bluuebunny/crossref_metadata_2025 huggingface dataset:
Active Control of Elastodynamic Vibrations of a Flexible Mechanism With Piezoelectric Actuator
Authors: Chen Ching-I
Published: February 2021

This study focused on the application of active vibration control strategies for flexible moving structures which degrade into transient dynamic vibration problem. These control strategies are based primarily on modal control methods in which the flexible moving structures are controlled by reducing their dominant vibration modes. This work numerically investigated active control of the elastodynamic response of a four-bar mechanical system, using a piezoelectric actuator. A controller based on the modified independent modal space control theory was also utilized. This control theory produced overall excellent performance in terms of achieving the desired closed-loop structural damping. The merits of this technique include its ability to manage the spill-over effect, i.e. eliminate the magnitude of vibrations associated with uncontrolled modes, using only a few selected modes for control. This control was accomplished using a time sharing technique, which reduces the number of piezoelectric actuators required to control a large number of vibration modes. Furthermore, this algorithm implements a procedure for determining the optimal locations for the piezoelectric actuators.

The dynamics of a steel four-bar linkage was selected with a flexible coupler separated by six elements and one piezoelectric actuator was used in the numerical simulation. The optimal actuator position was located at the third element from the right to the left. Results in this study demonstrated that a highly desired the structural vibration damping could be achieved. This control technique can be applied to transient dynamic systems.
Two-Degree-of Freedom Control Using H∞ and ANVC to Reduce the Vibration of Vehicle Engine-Body System
Authors: Ito Ryogo , Yang Jianming , Suematsu Yoshikazu , Shimizu Sohta , Arai Nomio
Published: February 2021

This paper presents a two-degree-of freedom (2DOF) controller, which is combined a feedback (FB) controller with feedforward (FF) controller, to control the vibration of vehicle engine-body system. The robust feedback controller is designed by H∞ theory to attenuate the influence of engine vibration disturbance by modelling the vehicle engine-body system as nominal four-degree-of freedom vibration system with unmodelled disturbance. Based on filtered-X LMS algorithm, an active noise and vibration control is used in a feedforward controller to improve control performance further. To demonstrate the effectiveness of the control scheme, we have made some experiments in an experimental device, which is designed to imitate a real vehicle engine-body system.
A Novel Technique for the Stability of Multiple Frequency Resonators
Authors: Olgac Nejat
Published: February 2021

A novel stability analysis is presented for feedback controlled systems with multiple unrelated time delays. The concern arises in an effort creating multi-frequency delayed resonators. Despite the broad treatment of single time delay cases there is no mechanism to analyze the stability of systems involving multiple delays. The proposed method is an advancement over the D-subdivision methodology. It reduces the stability based subdivisions and search to a single dimensional space instead of multiple dimensional platform. The method is very simple to implement and it results in the stability assessment of the given system as the number of unstable root pairs present.
The Nonlinear Behaviour of a Pantograph Current Collector Suspension
Authors: Drugge L. , Larsson T. , Berghuvud A. , Stensson A.
Published: February 2021

The pantograph-catenary system is a critical component for trains required to run at higher speeds. The pantograph often includes nonlinear characteristics and the scope of this work is to investigate if nonlinear dynamic phenomena can occur in an existing design. A model of a pantograph suspension subsystem has been developed according to physical parameter values of the head suspension of the Schunk WBL88/X2 pantograph, providing electric power to the Swedish high-speed train X2. Studies of the system response for different force excitation show both harmonic, subharmonic and chaotic behaviour for the investigated parameter regions.
Stabilization to Nonlinear Systems With Short Time Delay in State Feedback
Authors: Wang Zaihua , Hu Haiyan
Published: February 2021

Local stabilization lo critically stable nonlinear systems with a short time delay in state feedback is discussed in this paper. The stabilizing procedure is composed of two steps. The first step is to simplify the retarded differential equation to an ordinary differential equation by using a linear transform with memory controller and neglecting some high order terms. Then the system equation is simplified into the standard critical forms of ordinary differential equation, and consequently, the center manifold reduction is applied to stabilizing the simplified systems of critical cases. Both analysis and simulation show that the approach is effective if the time delay is short enough.
Uniformly Bounded Input Gives Ultimately Bounded Output: On the Dynamics of a Piecewise Linear Beam System
Authors: Heertjes Marcel F. , van de Molengraft Marinus J. G. , Kok Jan J.
Published: February 2021

A periodically excited piecewise linear beam system is studied. The beam system consists of a supported multi-degree-of-freedom beam with one-sided spring. This system is proved to have a 1-periodic solution to any uniformly bounded periodic force applied along the beam. The existence of a 1-periodic solution will be shown numerically and experimentally for both a harmonic force and a block-wave force.
Braille Printer Dynamics
Authors: Jerrelind J. , Stensson A.
Published: February 2021

A Braille printer forms dots in paper, which are read by blind people. The dots are produced by hammers, which basically consist of a spring loaded moving core that is excited by electromagnetic forces. The system is characterised by non-linear properties such as electromagnetic forcing and impacts. Problems with quality, high temperature and noise limit the operating speed of the printer. To investigate if printing quality problems are caused by the non-linear dynamics in the system, one existing design is modelled and used for evaluation. The simulations show that some mechanical parameters are critical in order to get satisfactory quality on the Braille text.
Nonlinear Dynamics of Percussive Drilling of Hard Materials
Authors: Krivtsov Anton M. , Wiercigroch Marian
Published: February 2021

It is postulated that the main mechanism of the enhancement of material removal rate (MRR) in percussive drilling is associated with generating impact forces, which act on the work-piece and help to develop micro-cracking in the cutting zone. The inherent non-linearity of the discontinuous impact process is modelled as a frictional pair, to generate the pattern of the impact forces. A novel formula for calculating the MRR is proposed, which explains the experimentally observed fall in MRR at higher static forces.
Fold Bifurcations in Discontinuous Systems
Authors: Leine Remco I. , van Campen Dick H.
Published: February 2021

This paper treats discontinuous fold bifurcations of periodic solutions of discontinuous systems. It is shown how jumps in the fundamental solution matrix lead to jumps of the Floquet multipliers of periodic solutions. A Floquet multiplier of a discontinuous system can jump through the unit circle causing a discontinuous bifurcation. Numerical examples are treated which show discontinuous fold bifurcations. The discontinuous fold bifurcation can connect stable branches to branches with infinitely unstable solutions.
Near-Grazing Behaviour of the Harmonic Ocsillator
Authors: Molenaar J. , de Weger J. G. , v. d. Water W.
Published: February 2021

Impacting systems are intrinsically nonlinear. They are found in a great variety of mechanical constructions. The control of the impact phenomena requires a thorough understanding of the dynamics involved. It is discussed that near-grazing systems, i.e. systems in which the impacts take place at low speed, can be described by discrete mappings. The form of this mapping for a harmonic oscillator with a stop is dealt with in detail. It is pointed out how these mappings can be derived and the results are compared to results earlier published. It is indicated how the present results could be checked experimentally.
Analysis of Piecewise Linear Systems With Displacement and Time Regions by Vector Fields
Authors: Nakai Mikio , Murata Shinji , Hagio Seiji
Published: February 2021

A generalized solution methodology based on piecewise linear vector fields is proposed for piecewise linear systems with singular regions or asymmetric restoring forces which vary spatially and temporally. In matrix representation for these systems, state variables in each region can be explicitly expressed as a function of the time the orbit spends between two boundaries or the time the orbit takes to pass through the boundary. The time can be determined by the Brent method, and periodic solutions can then be obtained. Analytical solutions are validated on a system with 3-regions of displacement and 2-regions of time, a circumferential vibration of gear meshing system, by using the newly developed numerical method.
Stability Analysis of Finite Difference Model of Orthogonal Metal Cutting in Presence of Random Noises
Authors: Rodkina Alexandra , Wiercigroch Marian
Published: February 2021

The dynamics of a nonlinear cutting process in the presence of random noise is defined and investigated. This approach is adequate for a wide range of models describing the orthogonal metal cutting processes by a single-degree-of-freedom oscillator, where the nonlinearity comes from the cutting force in form of a variable resistance force. The method of Lyapunov–Krasovskii functional was adopted to analyze the necessary conditions for a stable operation. The conditions ensuring an asymptotic stability in the presence of random noises are established.
Influence of Interaction Between Torsion and Bending on Long-Term Nonlinear Rotor Dynamics
Authors: Zhang Jiazhong , de Kraker Bram , van Campen Dick H.
Published: February 2021

An elementary system with gears and excited by unbalance mass has been constructed for analyzing the interaction between torsion and bending vibration in rotor dynamics. For this system, only the interaction caused primarily by unbalance mass has been investigated. The stability and bifurcation characteristics of the system have been studied by numerical computation based on Hopf bifurcation and Floquet theory. The results show that the interaction between torsion and bending vibrations can affect the stability and bifurcation of the unbalance response, in particular the onset speed of instability. In addition to the above, the interaction also affects the steady-state response. To investigate the influence of unbalance mass, the periodic solution and its stability have been studied near the first bending critical speed of the decoupled system. All the results show that the coupling of torsion and bending vibrations can have a significant influence on the nonlinear dynamics of the whole system.
Nonlinear Vibrations of an Elastic Structure Subjected to Vertical Excitation and Coupled With Liquid Sloshing in a Cylindrical Tank: Resonance With an Axisymmetric Mode
Authors: Ikeda Takashi , Murakami Shin
Published: February 2021

The nonlinear coupled vibrations of an elastic structure and liquid sloshing in a cylindrical tank are investigated. When the structure is vertically subjected to a sinusoidal excitation, and when the natural frequency of the structure is equal to twice the natural frequency of the first axisymmetric mode of sloshing, modal equations governing the coupled motions are derived. Then, the theoretical resonance curves are presented by using the method of harmonic balance and an FFT analysis. As a result, it is demonstrated that the resonance curve for the structure changes from a shape with a peak to a flat shape as the liquid level decreases. It is also clarified that amplitude-modulated motions appear when the tuning condition is deviated. In experiments, theoretical resonance curves were qualitatively in good agreement with the experimental results.
Dynamics of a Cubic Nonlinear Vibration Absorber
Authors: Oueini Shafic S. , Chin Char-Ming , Nayfeh Ali H.
Published: February 2021

We study the dynamics of a nonlinear active vibration absorber. We consider a plant model possessing curvature and inertia nonlinearities and introduce a second-order absorber that is coupled with the plant through user-defined cubic nonlinearities. When the plant is excited at primary resonance and the absorber frequency is approximately equal to the plant natural frequency, we show the existence of a saturation phenomenon. As the forcing amplitude is increased beyond a certain threshold, the response amplitude of the directly excited mode (plant) remains constant, while the response amplitude of the indirectly excited mode (absorber) increases. We obtain an approximate solution to the governing equations using the method of multiple scales and show that the system possesses two possible saturation values. Using numerical techniques, we perform stability analyses and demonstrate that the system exhibits complicated dynamics, such as Hopf bifurcations, intermittency, and chaotic responses.
Stability Limitations for Multiple Centrifugal Pendulum Vibration Absorbers
Authors: Al-suwaiyan Abdallah S. , Shaw Steven W.
Published: February 2021

Centrifugal pendulum vibration absorbers are a type of tuned dynamic absorber used for the attenuation of torsional vibrations in rotating and reciprocating machines. They consist of masses that are constrained to move along a specific path relative to the rotating shaft of the machine. Previous analytical studies have considered the performance of multi-absorber systems with a very specific path and of single absorber systems with general paths. In this paper we investigate the performance and dynamic stability of systems comprised of multiple, identical centrifugal pendulum vibration absorbers that have general paths. The study is carried out by considering a scaling of the system parameters based on physically realistic ranges of dimensionless parameters, which allows for application of the method of averaging. It is found that performance is limited by two distinct types of instabilities. In one of these, the systems of absorbers lose their synchronous character, while the other is a classical nonlinear jump behavior that affects all absorbers identically and leads to disastourous results. These results are used to evaluate the performance of systems with common types of absorber paths, namely circles and cycloids. The analytical results are compared against numerical simulations and good agreement is found.
The Impact of High Speed Machining Technology on the Design and Fabrication of Aerospace Components
Authors: Halley J. E. , Helvey A. M. , Smith K. S. , Winfough W. R.
Published: February 2021

Recently, several new machining techniques have been developed which have driven dramatic changes in the manufacture of aerospace components with thin ribs and webs. There are many such components in commercial and military aircraft, and until recently these components we fabricated as sheet metal assemblies. Through an improved understanding of the dynamic interaction between the tool and workpiece, it has now become economically competitive to create components with thin ribs and webs as monolithic units machined from a solid block by milling.

Ribs are those thin structures created at the periphery of the end mill, as opposed to webs, which are the thin structures created at the face of the end mill. It is easy to see that as the ribs and webs become thinner, the stiffnesses will decrease, and chatter will become more problematic. Chatter during the machining of such parts can result in damage to the part (even cutting through the thin structure) or at least poor surfaces which require hand finishing. This paper outlines the basic technology required to produce these kinds of components efficiently, and cites several examples.
Tool Oscillation and the Formation of Lobed Holes in a Quasi-Static Model of Reaming
Authors: Bayly Philip V. , Young Keith A. , Halley Jeremiah E.
Published: February 2021

A quasi-static model of reaming is used to explain oscillation of the tool during cutting and the resulting roundness errors in reamed holes. Tools with N evenly-spaced teeth often produce holes with N+1 or N-1 “lobes”. These profiles correspond, respectively, to forward or backward whirl of the tool at N cycles/rev. Other whirl harmonics (2N cycles/rev, e.g.) are occasionally seen as well. The quasi-static model is motivated by the observations that relatively large oscillations occur at frequencies well below the natural frequency of the tool, and that in this regime the wavelength of the hole profile is largely independent of both cutting speed and tool natural frequency. In the quasi-static approach, inertial and viscous damping forces are neglected, but the system remains dynamic because regenerative (time-delayed) cutting and rubbing forces are included. The model leads to an eigenvalue problem with forward and backward whirl solutions that closely resemble the tool behavior seen in practice.
Some Nonlinear Effects of Magnetic Bearings
Authors: Steinschaden Norbert , Springer Helmut
Published: February 2021

In order to get a better understanding of the dynamics of active magnetic bearing (AMB) systems under extreme operating conditions a simple, nonlinear model for a radial AMB system is investigated. Instead of the common way of linearizing the magnetic forces at the center position of the rotor with respect to rotor displacement and coil current, the fully nonlinear force to displacement and the force to current characteristics are used.

The AMB system is excited by unbalance forces of the rotor. Especially for the case of large rotor eccentricities, causing large rotor displacements, the behaviour of the system is discussed. A path-following analysis of the equations of motion shows that for some combinations of parameters well-known nonlinear phenomena may occur, as, for example, symmetry breaking, period doubling and even regions of global instability can be observed.
Nonlinear Modeling and Control of Hysteresis in Active Material Systems
Authors: Webb Glenn V. , Lagoudas Dimitris C. , Kurdila Andrew J.
Published: February 2021

Active material actuators present a significant challenge to researchers interested in applying them to aerospace structures. Materials such as shape memory alloys, piezo-ceramcs and electrorheological fluids exhibit hysteresis to varying degrees. Not only do they exhibit hysteresis, but in some cases the hysteresis is non-stationary. We present a methodology that allows for design of controllers for the structural system from linear system theory. This is accomplished by compensating, or linearizing, the hysteresis nonlinearity using an adaptive model of hysteresis. Experimental results for adaptive control of shape memory alloy actuators with non-stationary hysteresis are provided.
Reduced Order Nonlinear Navier Stokes Models for Synthetic Jets
Authors: Rediniotis Othon K. , Kurdila Andrew J.
Published: February 2021

While the potential for the use of synthetic jet actuators to achieve flow control has been noted fro some tme, most studies of these devices have been empirical or experimental in nature. Several technical issues must be resolved to achieve rigorous, model-based, closed loop control methodologies for this class of actuator. The goal of this paper is consequently two-fold. First, we seek to derive and evaluate model order reduction methods based on proper orthogonal decomposition that are suitable for synthetic jet actuators. Secondly, we seek to derive rigorously stable feedback control laws for the derived reduced order models. The readability of the control strategies is discussed, and a numerical study of the effectiveness of the reduced order models are summarized.
Chatter in Turning Process Incorporating the Effect of Ploughing Force
Authors: Wang Z. C. , Cleghorn W. L. , Yu S. D.
Published: February 2021

In this paper, the stability analysis of turning process is performed based on a new cutting force model which includes the effect of ploughing force. This approach utilized the Laplace transform to identify the characteristic roots of the examined machining system. The stability of the machining system can then be determined by examining the locations of the characteristic roots. The stability curve for a specific turning process can then be plotted. The effect of different cutting force models on the stability is also investigated. The results clearly demonstrate some chatter phenomena observed by other researchers.
Model Reduction of a Nonlinear Rotating Beam Through Nonlinear Normal Modes
Authors: Pesheck E. , Pierre C. , Shaw S. W.
Published: February 2021

Equations of motion are developed for a rotating beam which is constrained to deform in the transverse (flapping) and axial directions. This process results in two coupled nonlinear partial differential equations which govern the attendant dynamics. These equations may be discretized through utilization of the classical normal modes of the nonrotating system in both the transverse and extensional directions. The resultant system may then be diagonalized to linear order and truncated to N nonlinear ordinary differential equations. Several methods are used to determine the model size necessary to ensure accuracy. Once the model size (N degrees of freedom) has been determined, nonlinear normal mode (NNM) theory is applied to reduce the system to a single equation, or a small set of equations, which accurately represent the dynamics of a mode, or set of modes, of interest. Results are presented which detail the convergence of the discretized model and compare its dynamics with those of the NNM-reduced model, as well as other reduced models. The results indicate a considerable improvement over other common reduction techniques, enabling the capture of many salient response features with the simulation of very few degrees of freedom.
Forced Oscillations of Rotating Shaft With Nonlinear Spring Characteristics and Internal Damping: Subharmonic Oscillation of Order 1/3 and Entrainment
Authors: Ishida Yukio , Murakami Shin
Published: February 2021

An elastic rotating shaft supported by ball bearings may have nonlinear spring characteristics due to clearance and internal damping due to friction between the shaft and the bearings. In such a system, self-excited oscillations appear in the post critical region and nonlinear forced oscillations appear at various resonance points. In this paper, a phenomenon in the neighborhood of the critical speed of the subharmonic oscillation of order 1/3 of a forward whirling mode is discussed. It is clarified that, similar to the case of the subharmonic oscillation of order 1/2 of a forward whirling mode, an entrainment phenomenon appears due to the interplay between self-excited oscillations and forced oscillations.
Surface Waves on Solid Objects and Shells: Application of Alternate Theoretical Approaches
Authors: Gérard A. , Bao X. L. , Raju P. K. , Überall H.
Published: February 2021

Surface waves on elastic objects can be generated by a variety of forced excitation mechanisms. We choose to study them theoretically as excited by an incident acoustic wave, and to obtain their resonances which are caused by their phase match over closed path. The resonance frequencies then serve to obtain the surface wave phase velocity dispersion curves, and the “Regge trajectory” of their resonances.
Exact Stationary Response Solutions of Nine Classes of Nonlinear Stochastic Systems Under Stochastic Parametric and External Excitations
Authors: Wang Rubin , Yasuda Kimihiko
Published: February 2021

In this paper, a systematic procedure is developed to obtain the stationary probability density function for the response of a general nonlinear system under parametric and external Gaussian white noise excitations. In reference [15], nonlinear function of system was expressed to the polynomial formula. The nonlinear system described here has the following form: x¨+g(x,x˙)=k1ξ1(t)+k2xξ2(t), where g(x,x˙)=∑i=0∞gi(x)x˙i and ξ1,ξ2 are Gaussian white noises. Thus, this paper is a generalization for the results studied in reference [15]. The reduced Fokker-Planck (FP) equation is employed to get the governing equation of the probability density function. Based on this procedure, the exact stationary probability densities of many nonlinear stochastic systems are obtained, and it is shown that some of the exact stationary solutions described in the literature are only particular cases of the presented generalized results.
Dynamics of Spinning Disc Parametrically Excited by Noise
Authors: Ramakrishnan Narayanan , Namachchivaya N. Sri
Published: February 2021

The nonlinear dynamics of a circular spinning disc parametrically excited by noise of small intensity is investigated. The governing PDEs are reduced using a Galerkin reduction procedure to a two-DOF system of ODEs which, govern the transverse motion of the disc. The dynamics is simplified by exploiting the S1 invariance of the equations of motion of the reduced system and further, reduced by performing stochastic averaging. The resulting one-dimensional Markov diffusive process is studied in detail. The stationary probability density distribution is obtained by solving the Fokker-Planck equation along with the appropriate boundary conditions. The boundary behaviour is studied using an asymptotic approach. Some aspects of dynamical and phenomenological bifurcations of the stationary solution are also investigated. The scheme of things presented here can be applied in principle to a four-dimensional Hamiltonian system possessing one integral of motion in addition to the hamiltonian and having one fixed point.
The Effect of Tooth Wear on the Vibration Spectrum of a Spur Gear Pair
Authors: Kuang J. H. , Lin A. D.
Published: February 2021

In this paper, the effect of tooth wear on the vibration spectrum variation of a rotating spur gear pair is studied. In order to approximate the dynamic characteristics of an engaging spur gear pair, the load sharing alternation, position dependent mesh stiffness, damping factor and friction coefficient are considered in the mathematical model. The surface wear on the tooth is derived by Archard’s wear equation. The variation of the vibration spectra introduced from the interaction between the sliding wear and the dynamic load is simulated and analyzed. Numerical results indicate that the dynamic load histogram of an engaging spur gear pair may change greatly with the tooth wear. This finding implies that the variation of the gear vibration spectrum might be used to monitor the tooth wear of an engaging spur gear pair.
A Study on the Instability of Disk-Shaped Gear
Authors: Ren Guangming , Yan Litang
Published: February 2021

In this paper the theory and experiment concerning vibration instability of disk-shaped gear are presented. At first the self-exciting force of gear is searched and the works done by the exciting force and damping force are analyzed. Then the vibration instability of the disk-shaped plain gear is studied with multiple scale’s method of the nonlinear perturbation method. The vibration characteristics of a coupled pair of bevel gears are investigated experimentally. Both theoretical and experimental investigations show that there are actually self-exciting vibrations on the gear. Under certain conditions the forward traveling wave vibration of the driving gear and the backward traveling wave vibration of the driven gear can be instable.
Transmission Modelling for Gear Rattle Analysis
Authors: Wang Yu Michael , Radhakrishnan Manoj , Zhao Weijie
Published: February 2021

This paper describes a model for torsional vibration of automotive manual transmissions. The model is developed for the purpose of analysis and prediction of gear rattles. Elements of the model include engine, clutch, gear mesh, gear backlash, and shaft flexibility. A numerical method — finite element method in the time domain (FET) — is employed for the dynamic analysis. Results are presented which show the effectiveness of the modelling and analysis scheme.
Eigensensitivity of Planetary Gear Free Vibration Properties
Authors: Lin Jian , Parker Robert G.
Published: February 2021

The natural frequency and vibration mode sensitivities to system parameters are rigorously investigated for both tuned and mistimed planetary gears. Parameters under consideration include support and mesh stiffnesses, component masses, and moments of inertia. Using the well-defined vibration mode properties of tuned (cyclically symmetric) planetary gears [1], the eigensensitivities are calculated and expressed in simple, exact formulae. These formulae connect natural frequency sensitivity with the modal strain or kinetic energy and provide efficient means to determine the sensitivity to all stiffness and inertia parameters by inspection of the modal energy distribution.

While the terminology of planetary gears is used throughout, the results apply for general epicyclic gears.
Modeling Axial Vibrations in Herringbone Gears
Authors: Jáuregui Juan Carlos , González Oscar M.
Published: February 2021

This paper addresses the axial vibrations of herringbone gears. Theoretically, herringbone gears balance their axial loads due to their symmetry; however, in practice, they present high vibrations. The reasons are manufacturing deviations such as lead angle errors, pitch error differences between each side of the gear, misalignment between pinion and gear axes, etc. These errors can be represented as an error function of sinusoidal form acting as forced vibrations over the teeth.

Although axial and lateral motions of a gear pair are generally coupled, the symmetric geometry of herringbone gears makes possible to analyze the axial and lateral stiffness as uncoupled functions. It is viable then to represent the axial motion as a single degree of freedom model.

The effect of each parameter of the error function is analyze individually in order to determine which has the greater effect in the system. Results are compared to field data showing good agreement.
Dynamic Response and Stability of a Spur Gear Pair
Authors: Nataraj C. , Arakere N. K.
Published: February 2021

This paper deals with the linearized dynamics of a high-speed spur-gear pair supported on linear orthotropic bearings. The mating teeth are modeled accurately and the effect of the dynamic stiffness variation on the dynamic response is taken into account and, in fact, forms the essence of this work. The resulting six degree of freedom system is nondimensionalized in order to reduce the model to a minimum number of independent parameters and to make the results valid for a wide range of practical situations. The equations are solved using a recently developed approximation technique using Chebyshev polynomials. It is shown that not accounting for the periodic variation of the stiffness can lead to drastic differences in dynamic response and stability.
Active Segmented Trim Panels for Aircraft Interior Noise Control: Theory and Experiments
Authors: Hirsch S. M. , Sun J. Q.
Published: February 2021

An active segmented trim panel for use as a secondary source for noise control in aircraft is designed, analyzed and tested. It consists of a rectangular segment of aircraft trim panel which is suspended by a flexible support. This support converts the stiff composite trim panel into flexibly-mounted pistons which can be driven by light-weight and low-profile force actuators. The active segmented trim panel offers an acoustic source of lower profile and lower mass, and requires only a simple modification of materials already installed on aircraft. This paper presents a summary of recent results of modeling and testing of an active trim panel configuration. Real-time noise control experiments are conducted using the active trim panels as secondary sources indicating that the present active segmented trim is a promising technology.
Analysis of Impact Noise of Nail Ejection in Wire Nail Machines
Authors: Ding Jack , Al-Jumaily Ahmed , Wilson Doug
Published: February 2021

A wire nail production machine can be classified as one of the punch press machines. By nature, the production of wire nails involves the development of a series of force impulses which in turn generate various sound pressure levels with different frequencies. Typically, the machine operations generating impact noise include pressing, cutting, ejecting, wire gripping and feeding. The punch pressing is the movement of punch header to press forming the nail head. It produces a large force impulse which in turn generates a high level of impact noise and consequently high levels of ancillary impact noise such as the impact noise by the backlashes. It has been found that this type of impact noise is not necessarily the most annoying one. The impact noise generated by nail ejection, however, has been identified as one of the annoying noise components. The ejector used in a nail machine for executing the movement of nail ejection produces ringing noise at high frequencies when it is struck by the punch header in each cycle of the machine operations. This paper presents the analyses of and experiments on the ejection force impulse and the characteristics of the impact noise generated by nail ejection.
The Geometrical Mode Analysis of a Vibrating System With the Planes of Symmetry
Authors: Dan Byung Ju , Choi Yong Je
Published: February 2021

Vibration modes obtained from a modal analysis can be better explained from a screw theoretical standpoint. A vibration mode can be geometrically interpreted as a pure rotation about the vibration center in a plane and as a twisting motion on a screw in a three dimensional space. This paper presents a method to diagonalize a spatial stiffness matrix by use of a parallel axis congruence transformation when the stiffness matrix satisfies some conditions. It also describes that the diagonalized stiffness matrix can have the planes of symmetry depending on the location of the center of elasticity. For a system with the planes of symmetry, the vibration modes can be expressed by the axes of vibration. Analytical solutions for the axes of vibration have been derived. A numerical example of an application to the vibration analysis of an optical disc drive has been presented.
Rotational Shock Performance and Actuator Resonant Delatch Capability of a Computer Hard Disk Drive With Magnetic Cup Latch
Authors: Lin Chen-Chi , Casey Shawn , Wang David , Oveyssi Kamran , Edwards John
Published: February 2021

This paper presents the analytical and experimental studies of the rotational shock performance and actuator resonant delatch capability of a computer hard disk drive with magnetic cup latch. Higher stiffness of the latch board and stronger magnet retention force give better rotational shock performance but degrade the actuator resonant delatch capability. Optimizing the system stiffness and magnet strength is the key to meet both shock and delatch requirements. The effects of the shock pulse width on the shock performance and the numbers of resonant cycles on the delatch process are also investigated.
Dynamic Modeling and its Solving Method of Elastic Foundation for Dynamic Machine
Authors: Liao Dao-Xun , Huang Xiao-Cheng , Lu Yong-Zhong , Jin Wei-Jun
Published: February 2021

Engineering practices indicate that the soil as foundation has great effect on base vibration. In this paper, Vlasov model is applied to base-foundation (soil) system of dynamic machine. According to the elasticity theory and soil dynamics, the kinetic energy and potential of foundation can be derived. Based on the Hamilton’s variational principle, we are able to establish multivariable fonctionelle equation and Euler’s equations of foundation. Consequently, we can obtain the partial differential equation of free vibration for the foundation on condition that the damping of the system is neglected, which equations are different from the existing references. It is very difficult to solve the complicate differential equations. This paper proposes a new solving method that has great improvement for existing literatures. It provides theoretic basis of the dynamic modeling and dynamic characteristic analysis of bas-foundation system for dynamic machine.
Solution of the Moving Mass Problem Using Complex Eigenfunction Expansions
Authors: Lee Keh-Yang , Renshaw Anthony A.
Published: February 2021

A new solution technique is developed for solving the moving mass problem for nonconservalive, linear, distributed parameter systems using complex eigenfunction expansions. Traditional Galerkin analysis of this problem using complex eigenfunctions fails in the limit of large numbers of terms because complex eigenfunctions are not linearly independent. This linear dependence problem is circumvented in the method proposed here by applying a modal constraint on the velocity of the distributed parameter system (Renshaw, 1997). This constraint is valid for all complete sets of eigenfunctions but must be applied with care for finite dimensional approximations of concentrated loads such as found in the moving mass problem. A set of real differential ordinary equations in time are derived which require exactly as much work to solve as Galerkin’s method with a set of real, linearly independent trial functions. Results indicate that the proposed method is competitive with traditional Galerkin’s method in terms of speed, accuracy and convergence.
Stability of Out-of-Plane Vibration of a Uniform Beam Carrying an End Body and Attached Radially to a Rotating Hub
Authors: Naguleswaran S.
Published: February 2021

This paper reports an analytical study on the out-of-plane vibration and stability of a uniform beam attached to a rotating hub and carrying a rigid body at the other end. The parameters which govern the natural frequencies are the hub radius (root offset), speed of rotation of hub, the mass of the end body, its moment of inertia about an axis in the plane of rotation and through the centre of mass, the radial offset of the centre of mass from the beam end It is shown that for certain combinations of the system parameters a ‘tuned’ state (analogous to whirling of a shaft) is possible. It is also shown (hat for some combinations a natural frequency is zero (borderline of instability) even though the axial force distribution in the beam is tensile throughout. Negative centre of mass offset is a necessary but not sufficient condition for zero frequency to occur.
Modal Analysis of Ballooning Strings With Small Sag
Authors: Fan Rongjun , Singh Sushil K. , Rahn Christopher D.
Published: February 2021

During the manufacture and transport of textile products, yarns are rotated at high speed and form balloons. The dynamic response of the balloon to varying rotation speed, boundary excitation, and disturbance forces governs the quality of the associated process. Resonance, in particular, can cause large tension variations that reduce product quality and may cause yarn breakage. In this paper, the natural frequencies and mode shapes of a single loop balloon are calculated to predict resonance. The three dimensional nonlinear equations of motion are simplified via small steady state displacement (sag) and vibration assumptions. Axial vibration is assumed to propagate instantaneously or in a quasistatic manner. Galerkin’s method is used to calculate the mode shapes and natural frequencies of the linearized equations. Experimental measurements of the steady state balloon shape and the first two natural frequencies and mode shapes are compared with theoretical predictions.
Fundamental Frequencies of Cantilever Beams
Authors: Hoffmann Jon A. , Wertheimer Todd
Published: February 2021

A simple relationship which predicts the first mode natural frequency of a tapered cantilever beam is presented as a function of the stiffness to mass ratio and a mass distribution parameter for the beam. In this study the mass distribution parameter, obtained using referenced results, is presented as a function of the taper ratio of the beam for the case of beams with linear tapers. Conical truncated beams, truncated wedges with vibration perpendicular to the parallel sides of the taper, and truncated wedges with vibration parallel to the parallel sides of the taper have been investigated.
Proper Orthogonal Decomposition of an Experimental Cantilever Beam
Authors: Riaz M. S. , Feeny B. F.
Published: February 2021

We apply proper orthogonal decomposition (POD) to an experimental cantilevered beam and obtain a set of proper orthogonal modes (POMs) and proper orthogonal values (POVs). The POMs form a bases that represents the optimal distribution of energy in the system. A set of experiments was performed excited by impulse inputs and sensed with strain gages. The strains were converted to displacements and POD was performed on the displacements. The POMs were compared with the theoretical normal modes. The results confirmed the validity of this method for acquiring lower modes of vibration. The identification of lower modes was robust with respect to the choice of data acquisition parameters and input locations. We also used different types of basis functions for converting strains to displacements.
The Sliding of an Elastic Half-Space Against a Rigid Surface With Friction Reduction due to Incident Dilatational Waves
Authors: Adams George G.
Published: February 2021

The steady sliding of a flat homogeneous and isotropic elastic half-space against a flat rigid surface, under the influence of incident plane dilatational waves, is investigated. The interfacial coefficient of friction is constant with no distinction between static and kinetic friction. It is shown here that the reflection of a harmonic wave under steady sliding consists of a pair of body waves (a plane dilatational wave and a plane shear wave) radiated from the sliding interface. Each wave propagates at a different angle such that the trace velocities along the interface are equal and supersonic. The angles of wave propagation are determined by the angle of the incident wave, by the Poisson’s ratio, and by the coefficient of friction. The amplitude of the incident waves is subject only to the restriction that the perturbations in interface contact pressure and tangential velocity satisfy the inequality constraints for unilateral sliding contact.

It is also found that an incident rectangular wave can allow for relative sliding motion of the two bodies with a ratio of remote shear to normal stress which is less than the coefficient of friction. Thus the apparent coefficient of friction is less than the interface coefficient of friction. This reduction in friction is due to periodic stick zones which propagate supersonically along the interface. Under appropriate conditions, the bodies can move tangentially with respect to each other in the absence of an applied shear stress. The influences of the angle, amplitude, and shape of the incident rectangular wave, the interfacial friction coefficient, the sliding speed, and of the remotely applied normal stress, on friction reduction are determined.
Dynamic Response of Adhesively Bonded Beams Subjected to Harmonic Peeling Loads
Authors: Hamidzadeh H. R. , Prescher J. L. , Nayeb-Hashemi H.
Published: February 2021

The only viable method to join some components is by using adhesive. These components are often subjected to dynamic loading, which may cause initiation and propagation of failure in the joint. In order to insure the reliability of these structures, their dynamic response and factors affecting their response must be understood.

Dynamic response of a single lap joint subjected to an out of plane harmonic force is evaluated. The bonded joint is modeled as Euler Bernoulli beams joined with an adhesive and constrained at one end and subjected to a harmonic force at the free end. The results show that the system response is not sensitive to the damping characteristic of the adhesive. In contrast, the elastic properties, and geometry of adhesive and adherends dominate the response. Significant peel and shear stresses develop in the over lap. These stresses are confined to the edge of the overlap and their magnitude increases as the frequency approaches the natural frequency of the system. The results show that the direction of the shear stress changes as the frequency of applied load sweeps over the first natural frequency. In contrast the peeling stress direction does not change as result of sweeping frequency over the first natural frequency.
Effect of Localized Heat Damage on the Natural Frequency of Glass-Fiber Reinforced Plastics
Authors: Nayeb-Hashemi H. , Harrison A. , Kisnomo P. , Saniei N.
Published: February 2021

The effect of localized heat damage on the first natural frequency of fiber glass reinforced plastic is studied. The study is performed to determine the possibility of using natural frequency to evaluate the damage state of a composite. The natural frequency and its variation with the damage (size, location, and severity) are obtained using finite element analyses, continuum and lumped models. The results show that the natural frequency of composite specimen decreases with the growth of the damage size and increase of damage severity. However, its variation is much more sensitive to the damage size and location than to its severity. The natural frequency apparently does not change significantly with the number of damage spots as long as the total damage area is constant. A correlation between the natural frequency and the residual tensile strength of the composite is obtained, indicating its potential in predicting the residual strength of damaged composites.
Free Vibration of Uniform, Flexible, Cylindrical Shell Rotors
Authors: Wang Fei-Yue , Luo Albert C. J.
Published: February 2021

The critical speeds and responses of uniform, flexible, cylindrical rotors are predicted by use of the Riccati transfer matrix method. The critical speeds are also measured experimentally. The computational and experimental results are in good agreement. The balancing of two cylindrical shell rotors is completed. For the two balanced rotors, no large amplitude vibration occur when the operating, rotational speed passes through critical speeds, and that rotation speed can arrive to a very high value to meet the requirement of isotope separation in engineering.
Influence of Warping Effects on the Dynamic Behavior of Composite Beams Under Bending and Torsion Combined Loads
Authors: Tanghe-Carrier Frédérique , Gay Daniel
Published: February 2021

The dynamic behavior of composite beams under both bending and torsion combined loads is sought with a 1-D approach based on the integral parameter method. The developed theory takes into account side effects due to the deformation of the cross-section out of its plane. In case of beams with a center of symmetry, the effects of bending and torsion are uncoupled. For such beams we evaluate the eigenfrequencies of bending and torsion with non-uniform warping. The present theory is finally implemented through the study of an isotropic sandwich beam: we compare its bending and torsion theoretical eigenfrequencies with FEM and experimental results.