bluuebunny/crossref_metadata_2025_split huggingface dataset:
Nonlinear Modal Analysis of a Cracked Beam
Authors: Chati M. , Rand R. H. , Mukherjee S. 
Published: February 2021

Abstract
This paper addresses the problem of vibrations of a cracked beam. In general, the motion of such a beam can be very complex. This phenomenon can be attributed to the presence of the nonlinearity due to the opening and closing of cracks. The focus of this paper is the modal analysis of a cantilever beam with a transverse edge crack. The nonlinearity mentioned above has been modelled as a piecewise-linear system. In an attempt to define effective natural frequencies for this piecewise-linear system, the idea of a “bilinear frequency” is utilized. The bilinear frequency is obtained by computing the associated frequencies of each of the linear pieces of the piecewise-linear system. The finite element method is used to obtain the natural frequencies in each linear region.
In order to better understand the essential nonlinear dynamics of the cracked beam, a piecewise-linear two degree of freedom model is studied. Perturbation methods are used to obtain the nonlinear normal modes of vibration and the associated period of the motion. Results of this piecewise-linear model problem are shown to justify the definition of the bilinear frequency as the effective natural frequency. It is therefore expected that calculating piecewise mode shapes and bilinear frequencies is useful for understanding the dynamics of the infinite degree of freedom cracked beam.
Feed-Back Numerical Implementations of an Optimal Procedure for Chaos Control in a Two-Well Impact Oscillator
Authors: Lenci Stefano , Rega Giuseppe 
Published: February 2021

Abstract
The problem of controlling the chaotic dynamics of an inverted pendulum is addressed. Starting from the optimal excitation obtained in previous works, which gives satisfactory results but only on one side of the phase space, two different implementations have been developed in order to improve the controlled feature of the system.
The implementations consist in a shrewd alternation of one-side optimal and of harmonic excitation, and in an alternation of right and left optimal excitations. They are aimed at reducing the scattered nature of the response, which has been synthetized by the number of jumps between the two potential wells.
Some numerical simulations have been performed, showing the effectiveness of the proposed procedure. Furthermore, the comparison between the two cases has been discussed on both a local and a global basis.
Toward a Minimal Dynamic Model of a 6-DOF Parallel Robot
Authors: Beji L. , Pascal M. , Joli P. 
Published: February 2021

Abstract
In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.
Experimental and Numerical Investigation of a Nonlinear Autoparametric System
Authors: Berlioz Alain , Dufour Régis , Sinha Subhash C. 
Published: February 2021

Abstract
Experimental and numerical investigations are carried out on an autoparametric system consisting of a composite pendulum attached to a harmonically base excited mass-spring subsystem. The dynamic behavior of such a mechanical system is governed by a set of coupled nonlinear equations with periodic parameters. Particular attention is paid to the dynamic behavior of the pendulum. The instability threshold of the pendulum is determined from the semi-trivial solution of the linearized equations. The set of nonlinear differential equations is then integrated with respect to time using step-by-step methods. The developed experimental setup makes it possible to analyze the angular displacement of the pendulum using an opto-electronic sensor. The motion of the pendulum is numerically analyzed via phase-plane portraits and Poincaré maps. A subcritical bifurcation is plotted and chaos is observed. The predicted results are experimentally validated.
Experimental Investigation of a Piezoelectrically Actuated Rotating Parts Feeder
Authors: Chang S. H. , Yang T. W. 
Published: February 2021

Abstract
The parts feeder provides both horizontal and vertical forces to transfer the small parts between stations in automated manufacturing processes. In this paper, the dynamic characteristics of a piezoelectrically actuated rotating parts feeder was evaluated. The model of the piezoelectric bimorph, the key component of the parts feeder, is formulated under DC and AC excitation. Experiments using laser interferometer, impedance analyzer and spectrum analyzer were conducted to measure displacement sensitivity, resonance frequencies and antiresonance frequencies of the electrical/mechanical system. Relations between driving frequencies and vibration amplitudes under various driving voltages were reported. From experimental results, the resonance frequencies of the mechanical system were identified at 176.6 Hz and 535 Hz. The first resonance and anti-resonance frequencies of the electrical system were found at 176.0 Hz and 177.5 Hz. The electromechanical coupling coefficient for piezoelectric actuator using Mason formula is 13%. Operating at the first resonance frequency, the parts feeder feeds at 17.66 mm/sec with a vertical vibration amplitude of 14.2 μ m.
Dynamics of Rotor/Bearing System With Flexible Rotor and Flexible Bearing Support
Authors: Muszynska Agnes , Petchenev Alex , Goldman Paul 
Published: February 2021

Abstract
The paper analyzes, theoretically and experimentally, the lowest four lateral modes of an isotropic rotor/fluid-lubricated bearing system with flexible rotor and flexible bearing support. The parameters of the analytical model of the system are identified using sweep-frequency modal testing of the rotor rig. A nonsynchronous, circular-rotating-force excitation was applied sequentially at the rotor and at the fluid-lubricated bearing casing, in order to generate the response data. The approach used in this study emphasizes the dynamic features of the system which are invariant to the choice of coordinate system.
The system is described using Dynamic Stiffness matrix. This provides an advantage of simplicity, allowing a comprehensive stability study for various system parameters.
Distributed Transfer Function Synthesis of Multi-Body Flexible Rotor Systems
Authors: Yang Bingen , Fang Houfei 
Published: February 2021

Abstract
A distributed transfer function synthesis is proposed for modeling and analysis of rotor systems assembled from multiple flexible and rigid components. The method is capable of treating non-self-adjoint effects, general boundary conditions and multi-body coupling, and delivers exact and closed-form analytical solutions for various problems. The proposed method is illustrated in two numerical examples.
Vibration Analysis of High Speed Stepped Thrust Gas Film Bearings With Inertia Effects
Authors: Ochiai Masayuki , Hashimoto Hiromu 
Published: February 2021

Abstract
Stepped thrust gas film bearings are widely used for high speed rotating machinery because of their simple structure, relatively high load carrying capacity and stability. In such bearings, the gas film inertia forces may play an important role under high speed conditions. In this paper, the vibration analysis of high speed, stepped thrust gas film bearings considering the inertia effects is described. In the numerical analysis, the static and dynamic pressure distributions in pocket and land regions are evaluated from the generalized Reynolds equation considering the centrifugal force. The pressure values at the step are calculated by considering the conservation of mechanical energy and the continuity of gas film flow in pocket and land regions. Moreover, the dynamic response of bearings subjected to impulsive and sinusoidal excitations are analyzed for different values of film thickness ratios. From the numerical results, the effects of gas film inertia on the vibration characteristics of bearings are clarified.
Static and Dynamic Response of Plates With Curved Boundaries
Authors: Park Duk-Hyun , Yang Bingen 
Published: February 2021

Abstract
A semi-analytical method for analysis of flexible plates with curved boundaries is presented. Through an isoparametric transformation, the original spatial domain of the plate is mapped onto a rectangular region, where the strip distributed transfer functions of the plates are introduced. This transfer function formulation yields closed-form predictions of the displacement, stresses and eigensolutions of the plate. The accuracy and efficiency of the method is verified in numerical examples.
Spatial Modulation of Repeated Vibration Modes in Rotationally Periodic Structures
Authors: Kim Mintae , Moon Joonho , Wickert Jonathan A. 
Published: February 2021

Abstract
When a structure deviates from axisymmetry because of circumferentially varying model features, significant changes can occur to its natural frequencies and modes, particularly for the doublet modes that have non-zero nodal diameters and repeated natural frequencies in the limit of axisymmetry. Of technical interest are configurations in which inertia, dissipation, stiffness, or domain features are evenly distributed around the structure. Aside from the well-studied phenomenon of eigenvalue splitting, whereby the natural frequencies of certain doublets split into distinct values, modes of the axisymmetric structure that are precisely harmonic become contaminated by certain additional wavenumbers in the presence of periodically spaced model features. From analytical, numerical, and experimental perspectives, this paper investigates spatial modulation of the doublet modes, particularly those retaining repeated natural frequencies for which modulation is most acute. In some cases, modulation can be sufficiently severe that a mode shape will beat spatially as harmonics with commensurate wavenumbers combine, just as the superposition of time records having nearly equal frequencies leads to classic temporal beating. A straightforward algebraic relation and a graphical checkerboard diagram are discussed with a view towards predicting the wavenumbers present in modulated eigenfunctions given the number of nodal diameters in the base mode and the number of equally spaced model features.
Planar Finite Forced Dynamics of a Double Hinged Circular Arch: Theory and Experiments
Authors: Benedettini Francesco 
Published: February 2021

Abstract
The planar dynamics of an elastic circular arch undergoing large displacements under a sinusoidally varying, concentrated, vertical force at its tip is analyzed. First, a revision of theoretical models found in the literature and an analysis on different analytical approximations consistent with different simplifying assumptions is done; then, the analytical results are compared with those of an experimental steel model of a double hinged circular arch. The principal region of instability of the unimodal symmetric solution in which the nonlinear modal coupling excites the antisymmetric component is studied; moreover, inside this principal instability region, subregions of instability of any periodic solution are found and the corresponding increased complexity of the time laws is analyzed by using time series analysis tools.
Multimodal Resonances in Suspended Cables via a Direct Perturbation Approach
Authors: Rega Giuseppe , Lacarbonara Walter , Nayfeh Ali H. , Chin Char-Ming 
Published: February 2021

Abstract
We analyze the nonlinear three–dimensional response of an elastic suspended cable with small sag-to-span ratio to a harmonic excitation. We investigate the case of primary resonance of the first in-plane symmetric mode when it is involved in a one–to–one internal resonance with the first antisymmetric planar and nonplanar modes and a two–to–one internal resonance with the first symmetric nonplanar mode. We apply the method of multiple scales directly to the governing two integro–partial–differential equations and associated boundary conditions with no a priori assumption on the shape of the motion. The result is a system of four coupled nonlinear complex–valued equations describing the modulation of the amplitudes and phases of the four interacting modes. The spatial-temporal corrections to the displacement field at higher orders show that the solution is not separable in space and time. Prelimary comparisons with a companion Galerkin-type discretized model show that the latter must be used with some care in studying finite–amplitude motions of cables.
Near-Resonance Motion of a Rotating System With a Limited Source of Torque
Authors: Petchenev Alex , Bently Donald E. , Goldman Paul 
Published: February 2021

Abstract
The paper describes near-resonance, non-stationary motion of a system consisting of symmetric rotor with constant unbalance and isotropic support. The source of torque (drive) is considered limited, allowing linearization near the resonance.
The system is considered to be in planar motion.
Interaction between the rotor and stator of the system is nonlinear. It provides diverse effects on the rotor motion due to the limited power of the drive. An example of such interaction is the well known Sommerfeld effect, when the system cannot pass a critical speed because all of the power provided by the drive is dissipated by resonance vibration of the rotor supporting system.
Initial differential equations are reduced to a system of equations, mathematically similar to a system describing motion of a pendulum. Further reduction is possible using a specially developed hierarchic technique. An in-depth dynamic analysis makes it possible to apply control to the system, providing higher or lower resonance amplitudes.
Some Aspects of the Analysis of Stick-Slip Vibrations With an Application to Drill Strings
Authors: van de Vrande Bram L. , van Campen Dick H. , de Kraker Bram 
Published: February 2021

Abstract
This paper deals with a systematic procedure to calculate periodic solutions of dynamic systems experiencing dry friction. In this first attempt we limit ourselves to 1 and 2 dof autonomous models where a smooth approximation of the discontinuous friction force is applied. Using the simple shooting method with a numerical integration scheme suitable for stiff differential equations in combination with a path following algorithm, branches of periodic solutions can be followed for a varying design variable. This approach proves to work very well and will be the basis for developing a numerical tool to investigate more complex mdof dynamic systems with stick–slip phenomena.
Stabilization of 1/3-Order Subharmonic Resonance Using an Autoparametric Absorber
Authors: Yabuno Hiroshi , Endo Yasuhiro , Aoshima Nobuharu 
Published: February 2021

Abstract
The paper proposes a stabilization method for 1/3-order subharmonic resonance with an autoparametric vibration absorber. A main system with nonlinear spring stiffness and harmonic excitation, i.e., subjected to a sinusoidally changed magnetic force, is introduced as a model which produces 1/3-order subharmonic resonance. A damped pendulum system, whose natural frequency is in the neighborhood of one-half of the main system, is attached to the main system as an absorber, in order to induce 1:2 internal resonance. The 1/3-order subharmonic resonance which occurs in the case of locked pendulum is avoided due to energy transfer between the main system and the absorber, and due to energy dissipation by the absorber. It is also theoretically shown that a stable nontrivial steady state with respect to the 1/3-order subharmonic frequency component is changed into an unstable one due to the absorber. Experimental results show the validity of the autoparametric vibration absorber for the 1/3-order subharmonic resonance.
An Efficient Definition of Transmissibility for a General Equipment Isolation System
Authors: de Espíndola J. J. , Bavastri C. A. 
Published: February 2021

Abstract
A definition of transmissibility is introduced so that the efficiency of the isolation system is easily assessed. The system to be isolated may, in principle, be of any complexity: an elastic body isolated from an elastic foundation, a rigid body isolated from an elastic or rigid foundation, and so on. The isolators may be of any number and nature, their elastic centre located at any co-ordinates and their angular positions, with respect the isolated system, arbitrary. A numerical example consisting of an aircraft engine mounted with viscoelastic isolators is worked out.
Analysis of Operating Deflection Shapes Based on Subspace Method
Authors: Tsujiuchi Nobutaka , Matsumura Yuichi , Koizumi Takayuki 
Published: February 2021

Abstract
In this paper, we propose the new method to identify the Operating Deflection Shapes (ODSs) from the measurement data of time domain. At first, we present the identification scheme of ODSs based on a state-space model. Then the scheme is extended to identify the ODSs adaptively for the time-varying systems by using the URV Decomposition (URVD). Proposed scheme is able to decompose the deformation of a structure under operating condition into the underlying superposition of well excited frequency components. This paper introduces the algorithm and shows the effectiveness of our proposed scheme applyed for both synthesized and experimental data.
Modified Geometrical Acoustics Phenomena Exhibited by Computations for Hemi-Capped Cylinders in the Mid-Frequency Range
Authors: Ginsberg J. H. 
Published: February 2021

Abstract
The relation between surface pressure and normal velocity on a slender capped cylinder is examined. The data for this study are obtained from the wavenumber-based version of the surface variational principle (SVP), whose representation of the acoustic field is shown to consist of a discretely infinite sum of waves propagating in the circumferential and meridian directions. The circumferential wavenumbers are uncoupled, whereas coupling of the meridional spectra is described by the wet-surface impedance, whose value is obtained within an SVP analysis. Typical mid-frequency range results for this quantity in the case of a hemi-capped cylinder are examined. It is shown that the individual waves are essentially uncoupled, except at wavenumbers close to the pair at which a helical wave traveling along the surface transitions from subsonic to subsonic. The same type of phenomena are shown to occur over broad range of frequencies, even for reasonably short configurations. Interaction between wavenumber pairs, and the need to compute impedance values are the primary new aspects not encountered in ray theory analyses.
On Wavelet-Analyzed Seismic Response of SDOF Systems
Authors: Basu Biswajit , Gupta Vinay K. 
Published: February 2021

Abstract
This paper presents the technique using wavelet analysis to solve the response of a single-degree-of-freedom (SDOF) system subjected to transient excitations such as earthquakes. A brief review of the wavelet transform and its discretization, time-frequency representation of the ground motion and the input-output relation for a SDOF system is presented. A new orthogonal basis function has been used for describing the temporal and frequency characteristics of the input and the response in case of a recorded accelerogram during 1971 San Fernando earthquake. Also, the input-output relation in the wavelet domain has been illustrated through comparison with the time domain simulation results.
Some Recent Advances in Model Updating
Authors: Natke H. Günther , Cottin N. , Oeijeklaus M. 
Published: February 2021

Abstract
Model updating has now become a well-known field of application in engineering. The following is restricted to spatially discretized mathematical models.
First, the classical sensitivity (including sensitivities of the measuring errors) and the selective sensitivity within updating are mentioned. The latter leads to a computational construction of selective excitation force vectors. Reliable estimates can then be obtained.
The solutions of updating methods which result in nonlinear equations with respect to the parameters to be estimated are the global minima of these equations. This problem will be solved by applying interval arithmetic. Additionally, hints are given with regard to an efficient arithmetical procedure by massive parallel computing.
Large-sized problems need the reduction of the model orders. Substructuring and incomplete modal transformations are the methods that are well-known and applied. Some necessary and sufficient conditions are discussed in this context.
Examples will demonstrate the subjects discussed. The outlook mentions more advanced signal processing and identification methods which take non-stationary processes and non-linearly behaving systems into account.
Finite Element Error Localization Using the Error Matrix Method
Authors: Papadopoulos Michael , Garcia Ephrahim 
Published: February 2021

Abstract
A higher order version of the Error Matrix Method is proposed to increase the accuracy in the finite element error localization. The method retains a user specified number of terms from the appropriate binomial expansion. Jacobi’s iterative method is then proposed to solve the set of nonlinear equations. It is hypothesized that keeping the higher order terms will improve the error identification for the same number of coordinate degrees-of-freedom and modes. The method is implemented on a nine degree-of-freedom and an Euler-Bernoulli beam numerical examples. It is shown that while there needs to be a large number of measured coordinates and modes, the magnitude of the errors are more accurately identified.
Optimal Control of Nonlinear Parametrically Excited Beam Vibrations by Spatially Distributed Sensors and Actors
Authors: Kugi Andreas , Schlacher Kurt , Irschik Hans 
Published: February 2021

Abstract
This contribution is focused on a straight composite beam with multiple piezoelectric layers under the action of an axial support motion. In the sense of v. Karman a nonlinear formulation for the axial strain is used and the equations of motion are derived by means of the Hamilton formalism. This system turns out to be a special class of infinite dimensional systems, the so called Hamilton AI-systems with external inputs. In order to suppress the excited vibrations two infinite control laws are proposed. The first one is an infinite PD-feedback law and the second one is based on the nonlinear H∞-design, where an exact solution of the corresponding Hamilton Jacobi Isaacs equation is presented. The necessary quantities for the control laws can be measured by appropriate space-wise shaped sensors and the asymptotic stability of the equilibrium point can be proved.