) solved the problem of transverse vibration of an eccentric circular plate. Singh and Saxena (11) have studied the transverse vibration of circular plate with

The influence of a mistuned blade's staggle angle on the vibration and stability of a shaft-disk-blade assembly

Abstract: The influence on coupling vibrations and stability among shaft-torsion, disk-transverse and blade-bending of a rotor system with a mistuned blade's staggle angle was investigated analytically. A shaft-disk-blade system has been found existing two types of coupling vibrations, disk-blade (DB), and blade-blade (BB) modes when the shaft was assumed rigid. If the shaft's torsional flexibility was taken into account, an additional type of coupling modes, shaft-disk-blade (SDB), appeared. When an angle-mistuned blade existed, the blades periodicity was destroyed and it was found to change not only the natural frequencies but also the types of modes. Due to blade's mistune, the shaft torsion had to participate to balance such that DB modes vanished and replaced by SDB modes. A mistuned staggle angle was numerically found to alter the natural frequencies in an almost linear trend. At last, the rotational effects were found to merge frequency loci and eventually reached an instability point. Very interestingly, a mistuned blade diminished the possible instability caused by blade-dominating modes, which existed in a perfect and periodic rotor. In words, the rotor might benefit from a mistuned blade from the stability viewpoint. The shaft-dominating mode, yet, was unaffected by the mistune and retained a possible instability.

Structural parameter identification of fixed end beams by inverse method using measured natural frequencies

Abstract: Structural parameter identification based on the measured dynamic responses has become very popular recently. This paper presents structural parameter identification of fixed end beams by inverse method using measured natural frequencies. An added mass is used as a modification tool. The measurements of the flexural vibrations of a fixed end beam with and without added mass are performed by using experimental modal testing. The solution of free bending transverse vibration of the beam is obtained by solving the differential equation motion of Bernoulli-Euler beam. By introducing the natural frequencies from experimental measurements into the solution of differential equation, the structural parameters of the fixed end beam are calculated. It is seen from the results that the values of the mass distribution and elasticity modulus identified using the first natural frequency of the beam nearly close to the real values. Besides, the theoretical frequencies obtained using the identified structural parameters also close to the measured frequencies.

Geometrical nonlinear aeroelastic stability analysis of a composite high-aspect-ratio wing

Abstract: A composite high-aspect-ratio wing of a high-altitude long-endurance (HALE) aircraft was modeled with FEM by MSC/NASTRAN, and the nonlinear static equilibrium state is calculated under design load with follower force effect, but without load redistribution. Assuming the little vibration amplitude of the wing around the static equilibrium state, the system is linearized and the natural frequencies and mode shapes of the deformed structure are obtained. Planar doublet lattice method is used to calculate unsteady aerodynamics in frequency domain ignoring the bending effect of the deflected wing. And then, the aeroelastic stability analysis of the system under a given load condition is successively carried out. Comparing with the linear results, the nonlinear displacement of the wing tip is higher. The results indicate that the critical nonlinear flutter is of the flap/chordwise bending type because of the chordwise bending having quite a large torsion component, with low critical speed and slowly growing damping, which dose not appear in the linear analysis. Furthermore, it is shown that the variation of the nonlinear flutter speed depends on the scale of the load and on the chordwise bending frequency. The research work indicates that, for the very flexible HALE aircraft, the nonlinear aeroelastic stability is very important, and should be considered in the design progress. Using present FEM software as the structure solver (e.g. MSC/NASTRAN), and the unsteady aerodynamic code, the nonlinear aeroelastic stability margin of a complex system other than a simple beam model can be determined.

Dynamic Instability of Pile-Supported Structures in Liquefiable Soils during Earthquakes

Abstract: Piles are long slender columns installed deep into the ground to support heavy structures such as oil platforms, bridges, and tall buildings where the ground is not strong enough to support the structure on its own In seismic prone zones, in the areas of soft soils (loose to medium dense soil which liquefies like a quick sand) piles are routinely used to support structures (buildings/ bridges) The pile and the building vibrate, and often collapse, in liquefiable soils during major earthquakes In this paper an experimental and analytical approach is taken to characterize this vibration The emphasis has been given to the dynamic instability of piled foundations in liquefied soil The first natural frequency of a piled-structure vibrating in liquefiable soil is obtained from centrifuge tests The experimental system is modelled using a fixed-free Euler-Bernoulli beam resting against an elastic support with axial load and tip mass with rotary inertia Natural frequencies obtained from the analytical method are compared with experimental results It was observed that the effective natural frequency of the system can reduce significantly during an earthquake

Real Time Estimation of Modal Parameters and Their Quality Assessment

Abstract: In this paper the recursive method for modal parameters estimation is formulated and verified. Formulated algorithms are implemented in the FPGA electronic chip. As a result, the modal parameters and confidence bounds for the modal parameters are obtained in real time. The algorithms and their implementations are tested on laboratory test rig data and applied to – flight modal analysis of an airframe structure.

A New Fault Diagnosis Method of Rotating Machinery

Abstract: This paper presents a new fault diagnosis procedure for rotating machinery using the wavelet packets-fractal technology and a radial basis function neural network. The faults of rotating machinery considered in this study include imbalance, misalignment, looseness and imbalance combined with misalignment conditions. When such faults occur, they usually induce non-stationary vibrations to the machine. After measuring the vibration signals, the wavelet packets transform is applied to these signals. The fractal dimension of each frequency bands is extracted and the box counting dimension is used to depict the failure characteristics of the vibration signals. The failure modes are then classified by a radial basis function neural network. An experimental study was performed to evaluate the proposed method and the results show that the method can effectively detect and recognize different kinds of faults of rotating machinery.

Measurement of FRFs and modal identification in case of correlated multi-point excitation

Abstract: The modal identification of large and dynamically complex structures often requires a multi-point excitation. Sine sweep excitation runs are applied when it is necessary to concentrate more energy on each line of the frequency spectrum. The conventional estimation of FRFs from multi-point excitation requires uncorrelated excitation signals. In case of multi-point (correlated) sine sweep excitation, several sweep runs with altered excitation force patterns have to be performed to estimate the FRFs. An alternative way, which offers several advantages, is to process each sine sweep run separately. The paper first describes the conventional method for FRF estimation in case of multi-point excitation, followed by two alternative methods applicable in case of correlated excitation signals. Both methods generate a virtual single-point excitation from a single run with multi-point excitation. In the first method, an arbitrary structural point is defined as a virtual driving point. This approach requires a correction of the modal masses obtained from modal analysis. The second method utilizes the equality of complex power to generate virtual FRFs along with a single virtual driving point. The computation of FRFs and the modal identification using virtual single-point excitation are explained. It is shown that the correct set of modal parameters can be identified. The application of the methods is elucidated by an illustrative analytical example. It could be shown that the separate evaluation of symmetric and anti-symmetric multi-point excitation runs yield obviously better and more reliable results compared to the conventional method. In addition, the modal analysis of the separate symmetric and anti-symmetric excitation runs is easier, since the stabilization diagrams are easier to interpret. The described methods were successfully applied during the Ground Vibration Tests on Airbus A380 and delivered excellent results. The methods are highly advantageous and may thus be established as a new standard procedure for testing aerospace structures.

Design of a 20,000 pound variable stiffness actuator for structural vibration attenuation

Abstract: This paper describes the design of a novel actuator capable of protecting a full scale structure from severe load conditions. The design includes a cylinder filled with pressurized nitrogen and uses commercially available components. We demonstrate that the actuator behaves like a spring with an adjustable unstretched length, and that the effective spring stiffness can be changed easily by changing the initial cylinder pressure. In order to test the actuator on a full scale structure, an effective spring constant of approximately 10,000 pounds/inch was required over a two inch stroke. Because of the spring-like behavior, rather than damper-like behavior, the actuator does not transmit high forces to a vibrating structure like linear viscous dampers do when velocities are high. We analyze features of critical importance to the design of the actuator such as the cylinder dimensions, operating pressure, and valve selection. We then investigate the performance using a novel experimental apparatus that mimics the dynamics of a single story building, but has 1/400 the weight.

Horizontal bulk material pressure in silo subjected to impulsive load

Abstract: This paper describes laboratory tests carried out in the steel flat-bottomed silo model filled with sand, subjected to external dynamic loads. The model was placed on a system of springs, which represent subsoil. The loads in the form of horizontal impulses were applied to the bottom plate of the silo. Horizontal pressure-time courses were used to analyze the influence of subsoil vibrations on the distribution changes of these pressures. Basic conclusion: (1) the subsoil vibrations cause two types of changes of the horizontal pressures: stable changes which are observed when the model vibrations finish and cyclic of short duration (brief) changes; (2) the subsoil vibrations either generate stable increase or stable decrease of the pressures from before vibrations or do not generate any essential stable change; (3) the cyclic dynamic changes of the horizontal pressures depend on the direction of the silo wall displacements and they are the function of the values of these displacements.

Analysis of control policies and dynamic response of a Q-car 2-DOF semi active system

Abstract: Several control policies of Q-car 2-DOF semiactive system, namely skyhook, groundhook and hybrid controls are presented Their ride comfort, suspension displacement and road-holding performances are analyzed and compared with passive system The analysis covers both transient and steady state responses in time domain and transmissibility response in frequency domain The results show that the hybrid control policy yields better comfort than a passive suspension, without reducing the road-holding quality or increasing the suspension displacement for typical passenger cars The hybrid control policy is also shown to be a better compromise between comfort, road-holding and suspension displacement than the skyhook and groundhook control policies

Vibration Measurement of Rotating Blades Using a Root Embedded PZT Sensor

Abstract: Finite element and experimental studies are carried out to test the suitability of a piezoelectric (PZT) sensor in measuring vibrations of blades modeled as beams. The rotating system contains twelve blades mounted to the shaft through a rotor. The PZT sensor is secured in the root between the rotor and blade. First, finite element results are obtained using the finite element package ANSYS. A modal analysis is performed on the system to identify modes and mode shapes. Transient, harmonic and steady-state responses are then computed to test the ability of the PZT sensor in generating signals for blade vibrations. For the experimental part, the blade vibration signals are produced using the PZT sensor and a strain-gage, and the outputs are compared with each other. From both the finite element and experimental results, it is concluded that the root-embedded PZT sensor can be effectively used for blade vibration measurements in a wide range of cases.

Evaluation of the Performance of Three Different Methods Used in the Identification of Rigid Body Properties

Abstract: The identification of the rigid body properties of a structure is an important matter in various structural dynamic applications, namely in structural modification (coupling/uncoupling), optimization and vibration control. In most situations, the experimental route is the only via to obtain the desired dynamic properties. This goal is achieved by an inverse process which starts from the measurement of Frequency Response Functions (FRFs) and ends on matrices describing the mass distribution of a rigid body.

Simple models for the dynamic modeling of rotating tires

Abstract: Large Finite Element (FE) models of tires are currently used to predict low frequency behavior and to obtain dynamic model coefficients used in multi-body models for riding and comfort. However, to predict higher frequency behavior, which may explain irregular wear, critical rotating speeds and noise radiation, FE models are not practical. Detailed FE models are not adequate for optimization and uncertainty predictions either, as in such applications the dynamic solution must be computed a number of times. Therefore, there is a need for simpler models that can capture the physics of the tire and be used to compute the dynamic response with a low computational cost. In this paper, the spectral (or continuous) element approach is used to derive such a model. A circular beam spectral element that takes into account the string effect is derived, and a method to simulate the response to a rotating force is implemented in the frequency domain. The behavior of a circular ring under different internal pressures is investigated using modal and frequency/wavenumber representations. Experimental results obtained with a real untreaded truck tire are presented and qualitatively compared with the simple model predictions with good agreement. No attempt is made to obtain equivalent parameters for the simple model from the real tire results. On the other hand, the simple model fails to represent the correct variation of the quotient of the natural frequency by the number of circumferential wavelengths with the mode count. Nevertheless, some important features of the real tire dynamic behavior, such as the generation of standing waves and part of the frequency/wavenumber behavior, can be investigated using the proposed simplified model.

An inelastic beam element with hysteretic damping

Abstract: In this work, an inelastic beam macro-element that incorporates hysteretic damping is presented. Based on classical theory of plasticity, a Bouc-Wen type model is utilized that simulates the hysteretic behavior of an inelastic spring element. Using this model, an inelastic nonlinear beam element is formulated based on the appropriate combination of two coupled nonlinear spring elements. The equations of motion are determined and are cast in a state-space form for the vector of the end displacements, velocities and hysteretic forces. The system is solved by employing a Runge-Kutta type of algorithm. The proposed inelastic beam model is then employed to simulate the experimental dynamic behavior of steel beams. The model parameters are estimated with the aid of a nonlinear system identification algorithm using existing experimental data. The proposed element approximates the inelastic behavior of steel beams adequately within plastic regions that do not undergo substantial stiffness degradation, or other relevant phenomena. Finally, the hysteretic damping features of the model are demonstrated.

On the influence of welding residual stresses on the dynamic behavior of structures

Abstract: It is widely known that welding processes induce the generation of residual stresses, which, through the so-named stress stiffening effect, can influence the static and dynamic behavior of the welded components. Thus, accounting for this influence becomes important for the understanding of experimental observations and accurate modeling of the dynamic behavior. In this study, the numerical and experimental characterization of the influence of welding residual stresses on the flexural dynamic characteristics of rectangular plates is addressed. It is suggested a general modeling methodology based on finite elements comprising three subsequent analyses, namely: a thermal analysis to compute the transient temperature history due to welding thermal loading; a structural analysis accounting for plastic strains to obtain the welding residual stress fields and geometric distortions, and a dynamic analysis to compute the dynamic characteristics taking into account the stress-stiffening effect and geometric distortions. The results demonstrate the importance of considering the influence of welding residual stresses in the prediction of the flexural dynamic behavior of plates and the feasibility and efficiency of the simplified modeling approach, which can readily be extended to more complex situations, for characterizing this influence.

Satellite attitude control system simulator

Abstract: Future space missions will involve satellites with great autonomy and stringent pointing precision, requiring of the Attitude Control Systems (ACS) with better performance than before, which is function of the control algorithms implemented on board computers. The difficulties for developing experimental ACS test is to obtain zero gravity and torque free conditions similar to the SCA operate in space. However, prototypes for control algorithms experimental verification are fundamental for space mission success. This paper presents the parameters estimation such as inertia matrix and position of mass centre of a Satellite Attitude Control System Simulator (SACSS), using algorithms based on least square regression and least square recursive methods. Simulations have shown that both methods have estimated the system parameters with small error. However, the least square recursive methods have performance more adequate for the SACSS objectives. The SACSS platform model will be used to do experimental verification of fundamental aspects of the satellite attitude dynamics and design of different attitude control algorithm.

Energy flow boundary element method for vibration analysis of one and two dimension structures

Abstract: In this paper, Energy Flow Boundary Element Method (EFBEM) was developed to predict the vibration behavior of one- and two-dimensional structures in the medium-to-high frequency ranges. Free Space Green functions used in the method were obtained from EFA energy equations. Direct and indirect EFBEMs were formulated for both one- and two-dimensional cases, and numerically applied to predict the energy density and intensity distributions of simple Euler-Bernoulli beams, single rectangular thin plates, and L-shaped thin plates vibrating in the medium-to-high frequency ranges. The results from these methods were compared with the EFA solutions to verify the EFBEM.

Optimal Control of an 8-DOF Vehicle Active Suspension System Using Kalman Observer

Abstract: In this paper, an 8-DOF model including driver seat dynamics, subjected to random road disturbances is used in order to investigate the advantage of active over conventional passive suspension system. Force actuators are mounted parallel to the body suspensions and the driver seat suspension. An optimal control approach is taken in the active suspension used in the vehicle. The performance index for the optimal control design is a quantification of both ride comfort and road handling. To simulate the real road profile condition, stochastic inputs are applied. Due to practical limitations, not all the states of the system required for the state-feedback controller are measurable, and hence must be estimated with an observer. In this paper, to have the best estimation, an optimal Kalman observer is used. The simulation results indicate that an optimal observer-based controller causes both excellent ride comfort and road handling characteristics.

Subspace-based identification of nonlinear structures

Abstract: Conventional linear estimators give results contaminated in presence of nonlinearities and the extraction of underlying linear system properties is thus difficult. To overcome this problem, the implementation of a recently developed method, called Nonlinear Subspace Identification (NSI), is considered in this paper, by using the perspective of nonlinearities as unmeasured internal feedback forces. Although its formulation is very simple, particular care has to be taken to reduce the ill-conditioning of the problem, in order to find numerically stable solutions. To this purpose, the robustness and the high numerical performances of the subspace algorithms are successfully exploited, as shown by the implementation of the proposed method on simulated multi-degree-of-freedom systems with typical nonlinear characteristics as well as on an experimental case. These examples demonstrate that the application of subspace algorithms to nonlinear system identification gives better conditioning and computational efficiency with respect to the most recent nonlinear techniques. Moreover, the capability of the NSI method of simultaneously dealing with several nonlinear terms, with a light computational effort, may be also exploited in those situations where no a priori knowledge of the location and the type of nonlinearities is given, being this method well capable of detecting the contribution of the dominant nonlinearities.

Prognosis under Uncertainty – An Idealised Computational Case Study

Abstract: The object of this paper is to investigate computationally the possibility of damage prognosis in a structure under the most idealised circumstances. A simple isotropic material – Titanium alloy Ti-6Al-4V – is assumed. The structure is a simple finite plate under harmonic uniaxial loading and the damage is assumed to be a central mode 1 through crack for which various approximations to the stress intensity factor are known. The damage propagation model is the Paris-Erdogan law. Where the paper departs from complete simplicity is in the assumption that the parameters of the damage propagation law are uncertain. The paper investigates the effect of the parameter uncertainty on the estimated lifetime of the specimen. Two approaches are adopted for the uncertainty propagation, a statistical Monte Carlo scheme and one based on interval arithmetic.

A novel low-torque ball re-positioning scheme based on a sliding-mode ball observer for an automatic balancer system

Abstract: A novel low-torque ball re-positioning scheme based on a sliding-mode ball observer is developed in this study with the aim to precisely reside the rolling ball inside an automatic balancer system (ABS) to its desired position – 180 degree opposite to the inherent imbalance of the rotating system which the ABS is attached to. In this way, the ABS is capable of substantially reducing radial vibrations of the rotating system for a decent balancing. For preliminary feasibility, the case of a single ball is considered in this study. The first step is to establish the dynamic model of the system, which is followed by the analysis to ensure stability of the desired ball position. The second step is to forge a sliding-mode observer for estimating on-line position and velocity of the ball. With ball estimation capability, a low-torque speed regulator that essentially generates a series of speed drops to the neighborhood of suspension resonance is proposed to overcome practical ball rolling friction for residing the ball at the desired position. The design characteristic of low-torque required for the regulator is particularly suited to most of commercial spindle motors which can only output limited torques at high speeds. Finally, simulations and experiments are conducted for a benchmark problem of optical disc drives in order to verify the effectiveness of the proposed scheme of the sliding-mode observer and the low-torque speed regulator.

Structural Damage Detection Using Energy Flow Models

Abstract: The presence of a crack in a structure modifies the energy dissipation pattern. As a consequence, damaged structures can present high localized damping. Experimental tests have revealed that crack nucleation and growth increase structural damping which makes this phenomenon useful as a damage locator. This paper examines the energy flow patterns caused by localized damping in rods, beams and plates using the Energy Finite Element Method (EFEM), the Spectral Element Method (SEM) and the Energy Spectral Element Method (ESEM) in order to detect and locate damage. The analyses are performed at high frequencies, where any localized structural change has a strong influence in the structural response. Simulated results for damage detection in rods, beams, and their couplings calculated by each method and using the element loss factor variation to model the damage, are presented and compared. Results for a simple thin plate calculated with EFEM are also discussed.

Vibration Analysis of Circular Arch Element Using Curvature

Abstract: In this paper, a finite element technique was used to determine the natural frequencies, and the mode shapes of a circular arch element was based on the curvature, which can fully represent the bending energy and by the equilibrium equations, the shear and axial strain energy were incorporated into the formulation. The treatment of general boundary conditions dose need a consideration when the element is incorporated by the curvature-based formula. This can be obtained by the introduction of a transformation matrix between nodal curvatures and nodal displacements. The equation of the motion for the element was obtained by the Lagrangian equation. Four examples are presented in order to verify the element formulation and its analytical capability.

On the Modeling of Beam Reinforced Thin Plates Using the Spectral Element Method

Abstract: Modeling beam reinforced thin plates at mid and high frequencies through the most commonly used methods such as finite and boundary element methods frequently leads to unsatisfactory results, since the accuracy of these methods depends on the relation between the dimensions of the elements in which the structure was discretized and the wavelength. Due to this characteristic, the modeling using these techniques will require that the size of the elements becomes smaller as the frequency increases, while its number needs to be increased. For structures that are usual in some areas, like the aerospace industry, this will be possible only with an unreasonable computational effort, which is responsible for restricting the use of these methods practically to low-frequency applications. Semi-analytical methods such as the spectral element method do not need mesh refinement at higher frequencies, but they were very limited in the geometries and boundary conditions that can be treated. This paper presents a spectral element for rectangular thin plates reinforced symmetrically along the sides with Euler beams, which can be used to model plates with arbitrary boundary conditions. The method was verified by comparing its results with those obtained from a Finite Element model.

Combination of an improved FRF-based substructure synthesis and power flow method with application to vehicle axle noise analysis

Abstract: In this paper, an improved FRF-based substructure synthesis method combined with power flow analysis is presented and is used for performing a vehicle axle noise analysis. The major transfer paths of axle noise transmitted from chassis to vehicle body are identified and ranked based on power flows transmitted through bushings between the chassis and body. To calculate the power flows, it is necessary to know the reaction forces and the vibrations at the bushing locations on the body side. To this end, the body is represented in terms of experimentally derived frequency response functions (FRF's) at the bushing locations, and the FRF's are coupled with the FEA model of the chassis for performing a total system dynamic analysis. This paper also describes how the FRF's of the vehicle body and the frequency dependent stiffness data of the bushings can be combined together with a simple formulation to better represent the dynamic characteristics of a full vehicle. A classical example is used to illustrates the concept of the method, and the method is then applied to a vehicle axle noise analysis with detailed procedure. The theoretical predictions are compared with experimentally measured results. Good correlation has been obtained.

Design and control of nonlinear mechanical systems for minimum time

Abstract: This paper presents an integrated methodology for optimal design and control of nonlinear flexible mechanical systems, including minimum time problems. This formulation is implemented in an optimum design code and it is applied to the nonlinear behavior dynamic response. Damping and stiffness characteristics plus control driven forces are considered as decision variables. A conceptual separation between time variant and time invariant design parameters is presented, this way including the design space into the control space and considering the design variables as control variables not depending on time. By using time integrals through all the derivations, design and control problems are unified. In the optimization process we can use both types of variables simultaneously or by interdependent levels. For treating minimum time problems, a unit time interval is mapped onto the original time interval, then treating equally time variant and time invariant problems. The dynamic response and its sensitivity are discretized via space-time finite elements, and may be integrated either by at-once integration or step-by-step. Adjoint system approach is used to calculate the sensitivities.