Showing papers in "Journal of Vibration and Acoustics in 1994"

Wavelet Analysis of Vibration: Part 1—Theory

Abstract: The purpose of this paper is to introduce and review the theory of orthogonal wavelets and their application to signal analysis. It includes the theory of dilation wavelets, which have been developed over a period of about ten years, and of harmonic wavelets which have been proposed recently by the author

Structural Damage Detection Using a Minimum Rank Update Theory

Abstract: The algorithm makes use of an original finite element model and a subset of measured eigenvalues and eigenvectors The developed theory approaches the damage location and extent problem in a decoupled fashion First, a theory is developed to determine the location of structural damage With location determined, an extent algorithm is then developed The extent algorithm is a minimum rank update, which is consistent with the effects of many classes of structural damage on a finite element model If the actual damage results in a rank p change to the finite element model, then the extent algorithm produces exact results if p eigenvalues and eigenvectors are measured exactly

An impedance method for dynamic analysis of active material systems

Abstract: This paper describes a new approach to analyzing the dynamic response of active material systems with integrated induced strain actuators, including piezoelectric, electrostrictive, and magnetostrictive actuators. This approach, referred to as the impedance method, has many advantages compared with the conventional static impedance method, has many advantages compared with the conventional static approach and the dynamic finite element approach, such as pin force models and consistent beam and plate models. The impedance approach is presented and described using a simple example, a PZT actuator-driven one degree of freedom spring mass damper system

Piezothermoelasticity and Precision Control of Piezoelectric Systems: Theory and Finite Element Analysis

Abstract: Piezothermoelastic effects of distributed piezoelectric sensor/actuator and structural systems are studied . Distributed controls (static and dynamic) of pizeoelectric laminates subjected to a steady state temperature field are investigated. Piezothermoelastic constitutive equations are defined, followed by three energy functionals for the displacement, electric, and temperature fields, respectively. A new 3D piezothermoelastic thin hexahedron finite element with three internal degrees of freedom is formulated using a variational formulation which includes thermal, electric, and mechanical energies. A system equetion for the piezoelcectric continuum exposed to combined displacement, electic, and temperature fields is formulated. Thermal influences on the sensing and control of piezoelectric PZT/steel laminates are ivestigated

On Nonlinear Modes of Continuous Systems

Abstract: We use several methods to study the nonlinear modes of one-dimensional continuous systems with cubic inertia and geometric nonlinearities. Invariant manifold and perturbation methods applied to the discretized system and the method of multiple scales applied to the partial-differential equation and boundary conditions are discussed and their equivalence is demonstrated. The method of multiple scales is then applied directly to the partial-differential equation and boundary conditions governing several nonlinear beam problems.

Hybrid damping through intelligent constrained layer treatments

Abstract: This paper is to propose a viable hybrid damping design that integrates active and passive dampings through intelligent constrained layer (ICL) treatments. This design consists of a viscoelastic shear layer sandwiched between a piezoelectric constraining cover sheet and the structure to be damped. According to measured vibration response of the structure, a feedback controller regulates axial deformation of the piezoelectric layer to perform active vibration control. In the meantime, the viscoelastic shear layer provides additional passive damping. The active damping component of this design will produce adjustable and significant damping. The passive damping component of this design will increase gain and phase margins, eliminate spillover, reduce power consumption, improve robustness and reliability of the system, and reduce vibration response at high frequency ranges where active damping is difficult to implement. To model the dynamics of ICL, an eighth-order matrix differential equation governing bending and axial vibrations of an elastic beam with the ICL treatment is derived. The observability, controllability, and stability of ICL are discussed qualitatively for several beam structures. ICL may render the system uncontrollable or unobservable or both depending on the boundary conditions of the system. Finally, two examples are illustrated in this paper. The first example illustrates how an ICL damping treatment, which consists of an idealized, distributed sensor and a proportional-plus-derivative feedback controller, can reduce bending vibration of a semi-infinite elastic beam subjected to harmonic excitations. The second example is to apply an ICL damping treatment to a cantilever beam subjected to combined axial and bending vibrations. Numerical results show that ICL will produce significant damping.

Surface Waves in Functionally Gradient Piezoelectric Plates

Abstract: The hybrid numerical method, which has been proposed by the present authors for wave propagation analysis in anisotropic laminated plates, is extended for functionally gradient piezoelectric material (FGPM) plates. The properties of the plate changes continuously in the thickness direction. Characteristics of waves in the plates, and responses of the plates in the time and frequency domain are considered. A technique for calculating responses in the frequency domain is presented. Energy velocities, mode shapes of the waves in an FGPM plate, and the responses of the plate excited by mechanical loads and electrodes are computed. It is found that waves of lower modes in the FGPM plates for large wave numbers appear as surface waves and that a strong surface wave is excited on the softer surface of the FGPM plate. These surface waves can be expected to be used in surface acoustic wave devices.

Experiments on Active Control of Plate Vibration Using Piezoelectric Actuators and Polyvinylidene Fluoride (PVDF) Modal Sensors

Abstract: An experiment was performed to investigate the implementation of shaped PVDF modal sensors on a simply supported rectangular plate to control specific modes of the vibration. The plate was excited by a steady-state harmonic point force while the control was achieved by two independent piezoelectric actuators bonded to the surface of the plate. A two-channel adaptive controller based on the multi-input multi-output filtered X LMS algorithm was used to provide feed-forward control. Two PVDF modal sensors were shaped such that the (3,1) mode was the dominant structural mode observed by the sensors. With this configuration, the amplitude of the (3,1) mode can be minimized regardless of excitation frequency. A comparative test was performed by using two accelerometers as error sensors. Results indicate that for both on and off-resonance excitations, the shaped PVDF modal sensors are superior to point-error sensors, such as accelerometers for controlling specific structural modes.

Rotational response and slip prediction of serpentine belt drive systems

Abstract: A nonlinear model is developed which describes the rotational response of automotive serpentine belt drive systems. Serpentine drives utilize a single {long) belt to drive all engine accessories from the crankshaft. An equilibrium analysis leads to a closedform procedure for determining steady-state tensions in each belt span. The equations of motion are linearized about the equilibrium state and rotational mode vibration characteristics are determined from the eigenvalue problem governing free response. Numerical solutions of the nonlinear equations of motion indicate that, under certain engine operating conditions, the dynamic tension fluctuations may be sufficient to cause the belt to slip on particular accessory pulleys. Experimental measurements of dynamic response are in good agreement with theoretical results and confirm theoretical predictions of system vibration, tension fluctuations, and slip.

A Piezothermoelastic Thin Shell Theory Applied to Active Structures

Abstract: : 'Smart' structures with integrated sensors, actuators, and control electronics are of importance to next-generation high-performance structural systems. Piezoelectric materials possess unique electromechanical properties, the direct and converse effects. which can be used in sensor and actuator applications. In this study, piezothermoelastic characteristics of piezoelectric shell continua are studied and applications of the theory to active structures in sensing and control are discussed. A generic piezothermoelastic shell theory for thin piezoelectric shells is derived using the linear piezoelectric theory and Kirchhoff-Love assumptions. It shows that the dynamic equations, in three principal directions, include thermal induced loads as well as conventional electric and mechanical loads. The electric membrane forces and moments induced by the converse effect can be used to control the thermal and mechanical loads. A simplification procedure, based on Lame's parameters and radii of curvatures, is proposed and applications of the theory to 1) a piezoelectric cylindrical shell and 2) a piezoelectric beam are demonstrated.... Smart structures, Piezoelectricity, Distributed sensor/actuator

Predicting random high-cycle fatigue life with finite elements

Abstract: This paper extends the classical theory of random fatigue to multiaxial stress fields, using a quadratic criterion. An equivalent uniaxial random process is constructed by combining the power spectral densities of the normal and tangential stresses according to the von Mises criterion. This process, that we call the von Mises stress, is used to evaluate the damage with a uniaxial model of random fatigue. A finite element implementation is proposed. 17 refs.

An Energy-Based Formulation for Computing Nonlinear Normal Modes in Undamped Continuous Systems

Abstract: The nonlinear normal modes of a class of one dimensional, conservative, continuous systems ae examined. These are free, periodic motions during which all particles of the system reach their extremum amplitudes at the same instant of time. During a nonlinear normal mode, the motion of an arbitrary particle of the system is expressed in terms of the motion of a certain reference point by means of a modal function. Conservation of energy is imposed to construct a partial differential equation satisfied by the modal function, which is asymptotically solved using a perturbation methodology. The stability of the detected nonlinear modes is then investigated by expanding the corresponding variational equations in bases of orthogonal polynomials and analyzing the resulting set of linear differential equations with periodic coefficients by Floquet analysis

Energy Transfer From High-to Low-Frequency Modes in a Flexible Structure via Modulation

Abstract: An experimental study of the response of axially-symmetric (i.e., circular cross section) cantilever beams to planar external excitations is presented. Because of the axial symmetry, one-to-one internal resonances occur at each natural frequency. These resonances cause the planar motions to lose stability and nonplanar (Whirling) motions are observed. Under certain conditions, periodically- and chaotically-modulated motions may occur. In addition, when the beam is excited near one of its high natural frequencies, large first-mode response accompanied by slow modulations of the amplitudes and phases of high-frequency modes are observed

Navier-Stokes Computations of Cavity Aeroacoustics with Suppression Devices

Abstract: Effectiveness of two devices to suppress the cavity acoustics was computationally investigated. Two dimensional, computational simulations were performed for the transonic, turbulent flows past a cavity, which was first equipped with a rear face ramp and then with a spoiler. The Reynolds-averaged, unsteady, compressible, full Navier-Stokes equations were solved time accurately by a second-order accurate, implicit, upwind, finite-volume method. The effect of turbulence was included through the Baldwin-Lomax model with modifications for the multiple-wall effects and for the highly vortical flow with a shear layer. The results included instantaneous and time-averaged flow properties, and time-series analyses of the pressure inside the cavity, which compared favorably with the available experimental data. These results were also contrasted with the computed aeroacoustics of the same cavity (length-to-depth ratio of 4.5), but without a device, to demonstrate the suppression effectiveness.

Nonlinear vibrations of a beam-spring-mass system

Abstract: The nonlinear response of a simply supported beam with an attached spring-mass system to a primary resonance is investigated, taking into account the effects of beam midplane stretching and damping. The spring-mass system has also a cubic nonlinearity. The response is found by using two different perturbation approaches. In the first approach, the method of multiple scales is applied directly to the nonlinear partial differential equations and boundary conditions. In the second approach, the Lagrangian is averaged over the fast time scale, and then the equations governing the modulation of the amplitude and phase are obtained as the Euler-Lagrange equations of the averaged Lagrangian. It is shown that the frequency-response and force-response curves depend on the midplane stretching and the parameters of the spring-mass system. The relative importance of these effects depends on the parameters and location of the spring-mass system.

Nonlinear Resonances in a Flexible Cantilever Beam

Abstract: An experimental investigation into the response of a nonlinear continuous systems with many natural frequencies in the range of interest is presented. The system is a flexible cantilever beam whose first four natural frequencies are 0.65 Hz, 5.65 Hz, 16.19 Hz, and 31.91 Hz, respectively. The four natural frequencies correspond to the first four flexural modes. The fourth natural frequency is about fifty times the first natural frequency. Three cases were considered with this beam. For the first case, the beam was excited with a periodic base motion along its axis. The excitation frequency fe was near twice the third natural frequency f3 , which for a uniform isotropic beam corresponds to approximately the fourth natural frequency f4 . Thus the third mode was excited by a principal parametric resonance (i.e., fe ≈ 2f3 ) and the fourth mode was excited by an external resonance (i.e., fe ≈ f4 ) due to a slight curvature in the beam. Modal interactions were observed involving the first, third, and fourth modes. For the second case, the beam was excited with a band-limited random base motion transverse to the axis of the beam. The first and second modes were excited through nonlinear interactions. For the third case, the beam was excited with a base excitation along the axis of the beam at 138 Hz. The corresponding response was dominated by the second mode. The tools used to analyze the motions include Fourier spectra, Poincare sections, and dimension calculations.

Dynamic Analysis and Design of a Machine Tool Spindle-Bearing System

Abstract: The paper simulates a spindle-bearing system with a finite-element model; then compares it to the experimental results. Radial and tilting springs and dashpots are considered in angular contact spindle ball bearings. This FEM model shows that additional tilting characteristics make significant effect on higher-order vibration modes. The design parameters used in this study are bearing preloads, bearing spacings, mass inserts on spindle and damping. Computations and experimental results show that improvements can be made by adjusting the forementioned parameters.

Modeling and Control of Acoustic Structure Interaction Problems Via Piezoceramic Actuators: 2-D Numerical Examples

Abstract: : The modeling and active control of acoustic pressure in a 2-D cavity with a flexible boundary (a beam) is considered. Control is implemented in the model via piezoceramic patches on the beam which are excited in a manner so as to produce pure bending moments. The incorporation of the feedback control in this manner leads to a system with an unbounded input term. Approximation techniques are discussed and by writing the resulting system as an abstract Cauchy equation, the problem of reducing interior pressure fluctuations can be posed in the context of an LQR time domain state space formulation. Examples illustrating the dynamic behavior of the coupled system as well as demonstrating the viability of the control method on a variety of problems with periodic forcing functions are presented.

An Improved Theoretical Model of Acoustic Agglomeration

Abstract: An improved theoretical model is developed to describe the acoustic agglomeration of particles entrained in a gas medium. The improvements to the present theories are twofold: first, wave scattering is included in the orthokinetic interaction of particles and second, hydrodynamic interaction, shown to be an important agglomeration mechanism for certain operation conditions, is incorporated into the model. The influence of orthokinetic and hydrodynamic interactions introduce associated convergent velocities that cause particles to approach each other and collide. The convergent velocities are related with an acoustic agglomeration frequency function (AAFF) through a semi-statistical method. This function is the key parameter for the theoretical simulation of acoustic agglomeration.

Dynamic Effects in Mechanical Structures with Gaps and Impacting: Order and Chaos

Abstract: The paper discusses orderly and chaotic dynamic responses of simple mechanical structures with clearances and impacting. Experimental results from a simulator of a rotating machine with one loose pedestal are presented, and a summary of analytical results for this case is given. The orderly and chaotic responses obtained through numerical integration are presented in the form of bifucation diagrams. The second part of the paper discusses an existence of the main and higher order resonances in structures with clearances and impacting, which are excited by external periodic forces. For a one degree of freedom nonlinear system, the application of a discontinuous variable transformation, followed by an averaging method provides analytical formulae describing the system response amplitudes and phases in the proximity fo the main and harmonic resonances

Natural Frequencies Formula for Simply Supported Mindlin Plates

Abstract: This paper presents an explicit formula for the vibration frequencies of simply supported Mindlin plates in terms of the corresponding thin (Kirchhoff) plate frequencies. The formula has been obtained from an exact vibration analysis of simply supported rectangular Mindlin plates. When the formula was applied to other simply supported plate shapes such as skew plates, circular and annular sectorial plates, it was found to give almost exact solutions. It appears that the formula can be used to predict the frequencies accurately for any simply supported plate shape and thus should be valuable to designers as Mindlin vibration solutions are scarce.

Vibration of rectangular mindlin plates with intermediate stiffeners

Abstract: A first known investigation into the vibratory characteristics of rectangular Mindlin plates with intermediate stiffeners is presented. The Rayleigh-Ritz method is used, with displacement and rotational functions assumed in the form of mathematically complete algebraic polynomials. Sets of numerical frequency parameters for rectangular plates of various boundary conditions, thicknesses and plate dimensions are presented. In the study, the effects of shear deformation and rotary inertia on the vibrational response of the plate structures are investigated. The influence of torsional rigidity and geometric properties of stiffeners on the natural frequency parameters are included. To validate the proposed formulation, numerical results for some simplified problems have been determined where existing literature for these problems can be found. Finally sets of new vibration frequencies for plates with one or more stiffeners in various directions are presented.

Dynamic Characteristics of Layered Beam with Flexible Core

Abstract: The flexible core may be made of a kind of viscoelastic material in order to achieve a high shock absorbing performance. The dynamic interaction between these two parallel beams are especially studied. The dynamic shape functions and the dynamic stiffness matrix of a layered beam element are established based on the analytical model of two parallel damped Timoshenko beams, connected to each other by the vertical springs and dashpots uniformly distributed along the beam length

Collocated sensor/actuator positioning and feedback design in the control of flexible structure system

Abstract: This paper presents a new control design method for the control of flexible systems that not only guarantees closed-loop asymptotic stability but also effectively suppresses vibration. This method allows integrated determination of actuator/sensor locations and feedback gain via minimization of an energy criterion, which is chosen as the integrated total energy stored in the system. The energy criterion is determined via an efficient solution of the Lyapunov equation and minimized with a quasi-Newton or recursive quadratic programming algorithm. The prerequisite for this optimal design method is that the controlled system be asymptotically stable. This study shows that when the controller structure is a collocated direct velocity feedback design with positive definite feedback gain, the number and placement of actuators/sensors are the only factors needed to determine necessary and sufficient conditions for ensuring closed-loop asymptotic stability. The application of this method to a simple flexible structure confirms the direct relationship between our optimization criterion and effectiveness in vibration suppression.

On the Vibration of Bolted Plate and Flange Assemblies

Abstract: The vibration of an annular plate that is free along its outer edge, and that is connected to a flange along its inner edge by bolts that are equally spaced in the circumferential direction, is studied. A disk with this geometry, or a stacked array of such disks, is common in application involving data storage, rotating machinery or brake systems. The periodic structural imperfections that are associated with the bolt pattern can have interesting implications for the plate's dynamic response. Changes that occur in the natural frequencies and mode shapes as a result of such deviations from an ideally clamped inner edge are studied through laboratory measurements, and through an approximate model that captures the rotationally periodic character of the bolted plate and flange system

Membrane and flexural waves on thin shells

Abstract: Membrane and flexural waves are limiting short wavelength solutions of the equations of motion for arbitrarily curved, smooth shells. Each distinct wave type is found using a geometrical or ray method based upon asymptotics in the small parameters h/R, where h is thickness and R a minimum radius of curvature

Vibration Measurements on Rotating Machinery Using Laser Doppler Velocimetry

Abstract: This paper explores the use of laser vibrometry for vibration measurement directly from a rotating component. The presence of a surface velocity component due to the rotation itself is shown to create a strong measurement dependency on vibration perpendicular to the intended measurement direction. Particular ambiguity results at synchronous frequencies. A mathematical means to resolve the genuine vibration components from two simultaneous laser vibrometer measurements is presented and shown to be effective in the study of nonsynchronous rotor vibrations.