bluuebunny/crossref_metadata_2025 huggingface dataset:
Internal Resonance Phenomena of an Asymmetrical Rotating Shaft: Critical Speed of Twice the Major Critical Speed
Authors: Ishida Yukio , Inoue Tsuyoshi
Published: February 2021

Unstable vibrations appear in the vicinities of several critical speeds in asymmetric rotor systems with nonlinear spring characteristics. However, when the natural frequencies satisfy internal resonance relation exactly or approximately, these phenomena may change remarkably. In this paper, such internal resonance phenomena of an asymmetric shaft-disk system are studied theoretically and experimentally. The changes in nonlinear phenomena during the transition from the system with internal resonance to the system with no internal resonance are also investigated.
Non-Smooth Dynamics and Non-Classical Bifurcations in Impulse-Impact Oscillators
Authors: Lenci Stefano , Rega Giuseppe
Published: February 2021

Some aspects of the nonlinear dynamics of an impulse-impact oscillator are investigated. After an initial description of the prototype mechanical model used to illustrate the results, attention is paid to the classical local and global bifurcations which are at the base of the changes of dynamical regime.

Some non-classical phenomena due to the particular nature of the investigated system are then considered. At a local level, it is shown that periodic solutions may appear (or disappear) through a non-classical bifurcation which involves synchronization of impulses and impacts. Similarities and differences with the classical bifurcations are discussed.

At a global level, the effects of the non-continuity of the orbits in the phase space on the basins of attraction topology are investigated. It is shown how this property is at the base of a non-classical homoclinic bifurcation where the homoclinic points disappear after the first touch between the stable and unstable manifolds.
Analysis and Simulation of Radial Chatter in Drilling and Reaming
Authors: Metzler Sandra A. , Bayly Philip V. , Young Keith A. , Halley Jeremiah E.
Published: February 2021

At high cutting speeds, self-excited regenerative vibrations (“chatter”) of drilling and reaming tools may occur. Chatter is an instability in which oscillation of the tool causes variation in the chip load, which in turn amplifies tool motion. This phenomenon is well known in turning and milling, and has also been studied in boring. In drilling and reaming, both axial motion and radial (bending) motion of the tool may affect the chip load, but dynamic stiffness is often much higher axially. Analysis of radial chatter requires consideration of at least two degrees of freedom as well as consideration of the special geometry of the drilling and reaming tools. In this paper we find analytical stability boundaries for drilling; the analysis extends a boring model developed by Li and Ulsoy (1998). We also show that it is necessary to use a different approach to predict instability in reaming. Stability boundaries for reaming were found by a method proposed for milling by Altintas and Budak (1995). A dynamic time-domain simulation suitable for both drilling and reaming was used to confirm analytical predictions and obtain qualitative insight into the instabilities, which involve both forward and backward whirling modes.
Parameter Estimation in a Nonlinear Vibrating System Using an Observer for an Extended System
Authors: Chatterjee Anindya , Cusumano Joseph P.
Published: February 2021

We present a new observer-based method for parameter estimation for nonlinear oscillatory mechanical systems where the unknown parameters appear linearly (they may each be multiplied by bounded and Lipschitz continuous but otherwise arbitrary, possibly nonlinear, functions of the oscillatory state variables and time). The oscillations in the system may be periodic, quasiperiodic or chaotic. The method is also applicable to systems where the parameters appear nonlinearly, provided a good initial estimate of the parameter is available.

The observer requires measurements of displacements. It estimates velocities on a fast time scale, and the unknown parameters on a slow time scale. The fast and slow time scales are governed by a single small parameter ϵ.

Using asymptotic methods including the method of averaging, it is shown that the observer’s estimates of the unknown parameters converge like e−ϵt where t is time, provided the system response is such that the coefficient-functions of the unknown parameters are not close to being linearly dependent. It is also shown that the method is robust in that small errors in the model cause small errors in the parameter estimates.

A numerical example is provided to demonstrate the effectiveness of the method.
Compact Nonlinear Signal Representation in Machine Tool Operations
Authors: Bukkapatnam Satish T. S.
Published: February 2021

Effective processing and compact representation of signals from manufacturing processes is necessary for sensor-based modeling (Venuvinod 98), and real-time diagnosis and control purposes. However, the processing and the representation of signals emerging from nonlinear processes remains largely ignored. This article focuses on the compact representation of near-periodic signals (signals containing a dominant period), emerging from nonlinear dynamical systems with known initial conditions. Such signals commonly occur in machine tool operations. We propose the concept of pseudoprobability space and provide an approach based on lifting scheme to customize wavelet filters to compactly represent near-periodic signals, and validate the approach for acoustic emission signals emanating from machine tool operations. Here, we focus on the concentration of the reconstructed signal using the coefficients from lifting on a single scale. We provide a detailed assessment of our approach, including a detailed study of the relationship between the discrete wavelet transform (DWT) and the discrete-time wavelet transform (DTWT). We derive the pyramid algorithm for DTWT with non-biorthogonal wavelets, which is necessary for our assessment. Our numerical experiments establish the viability of our approach.
Cancelling of Self-Excited Vibrations by Means of Parametric Excitation
Authors: Tondl Aleš , Ecker Horst
Published: February 2021

The possibility of cancelling self-excited vibrations of a mechanical system using parametric excitation is discussed. A two-mass system is considered, with the top mass excited by a flow-generated self-exciting force. The parameter of the connecting stiffness between the base mass and the foundation is a harmonic function of time and represents a parametric excitation.

For such a system general conditions for full vibration cancelling are derived and presented. By means of numerical simulation the system is investigated for several sets of parameters. The theoretical results are found to be in very good agreement with the results obtained by simulation. Parameter variations show the extent of the parameter space where significant vibration cancelling can be achieved and illustrate possible applications.
Dynamically Stable Non-Linear Modes of Multiple Subharmonic Torsional Vibration Absorbers
Authors: Chao Chang-Po , Shaw Steven W.
Published: February 2021

Recent studies have demonstrated an arrangement of centrifugal pendulum vibration absorbers that is very effective at reducing torsional vibrations in rotating machinery. The basic system is composed of a pair of identical absorbers that are tuned to a one-half subharmonic order relative to the applied fluctuating torque. These absorbers, when moving in an out of phase manner along a particular path relative to the rotor, are capable of significantly reducing torsional vibrations of a desired order. In this paper we consider the response of systems composed of multiple pairs of these absorbers, with the goal of determining the dynamic stability of the desired response and the effects of small imperfections in the absorbers’ paths. The desired response of this system is one in which the N absorbers act as a single pair, with two groups of N/2 each moving with equal amplitude but exactly out of phase with respect to one another. It is shown that this response can be made to be dynamically stable and robust to certain model uncertainties by a slight, identical overtuning of each absorber. The analytical results, obtained by the method of averaging and symmetric bifurcation theory, are confirmed by simulations for the cases with two and three pairs of absorbers.
Dynamics of Friction Damped Braced Frames With Secondary Structures
Authors: Adam C. , Ziegler F.
Published: February 2021

The influence of light-weight secondary structures on the dynamic response of earthquake excited hysteretically damped shear frames with various elastic and inelastic substructure properties is studied numerically. The numerical procedure used in this paper is based on an iterative synthesis, where interface conditions as well as inelastic deformations are treated as additional fictitious loads and their intensities are updated in an iterative process. Acceleration response spectra of shear frames as well as floor response spectra are generated for various modal primary to secondary mass ratios. Also spectra of the standard deviation of primary and secondary accelerations are computed. Results, efficiently derived by the proposed method, are set in contrast to those derived by decoupled analyses to estimate their capability with respect to hysteretic structural behavior.
Distributed Jenkin Elements in Modeling Hysteresis in Cables
Authors: Hagedorn Peter , Gutzer Ulrich
Published: February 2021

In several previous papers the authors discussed the experimental determination and the mathematical modeling of hysteresis via the Masing model, in particular with view to the hysteresis in the transverse vibrations of cables (see [1–7]). In these papers, the authors focused on the energy dissipation in periodic (forced) or slowly decaying vibrations rather than an arbitrary, general motion. Locally in the cable, the relation between the bending momerts and the curvature was described by several Jenkin elements in addition to a constant bending stiffness term. Experimental data obtained in a simple test rig were then used to identify the parameters of the Jenkin elements.

The number of Jenkin elements in parallel used in the mathematical model depends on the design of the cable, i.e. on the number of layered strands. It can possibly be large in a complex steel cable. A different possibility to model the hysteresis in the case of many Jenkin elements, is to assume a continuous, distributed Masing model at each point of the cable. This corresponds to the assumption of an infinite number of layered strands, which of course is unrealistic in the physical system. Nevertheless, it may how ever lead to a good description of static hysteresis in certain systems. In addition, convenient assumptions on the distributed parameters of the Masing model may give rise to a well manageable identification problem. It then turns out that the hysteresis cycle can be conveniently described by a single initial loading function. In the present paper, it is shown how this function can be obtained from measurements carried out with the Darmstadt test rig, as also described in [5].
Study of Some Rheological Elastoplastic Models With a Finite Number of Degrees of Freedom
Authors: Bastien J. , Lamarque C. H. , Schatzman M.
Published: February 2021

A large number of rheological models can be covered by the existence and uniqueness theory for maximal monotone operators. Numerical simulations display hysteresis cycles when the forcing is periodic. A given shape of hysteresis cycle in an appropriate class of polygonal cycles can always be realized by adjusting the physical parameters of the rheological model.
Experimental Identification of Hysteretic Systems Using the Differential Evolution Algorithm
Authors: Kyprianou A. , Worden K. , Panet M.
Published: February 2021

Hysteretic or memory dependent phenomena are observed in many areas such as magnetism, electricity, materials’ phase transitions and elasto-plasticity of solids [1]. In mechanical vibrations, the elasto-plasticity of some vibrating components introduces non-linearities which can be identified as of hysteretic type. A model, which describes accurately many random non-linear vibrations of the above type, is the Bouc-Wen model. This model is shown in equation (2) below in the context of the forced one-degree of freedom oscillator: (1)mx¨+cx˙+kx+z=f(t) where m, c and k are the mass, damping and spring coefficients respectevely. The restoring force z is given by the Bouc-Wen model (2): (2)z˙=−a|x˙|zn−β|zn|x˙+Ax˙ n oddz˙=−a|x˙|zn−1|z|−βx˙zn+Ax˙ n even The model was firstly introduced by Bouc in its rudimentary form with n equal to unity [2]. This was able to describe the hysteresis loop peculiar to the relationship between the restoring force z and displacement x. The paramaters α and β govern the shape of the loop. Wen generalised the Bouc equation to its final form by introducing the parameter n as given in 2 [3]. This parameter controls the smoothness of the hysteresis loop. The parameter A contributes to the linear striffness of the oscillator.

Because of the versatility of this model to represent various shapes of hysteresis loops, it has attracted many applications in the area of hysteretic vibrations. As a consequence the model is studied for various parameter sets in order to fit in different applications. Therefore a need emerges to identify the parameters for each different case.

This paper presents results of experimental identification of the Bouc-Wen model for an experimental oscillator. The parameters are estimated using the differential evolution method. The authors reported results for simulated data using this method in a previous paper [4].
Response of Hysteretic Multidegree-of-Freedom Systems Using Harmonic Balance Method
Authors: Capecchi Danilo , Masiani Renato , Vestroni Fabrizio
Published: February 2021

This article illustrates the nonlinear response of a hysteretic two degree of freedom system. The constitutive laws which define the force-displacement relation are based on a hysteretic model with Masing rules linked to a suitable nonlinear elastic model. Attention is focused on the periodic response, though an insight is also given to the non-periodic response. The method of analysis used is the harmonic balance with many components. Frequency-response curves are evaluated for different system characteristics. Ratios of small amplitude vibration frequency 3 and 2 are considered, with different hysteresis degree. Notwithstanding the dissipation due to hysteresis usually destroys most of the phenomena evidenced by the classical nonlinear oscillators, in the present analysis a rich behavior is found: IT symmetric and non symmetric, 2T periodic responses are found and so on.
Visualization of the A0 Lamb Wave and a Scholte-Stoneley Wave Interaction
Authors: Latard V. , Merlen A. , Pernod P. , Ahyi A.
Published: February 2021

Previous studies have shown the efficiency of the experimental impulsive acoustic approach for a fine understanding of acoustic scattering processes. The association of a high speed shadowgraph system and a spark generated acoustic pulse allowed the first visualization of the radiation into a fluid of a A0 Lamb wave travelling along an elastic plate (Ahyi and al., 1998) or the interaction of the A (Scholte Stoneley) and A0 on more complex geometries (Latard, 1998). Moreover it allows to follow the evolution in time and determine the generation points of the waves. It is shown in this paper that this visualization technique of impulsive scattering is a quantitative method providing not only wave velocities or frequencies, but also dispersion curves thanks to a single view of the phenomena. This paper presents also the visualization of the A wave by its interaction with the A0 radiation. Numerical simulations of this interaction are compared successfully with visualizations.
Influence of Mechanical Architecture and Coupling Effects on the Vibratory Behavior of Complex Gear Transmissions
Authors: Bourdon Adeline , Yakhou Karim , Chaloyard Laurent , Play Daniel
Published: February 2021

This paper describes a dynamic model for gear transmissions acting around a static working point, and taking into account the complete mechanical components. Gearbox casing behavior is introduced by using substructure analysis, and a tangent stiffness matrix is defined for each roller body bearing element. This model is used to compare the pullup and pulldown dynamic behavior of a five speed medium size automobile gearbox where the gear meshing phenomena are assumed to be identical. The eigenmodes of the pullup and pulldown models are compared and frequency responses to meshing excitation are studied. Substantial differences between pullup and pulldown behavior are observed and associated with to the orientation of static load.
Analysis of the Forces Between Gear Teeth by the Photoelasticity Method
Authors: Podzharov Evgueni I. , Villela Gonzalez Victor R.
Published: February 2021

The photoelasticity method was used to study the change of forces during the gear engagements. The cinetostatic analysis forecasts a change of normal force between teeth when the point of contact passes the pitch point. This happens because of the action of friction forces between teeth when the torques on the gear wheels are constants. To prove this measurements of forces between teeth by the photoelacticity method were implemented in a test bench with a gear test rig with closed mechanical circuit.
Spectral Element Modeling of the Power Flow in a T-Beam Structure: A Computational Experiment
Authors: Ahmida Khaled M. , Arruda José Roberto F.
Published: February 2021

An alternative approach is proposed to predict the power flow pattern and the power dissipated in a T-beam structure. The T-beam used is the same chosen by Burroughs et al. (1994) as part of a round-robin study on structure-borne sound analysis. The Spectral Element Method, which is formulated directly in the frequency domain, is used to predict the energy distribution in the beam. The structure is also modeled using Statistical Energy and Finite Element Analyses. The results obtained by these three approaches are compared to previous FEA results obtained by Hambric (1995). The SEM and FEA results are shown to match well at lower frequencies. The spectral element analysis is shown to be more accurate in predicting the power flow at higher frequencies.
Friction-Induced Vibration in a Dynamometer Utilizing a Two-Disk Friction Interaction
Authors: Anabtawi Ahmed , Farhang Kambiz
Published: February 2021

A mathematical model is developed for a dynamometer for testing a two-disk friction brake system. The model accounts for the compressive shear properties of the friction disks as well as stiffness and inertial characteristics of the dynamometer. Friction coefficient/velocity relations are established using the measurement data and employed in the mathematical model to perform simulations of the dynamometer’s vibration response and instability.

Five different simulations are performed. The first four employ a fifth order polynomial fit from the coefficient friction measured experimentally. One of these four simulations uses data from noisy test while the other three utilize relatively low-noise tests. The fifth and last simulation is carried out using a theoretical coefficient of friction, being assumed to experience certain sinusoidal variation. Such function is used to study the effect of variability in kinetic coefficient of friction of the experimental data.

In the first four simulations (i.e. the experimental cases), it is observed that the simulations turn unstable when the friction-velocity slope becomes negative. That phenomenon is alleviated when higher damping is used. In the fifth simulation (i.e. the sinusoidal case), variation in the coefficient of friction is found to increase vibration in the dynamometer system.
Brake Squeal Analysis by Finite Elements and Comparisons to Dyno Results
Authors: Nack W. V.
Published: February 2021

An approximate analysis method for brake squeal is presented. Using MSC/NASTRAN a geometric nonlinear solution is run using a friction stiffness matrix to model the contact between the pad and rotor. The friction coefficient can be pressure dependent. Next, linearized complex modes are found where the interface is set in a slip condition. Since the entire interface is set sliding, it produces the maximum friction work possible during the vibration. It is a conservative measure for stability evaluation. An averaged friction coefficient is measured and used during squeal. Dynamically unstable modes are found during squeal. They are due to friction coupling of neighboring modes. When these modes are decoupled, they are stabilized and squeal is eliminated. Good correlation with experimental results is shown. It will be shown that the complex modes baseline solution is insensitive to the type of variations in pressure and velocity that occur in a test schedule. This is due to the conservative nature of the approximation. Convective mass effects have not been included.
Studies on the Dynamic Behavior of a Printed Circuit Board
Authors: Wang Hongfang , Zhao Mei
Published: February 2021

The dynamic behavior of printed circuit (PC) boards exercises strong influence on the reliability of electronic equipment. In this paper, the dynamic behavior of a PC board is studied by means of computation and verified by experiment with results compared favorably. This shows that FE modeling strategy used is sound. In general, excitement frequencies induced by external environment are in the range from several Hz to several hundred Hz. In order to avoid product failures due to resonance, it is desirable to make the fundamental natural frequency of PC boards as high as possible. Two structural modified design methods to raise the fundamental frequency are given with a numerical example.
Thickness Profiles for Rotating Circular Disks That Maximize Critical Speed
Authors: Renshaw Anthony A. , Warner Grant M.
Published: February 2021

Thickness profiles for rotating disks that maximize critical speed are determined for use by designers of industrial circular saws. The disk thickness is permitted to vary between fixed lower and upper bounds, the lower bound corresponding to the minimum thickness saw capable of supporting the in-plane stresses associated with cutting forces and rotation, the upper bound corresponding to the thickness of the saw teeth. The optimal thickness profile consists of two annuli, the inner one with thickness equal to the upper bound, the outer one with thickness equal to the lower bound. With the optimal thickness profile, the critical speed can be raised up to 24%, depending on the clamping ratio of the disk and the lower bound. Optimal thickness profiles and increases in critical speeds are described and compared to existing saw designs.
The Influence of Transverse Clamping Flexibility on Centrally Clamped, Centripetally Tensioned, Rotating Circular Disks
Authors: Kim Hong-Ryul , Renshaw Anthony A.
Published: February 2021

A detailed design study is presented analyzing the influence of transverse clamping flexibility on the critical speeds and transverse stiffness of centrally clamped, centripetally tensioned, rotating circular disks. Tensioning techniques, which introduce in-plane stresses into thin plates, are commonly used to improve the critical speed and transverse stiffness of industrial circular saws. In centripetal tensioning, the magnitude of tensioning increases with the rotation speed of the disk, an objective that requires the disk to expand radially within the clamp as it rotates. Clamp designs that allow this radial expansion are necessarily more flexible in the transverse direction than traditional clamps, an effect that can be detrimental to the performance of high speed circular saws. The analysis here provides quantitative design guidelines for centripetal tensioning clamps to ensure that they improve circular saw performance.
Nonlinear Vibration of Parametrically Excited Viscoelastic Moving Belts
Authors: Zhang Lixin , Zu Jean W.
Published: February 2021

The dynamic response and stability of parametrically excited viscoelastic belts are investigated in this paper. The linear viscoelastic differential constitutive law is employed to characterize the material property of belts. The generalized equation of motion is obtained for a viscoelastic moving belt with geometric nonlinearity. The method of multiple scales is applied directly to the governing equation, which is in the form of continuous gyroscopic systems. Closed-form expressions for the amplitude, existence conditions and stability conditions of non-trivial limit cycles of the summation resonance are obtained. Effects of viscoelastic parameters, excitation frequencies, excitation amplitudes and axial moving speeds on stability boundaries are discussed.
Combinations for the Free Vibration Behaviors of Anisotropic Rectangular Plates Under General Edge Conditions
Authors: Narita Yoshihiro
Published: February 2021

The free vibration behavior of rectangular plates provides important technical information in structural design, and the natural frequencies are primarily affected by the boundary conditions as well as aspect and thickness ratios. One of the three classical edge conditions, i.e., free, simple supported and clamped edges, may be used to model the constraint along an edge of the rectangle. Along the entire boundary with four edges, there exist a wide variety of combinations in the edge conditions, each yielding different natural frequencies and mode shapes. For counting the total number of possible combinations, the present paper introduces the Polya counting theory in combinatorial mathematics, and formulas are derived for counting the exact numbers. A modified Ritz method is then developed to calculate natural frequencies of anisotropic rectangular plates under any combination of the three edge conditions and is used to numerically verify the numbers. In numerical experiments, the number of combinations in the free vibration behaviors is determined for some plate models by using the derived formulas, and are corroborated by counting the numbers of different sets of the natural frequencies that are obtained from the Ritz method.
A Closed-Form Approach to Transient Dynamic Response of One-Dimensional Distributed Systems
Authors: Wu Xuqiang , Yang Bingen
Published: February 2021

A closed-form transient analysis of one-dimensional distributed dynamic systems is presented. The proposed approach, called the Z-Prime Method, starts with inverse Laplace transform of a distributed transfer function formulation. Through establishment of a relation between transfer function residues and system eigensolutions, the closed-form transient response of the distributed system under general external, boundary and initial disturbances is obtained. Unlike conventional modal expansion, the proposed method does not depends on any orthogonal eigenfunctions.
Modal Analysis for the Active Multi-Layer Beams by Using Spectrally Formulated Exact Eigenfunctions
Authors: Lee Usik , Kim Joohong
Published: February 2021

In this paper, a modal analysis method (MAM) is introduced for the active multi-layer laminate beams. Two types of active multi-layer laminate beams are considered: the elastic-viscoelastic-piezoelectric three-layer beams and the elastic-piezoelectric two-layer beams. The dynamics of the multi-layer laminate beams are represented by a set of fully coupled equations of motion, derived by using Hamilton’s principle. The exact eigenfunctions are spectrally formulated and the orthogonality of eigenfunctions is derived in a closed form. The present MAM is evaluated through some numerical examples. It is shown that the dynamic characteristics obtained by the present MAM certainly converge to the exact ones obtained by SEM as the number of eigenfunctions superposed in MAM is increased. The modal analysis results are also compared with the results obtained by FEM.
Forced Vibration and Dynamic Stability of a Rotating Tapered Composite Timoshenko Shaft
Authors: Kim Wonsuk , Argento Alan , Scott Richard A.
Published: February 2021

The response and stability of a high speed extended length tool holder subjected to cutting forces typical of milling operations are studied. The system is modeled as a rotating, tapered, filament-wound composite. Timoshenko shaft having clamped-free supports, and subjected to fluctuating, deflection-dependent, cutting-type end loads. Viscous damping is also included in the model. The general Galerkin method is used to satisfy spatial dependence in the system equations, and the monodromy matrix method and numerical integration are used to determine the system’s stability and response, respectively.
Analysis of the Natural Vibration Properties of a Timoshenko Beam Supported by Springs (by Finite Integral Transform Method)
Authors: Xu Zhixiang , Tamura Hideyuki , Seto Kunisato
Published: February 2021

This paper presents analytical results of transverse vibration of a Timoshenko beam supported by spring-spring which stiffness is variable, that is a simplified model of magnetically levitated vehicle body’s vibration problem and magnetic bearings support shaft’s vibration problem. By applying the finite integral transform technique, the analytical solution of this dynamic model is successfully obtained. Especially, by investigating the frequency equation, the effect of the stiffness of two supporting-springs to the natural frequencies is clarified. From the results, it is cleared that the natural frequencies of the beam system can be effectively controlled by changing the supporting-spring’s stiffness.
Free Response of Twisted Plates
Authors: Mockensturm Eric M. , Mote C. D.
Published: February 2021

In previous work, Mockensturm and Mote (1999) investigated the effects of twist on steady motions of an axially moving plate. It was found that twisting produces compressive stresses that increase with twist, aspect ratio, and initial, longitudinal tension. In this work, we study the effects of the stresses and non-flat equilibrium produced by twist on the free response. To accomplish this, the equations of motion are linearized about the equilibrium configuration, yielding a set of three, coupled, linear partial differential equations. The equations are discretized and the free response is predicted from the resulting discrete eigenvalue problem. As a function of twist angle, the natural frequencies first increase and then decrease rapidly to zero as the compressive lateral stresses become sufficiently large to cause wrinkling. The effects of thickness, aspect ratio, and initial tension on natural frequencies are also studied.
Nonlinear Dynamics of a Taut Spatial String With Material Nonlinearities
Authors: Leamy Michael J. , Gottlieb Oded
Published: February 2021

A spatial string model incorporating a nonlinear (and non-conservative) material law is proposed using finite deformation continuum mechanics. The influence of material nonlinearities on the string’s dynamic response to excitation near a transverse natural frequency is shown to be small due to their appearance at high orders only. Material nonlinearities appear at low order in the equations for excitation near a longitudinal natural frequency and a solution for this case is developed by applying the method of multiple scales directly to the partial differential equations. An example string is considered to explore the influence of material nonlinearities on the dynamic response. Rich modal content is found, which can not be predicted by simpler models. Additionally, the material nonlinearities are shown to exert their greatest, influence away from resonance, where they serve to limit the response amplitudes.
Modal Overlap and Dissipation Effects in a Fuzzy Structure Containing a Continuous Master Element
Authors: Drexel M. V. , Ginsberg J. H.
Published: February 2021

This work was prompted by a study performed by Strasberg (1997) in which numerous small spring-mass-damper systems are attached to a large suspended mass representing the master structure. The isolated natural frequency of each attached system was selected to match in average the natural frequency of the isolated master structure. Strasberg found that the critical issue when an impulse excitation is applied to the master structure is the bandwidth of the isolated attached systems in comparison to the spacing between the natural frequencies of the system. Modal overlap, which corresponds to the bandwidths that exceed the spacing of those frequencies, was shown to greatly influence the response of the master structure. Light damping, for which there is little modal overlap, corresponds to an impulse response that consists of a sequence of nearly periodic exponentially decaying pulses, and the transfer function for harmonic excitation of the master structure indicates that the sub-structure acts as a vibration absorber for the master structure. Increased damping leads to modal overlap, with the result that the impulse response consists of a single decaying pulse. The frequency domain transfer function indicates that the vibration absorber effect is enhanced. The present work explores these issues for continuous systems by replacing the one degree of freedom master structure with a cantilever beam. The system parameters are selected to match Strasberg’s model, with the suspended sub-structure placed randomly along the beam. The beam displacement is represented as a Ritz series whose basis functions are the cantilever beam modes. The coupled equations are solved by a state-space eigenmode analysis that yields a closed form representation of the response in terms of the complex eigenmode properties. The continuous fuzzy structure is shown not to display the transfer of energy between the master structure and the substructure that was exhibited by the discrete fuzzy structure, apparently because of the asynchronous motion of the attachment points resulting from the spatial variability of the beam’s motion. The vibration absorber effect for harmonic excitation is only obtained for the heavy damping in the case of a beam.
Simplified Dispersion Relations for Floquet Waves in a Plate With Multiple Arrays of Attachments
Authors: Gueorguiev Dimitar , McDaniel J. Gregory , DuPont Pierre
Published: February 2021

Recently, the authors developed analytical expressions for the dispersions of Floquet waves that propagate in a structure consisting of a plate with multiple arrays of line attachments. The dispersions of these Floquet waves, and in particular the imaginary parts of their wavenumbers, quantify the attenuation of vibrational energy in space as the frequency of a local excitation is varied. Understanding how the parameters of the attached structures, such as their spacings and impedances, affect the Floquet wave dispersions could provide further means to include consideration of energy localization or distribution in the structural design process. Such an understanding is developed in the present work by identifying those cases in which the treatment of certain arrays can be greatly simplified. In particular, limiting cases of small and large array spacings are investigated for which the treatment of particular arrays can be greatly simplified. Such simplifications are not immediately obvious without access to analytical expressions for the Floquet wavenumbers, as the dynamics of all arrays are coupled through the plate. Results presented here will aid the structural design community by indicating which design changes most effectively control energy distribution and by indicating when simplified finite element models of multiple-array structures are possible.
Free Vibration of Coupled Disk-Hat Structures
Authors: Bae Jun-Chul , Wickert Jonathan
Published: February 2021

The free vibration of disk-hat structures, such as automotive brake rotors, is investigated analytically and through laboratory experimentation. Of particular interest are the role played by the hat element’s depth in influencing the three-dimensional vibration of the disk, and the manner in which the bending and in-plane modes of the disk alone evolve as a hat of increasing depth is incorporated in the model. The lower vibration modes of disk-hat structures are shown to be characterized by the numbers of nodal circles NC and diameters ND present on the disk, as well as the phase relationship between the disk’s transverse and radial displacements due to coupling with the hat element. Such modes map continuously back to the pure bending and in-plane modes of the disk alone, appear in ordered pairs, and can exist at close frequencies. Those characteristics are explored particularly with respect to sensitivities in the disk’s thickness and the hat’s depth with a view towards shifting particular natural frequencies, or minimizing transverse disk motion in certain vibration modes. Results obtained through analysis and measurement of a prototypical disk-hat structure are applied in a case study with a ventilated automotive brake rotor.
A Free-Free Beam Rotationally Restrained at One End
Authors: Hirsch Richard A.
Published: February 2021

In ground vibration testing of flexible missiles to determine their in-flight vibration modes, it is desirable that the support stiffness be as small as possible relative to the missile beam stiffness. This paper analyzes the effect of a rotational stiffness applied to one end of a uniform free-free beam. The changes in the natural frequency and node locations for the first two modes are calculated as a function of the support stiffness. The Saturn V Apollo Launch Vehicle is used as a numerical example.
Gyro Drift Calibration in Low Cost Inertial System
Authors: Zhao Zhong , Ma Rong , Zhang Weiguo
Published: February 2021

An intelligent gyro drift calibration method for low-cost inertial system is presented in this paper. This method based on fuzzy reasoning and dynamic estimation can calibrate time-varying gyro drift in the motion of vehicle. Experiments have been done on three strapdown inertial all-attitude systems constituted of piezoelectric rate gyros. The result shows that this method is effective by which the residual of piezoelectric gyro drift can be reduced to about one percent of its original drift value.
Genetic Optimization Applied to the Dynamic Design of an Engine Cradle
Authors: Baldanzini Niccolò , Citti Paolo , Pierini Marco
Published: February 2021

An innovative approach to dynamic design is presented that has the notable advantage of allowing the dynamic requirements to be specified from the earliest design stage. The method applies genetic algorithms to optimize the dynamic behavior of the engine-cradle system and its links to the chassis. The optimization minimizes the sum of the amplitudes of the forces transmitted to the chassis, while complying with the static and dynamic constraints. The genetic algorithm was applied to a multibody system model of the engine-cradle system and its links to derive new, improved configurations.
Genetic Algorithm Approach for Optimization of FRP Laminated Cylindrical Shells Under Constraint
Authors: Ohta Yoshiki
Published: February 2021

Fiber Reinforced Plastic (FRP) materials have been increasingly used in many structural applications of space shuttles, airplanes and automobiles, and the structural optimization of FRP laminated composite shells has been studied for stiffer structural design by many researchers. This paper studies the maximization of fundamental frequencies of FRP laminated cylindrical shells under stiffness constraint by using Genetic Algorithm (GA). For this purpose, the frequency equation for simply-supported shells with symmetrically balanced stacking sequence is derived analytically based on Classical Lamination Theory. In optimization the fiber angles and the thickness ratio of each FRP ply, which have continuous real values, are taken as design variables, and fundamental frequency of the shell is maximized under in-plane stiffness constraints. In numerical experiments, extensive numerical calculations are carried out to determine better genetic operators that would be suitable for FRP laminates design, and genetic parameters are tuned for better reliabilities and lower computational costs in the present GA. Optimal design solutions for various laminated cylindrical shells are obtained and then the applicability of the GA to the maximization of frequencies of the shells is studied from numerical results obtained.
An Impact Oscillator With Finite Time Collisions
Authors: Quinn D. Dane
Published: February 2021

We study a simple one-and-a-half degree-of-freedom impact oscillator in which the dynamical behavior is characterized by two regimes — modeling contact and non-contact dynamics, subject to a description of the impactive event. The contact is modeled as a linearly elastic element and the time interval over which contact occurs is of finite duration. This model allows for a coefficient of restitution to be defined which depends on not only the system parameters, but the relative velocity at the point of impact. For sufficiently small impact velocities the colliding bodies remain in contact while for larger relative speeds, the coefficient of restitution is positive. With this model for the collision, an impact oscillator is described and is shown to contain rich dynamical behavior, including periodic and non-periodic motions.
Forced Vibration of Elastic Structures With Friction Contacts
Authors: Sextro Walter
Published: February 2021

In many technical contacts energy is dissipated because of dry friction and relative motion. This can be used to reduce the vibration amplitudes. For example, shrouds with friction interfaces are used to reduce the dynamic stresses in turbine blades. The three-dimensional motion of the blades results in a three-dimensional relative motion of the contact planes. The developed Point-Contact-Model is used to calculate the corresponding tangential and normal forces for each contact element. This Point-Contact-Model includes the roughness of the contact surfaces, the normal pressure distribution due to roughness, the stiffness in normal and tangential direction and dry friction. An experiment with two non-Hertzian contacts is used to verify the developed contact model. The comparison between measured and calculated frequency response functions for three-dimensional forced vibrations of the elastic structures shows a very good agreement.
Effects of Clearance on Normal Mode Frequencies of a Nonsmooth System
Authors: Butcher Eric A.
Published: February 2021

The effects of a clearance or interference on the normal mode frequencies of a two-dof system with bilinear stiffness and without damping are investigated through various modifications of the bilinear frequency relation. First, the exact bilinear natural frequencies of a single degree-of-freedom system are analytically obtained in terms of the amount of clearance and the strength of nonlinearity, and an equivalent linear system is derived. These results are in turn used to construct three methods which approximate the bilinear frequencies for the 2-dof system in which the resulting approximate frequencies are compared with those obtained from numerical simulations. The results demonstrate how these bilinear normal mode frequencies vary with the magnitude of the clearance/interference and thus point toward the need of including such effects in methods which utilize the bilinear frequency relation.
Mesoscale Dynamic Ice Formation and Breaking on a Vibrating Thin Membrane
Authors: Fullilove Jeff , Miller Norman , Shannon Mark , Philpot Michael , Vakakis Alexander , Georgiadis John , Ge Hongming
Published: February 2021

We study dynamic ice formation and breaking (IF/B) on a thin vibrating membrane. The complicated discontinuous dynamics of the membrane is studied experimentally using laser vibrometry. Although the fluid- and coolant-membrane interaction with simultaneous ice forming and breaking is a complicated dynamical phenomenon, the average rate of ice formed and broken can be approximately quantified. The analytical results are compared to experimental measurements.
Characteristic Constraint Modes for Component Mode Synthesis
Authors: Castanier Matthew P. , Tan Yung-Chang , Pierre Christophe
Published: February 2021

In this paper, a technique is presented for improving the efficiency of the Craig-Bampton method of Component Mode Synthesis (CMS). An eigenanalysis is performed on the partitions of the CMS mass and stiffness matrices that correspond to the so-called constraint modes. The resultant eigenvectors are referred to as “characteristic constraint modes,” since they represent the characteristic motion of the interface between the component structures. By truncating the characteristic constraint modes, a CMS model with a highly-reduced number of degrees of freedom may be obtained. An example of a cantilever plate is considered. It is shown that relatively few characteristic constraint modes are needed to yield accurate approximations of the lower natural frequencies. This method also provides physical insight into the mechanisms of vibration transmission in complex structures.
Friction Control for Vibration Suppression
Authors: Gaul L. , Nitsche R.
Published: February 2021

Friction damping in bolted joint connections of large space structures turned out to be a major source of damping (Gaul and Bohlen, 1987). For vibration suppression, the joints are designed such that the normal force in a frictional interface is controlled which improves damping performance. The use of active control to vary the normal contact force in a joint by means of a piezoelectric element is explored. A model consisting of two elastic beams connected by a single active joint is considered. A friction model with velocity dependent dynamics is used to describe the friction phenomena. A control law for friction dampers which maximizes energy dissipation instantaneously by controlling the normal force at the friction interface is proposed. The effect of displacement- and velocity-induced friction dynamics is considered for the design of the control law. We arrive at a dynamic controller which prevents frictional energy stored as potential energy in a bristle model from being returned to the system.
Modeling Extruded Profiles for Railway Coaches Using SEA
Authors: Geissler Paul , Neumann Dirk
Published: February 2021

The acoustical properties of extruded profiles and typical trimmed wall constructions for railway coaches are reviewed. It will be shown how Statistical Energy Analysis (SEA) can be used to calculate these properties. Calculated and measured results for two different extruded profiles and three different trim constructions will be compared and discussed.
The Use of Experimental SEA for Modeling Road Noise in Cars
Authors: Hermans L. , De Langhe K. , Iadevaia M.
Published: February 2021

Over the last years, SEA has been recognized as a useful tool to model and analyze the high-frequency vibro-acoustic behavior of fully assembled complex structures. This paper discusses the experimental derivation of the loss factor model of a passenger car. The paper outlines the different steps which need to be taken to obtained a fully validated experimental SEA model. This includes the subdivision into subsystems, the PIM measurement campaign, the derivation of the loss factors and their associated confidence levels and the model validation. The paper further details how the experimental SEA model was used to quantify and investigate the airborne and structure-borne contributions to the interior noise level for a road noise test condition. The operational power inputs to the vehicle were indirectly determined from operational response measurements. A contribution analysis showed that airborne noise sources dominated structure-borne noise sources above 500Hz. A sensitivity study allowed to propose an effective design modification. This modification was implemented and successfully tested on the road.