Reference health
Chaos in mechanical systems — A review
295/295 checkable references clean · checked 2026-08-30
Every reference with a DOI in the deposited reference list resolved to a known work in Crossref or DataCite at the dated check, and none carried a retraction, withdrawal, or removal notice.
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The 295 checked references that resolve
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A computer algorithm to determine the steady-state response of nonlinear oscillators
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Geometrical Methods in the Theory of Ordinary Differential Equations
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An intrinsic method of harmonic analysis for non-linear oscillations (a perturbation technique)
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Bifurcations and chaos of a particular van der Pol-Duffing oscillator
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Bifurcations in Three-Dimensional Motions of Articulated Tubes, Part 2: Nonlinear Analysis
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Flow Induced Bifurcations to Three-Dimensional Oscillatory Motions in Continuous Tubes
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On dynamic control of chaos: A study with reference to a reacting system
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Analytical approach to the torus bifurcations in the quasiperiodically forced van der Pol oscillator
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A modification and extension of an algorithm for generalized cell mapping
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A Galerkin multiharmonic procedure for nonlinear multidimensional random vibration
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A collocation algorithm for calculating the periodic solutions of non‐linear oscillators
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A hybrid symbolic-numerical method for integrating ordinary differential equations
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An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems
resolves10.1112/jlms/s1-20.3.180
On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ −
<i>k</i>
(1-
<i>y</i>
<sup>2</sup>
)y˙ +
<i>y</i>
=
<i>b</i>
λ
<i>k</i>
cos(λ
<i>l</i>
+ α),
<i>k</i>
Large
resolves10.1016/S0889-9746(87)90170-8
A general theory for dynamic instability of tube arrays in crossflow
resolves10.1016/0020-7462(91)90084-7
Invariant torus bifurcation series and evolution of chaos exhibited by a forced non-linear vibration system
resolves10.1016/0022-460X(90)90528-8
Application of the incremental harmonic balance method to cubic non-linearity systems
resolves10.1016/S0022-460X(88)80064-6
Forced periodic vibration of unsymmetric piecewise-linear systems
resolves10.1016/0020-7462(91)90002-B
Non-linear behavior and chaotic motions of an sdof system with piecewise-non-linear stiffness
resolves10.1016/0022-460X(82)90259-0
Flutter of a buckled plate as an example of chaotic motion of a deterministic autonomous system
resolves10.1115/1.3171739
On the Understanding of Chaos in Duffings Equation Including a Comparison With Experiment
resolves10.1016/S0022-460X(88)80023-3
On necessary and sufficient conditions for chaos to occur in Duffing's equation: an Heuristic approach
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Observations of Subcritical Superharmonic and Chaotic Response in Rotordynamics
resolves10.1016/0020-7462(87)90033-3
Numerical simulations of periodic and chaotic responses in a stable duffing system
resolves10.1016/0375-9601(89)90856-6
Autocorrelation on symbol dynamics for a chaotic dry-friction oscillator
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Scaling at the Transition from Quasiperiodicity to Chaos in a Hydrodynamic System
resolves10.1115/1.3171780
On the Equivalence of the Incremental Harmonic Balance Method and the Harmonic Balance-Newton Raphson Method
resolves10.1016/0020-7462(88)90026-1
A computational approach for studying domains of attraction for non-linear systems
resolves10.1016/0022-460X(92)90809-C
Chaotic dynamical behavior in a simplified rotor blade lag model
resolves10.1016/0045-7825(91)90049-C
Geometrical concepts and computational techniques of nonlinear dynamics
resolves10.1103/PhysRevLett.51.339
Are Three-Frequency Quasiperiodic Orbits to Be Expected in Typical Nonlinear Dynamical Systems?
resolves10.1007/978-1-4612-1140-2
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
resolves10.1007/BF00534063
On the accuracy of the harmonic balance method concerning vibrations of beams with nonlinear supports
resolves10.1103/PhysRevLett.59.157
Scaling structure of attractors at the transition from quasiperiodicity to chaos in electronic transport in Ge
resolves10.1115/1.3167107
Forced Nonlinear Oscillations of an Autoparametric System—Part 2: Chaotic Responses
resolves10.1016/0020-7462(69)90003-1
Transformation theory as applied to the solutions of non-linear differential equations of the second order
resolves10.1016/S0022-460X(88)81405-6
Periodic motions and bifurcations in dynamics of an inclined impact pair
resolves10.1016/0020-7462(91)90071-Z
Effect of constant transverse force on chaotic oscillations of sinusoidally excited buckled beam
resolves10.1016/0370-1573(90)90012-Q
Poincaré, celestial mechanics, dynamical-systems theory and “chaos”
resolves10.1016/0022-460X(77)90521-1
Bifurcations to divergence and flutter in flow-induced oscillations: A finite dimensional analysis
resolves10.1016/0020-7462(80)90031-1
Phase portraits and bifurcations of the non-linear oscillator: ẍ + (α + γx2 + βx + δx3 = 0
resolves10.1016/S0022-460X(82)80002-3
The dynamics of repeated impacts with a sinusoidally vibrating table
resolves10.1016/0375-9601(84)90800-4
Bifurcation sequences in horseshoe maps: Infinitely many routes to chaos
resolves10.1016/0005-1098(78)90036-5
Bifurcation to divergence and flutter in flow-induced oscillations: an infinite dimensional analysis
resolves10.1115/1.3162633
A Probabilistic Theory of Nonlinear Dynamical Systems Based on the Cell State Space Concept
resolves10.1115/1.3153817
An Unravelling Algorithm for Global Analysis of Dynamical Systems: An Application of Cell-to-Cell Mappings
resolves10.1115/1.3423981
Determination of Global Regions of Asymptotic Stability for Difference Dynamical Systems
resolves10.1016/0022-460X(90)90459-D
Complex in-line and whirling response of structures to oscillatory flow
resolves10.1103/PhysRevLett.67.1953
Stabilizing high-period orbits in a chaotic system: The diode resonator
resolves10.1016/0020-7462(91)90023-M
An intrinsic multiple-scale harmonic balance method for non-linear vibration and bifurcation problems
resolves10.1016/0022-460X(91)90584-7
An extension of the intrinsic harmonic balancing technique to the analysis of forced vibrations
resolves10.1006/jsvi.1993.1142
Stabilization Of An Impact Oscillator Near Grazing Incidence Owing To Resonance
resolves10.1016/0022-460X(89)90682-2
Amplitude modulated and chaotic dynamics in resonant motion of strings
resolves10.1080/00423118608969137
PERIODIC, BIPERIODIC AND CHAOTIC DYNAMICAL BEHAVIOUR OF RAILWAY VEHICLES
resolves10.1016/0022-460X(91)90564-Z
Non-linear dynamics of a geared rotor-bearing system with multiple clearances
resolves10.1016/0022-460X(92)90638-E
Dynamics of an oscillator with both clearance and continuous non-linearities
resolves10.1016/0094-114X(92)90065-P
A Galerkin method for the steady state analysis of harmonically excited non-linear systems
resolves10.1016/0022-460X(90)90710-H
Strange non-chaotic attractors of a quasi-periodically forced van der pol's oscillator
resolves10.1007/BF01033076
Computation of the largest Lyapunov exponent by the generalized cell mapping
resolves10.1115/1.2897218
Stability and Bifurcation Analysis of Oscillators With Piecewise-Linear Characteristics: A General Approach
resolves10.1007/978-94-009-0659-4_8
Bifurcation Analysis: A Combined Numerical and Analytical Approach
resolves10.1299/jsme1958.29.525
On a Method of Higher Approximation and Determination of Stability Criterion for Steady Oscillations in Nonlinear Systems
resolves10.1299/kikaic.52.1883
Chaotic behaviour in an impact vibration system (2nd report, Influence of damping coefficient and coefficient of restitution)
resolves10.1007/978-3-642-85957-1
Computational Methods in Bifurcation Theory and Dissipative Structures
resolves10.1016/0375-9601(90)90231-C
Incursive fractals: a robust mechanism of basin erosion preceding the optimal escape from a potential well
resolves10.1103/PhysRevA.40.4028
Characterization of an experimental strange attractor by periodic orbits
resolves10.1115/1.3157762
Amplitude Incremental Variational Principle for Nonlinear Vibration of Elastic Systems
resolves10.1115/1.3162626
A Variable Parameter Incrementation Method for Dynamic Instability of Linear and Nonlinear Elastic Systems
resolves10.1115/1.3167160
Incremental Harmonic Balance Method With Multiple Time Scales for Aperiodic Vibration of Nonlinear Systems
resolves10.1016/0045-7825(91)90065-E
The Hopf bifurcation and limit cycle by the incremental harmonic balance method
resolves10.1115/1.2899421
Nonlinear Vibrations of Piecewise-Linear Systems by Incremental Harmonic Balance Method
resolves10.1007/BF01046880
Nonlinear natural vibration analysis of beams by selective coefficient increment
resolves10.1002/eqe.4290190309
Non‐linear steady state vibration and dynamic snap through of shallow arch beams
resolves10.1016/0022-460X(90)90774-T
Geometrically non-linear vibration of spinning structures by finite element method
resolves10.2307/1969299
Transformation Theory of Non-Linear Differential Equations of the Second Order
resolves10.1016/0045-7949(92)90248-X
Non-linear, steady-state vibration of structures by harmonic balance/finite element method
resolves10.1016/0022-460X(90)90934-R
Criteria for chaos of a three-well potential oscillator with homoclinic and heteroclinic orbits
resolves10.1016/0020-7462(90)90030-D
Bifurcations and chaos in a forced zero-stiffness impact oscillator
resolves10.1016/0141-0296(88)90037-5
Bifurcations of subharmonics and chaotic motions of articulated towers
resolves10.1016/0375-9601(89)90854-2
A fast algorithm to determine fractal dimensions by box counting
resolves10.1115/1.2888315
Discussion: “An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems” (Cameron, T. M., and Griffin, J. H., 1989, ASME J. Appl Mech., 56, pp. 149–154)
resolves10.1016/0020-7462(87)90012-6
Fast galerkin method and its application to determine periodic solutions of non-linear oscillators
resolves10.1299/jsme1958.4.201
Steady, Forced Vibration of Unsymmetrical Piecewise-linear System : 1st Report, Explanation of Analytical Procedure
resolves10.1299/jsme1958.16.931
Superharmonic Resonance in Piecewise-Linear System : Effect of Damping and Stability Problem
resolves10.1299/jsme1958.23.68
Forced Vibrations in an Unsymmetric Piecewise-Linear System Excited by General Periodic Force Functions
resolves10.1016/0022-460X(92)90484-F
Some numerical studies of chaotic motions in tubes conveying fluid
resolves10.1007/BF01013307
Period-doubling bifurcations and chaotic motion for a parametrically forced pendulum
resolves10.1098/rspa.1992.0125
Bifurcational precedences in the braids of periodic orbits of spiral 3-shoes in driven oscillators
resolves10.1002/nme.1620320811
Direct determination of periodic solutions of the dynamical equations of flexible mechanisms and manipulators
resolves10.1016/S0022-460X(88)81415-9
Bounds on the Fourier coefficients for the periodic solutions of non-linear oscillator equations
resolves10.1016/0022-460X(90)90796-3
Torus doubling and chaotic string vibrations: Experimental results
resolves10.1115/1.3153746
Experiments on Chaotic Motions of a Forced Nonlinear Oscillator: Strange Attractors
resolves10.1103/PhysRevLett.55.1439
Fractal Basin Boundaries and Homoclinic Orbits for Periodic Motion in a Two-Well Potential
resolves10.2514/3.25139
Experimental study of chaotic vibrations in a pin-jointed space truss structure
resolves10.1016/0020-7462(83)90033-1
Chaotic vibrations of a beam with non-linear boundary conditions
resolves10.1016/0022-460X(91)90520-T
Chaotic vibration in a non-linear oscillator with Coulomb damping
resolves10.1006/jsvi.1995.0317
Periodic and chaotic responses of an sdf system with piecewise linear stiffness subjected to combined harmonic and flow induced excitations
resolves10.1016/0020-7462(91)90065-2
Dynamics of piecewise linear oscillators with van der Pol type damping
resolves10.1007/BF00934742
Galerkin's procedure, quasilinearization, and nonlinear boundary-value problems
resolves10.1007/BF01940759
Occurrence of strange AxiomA attractors near quasi periodic flows onT m ,m≧3
resolves10.1016/0022-460X(91)90592-8
Non-periodic motion caused by grazing incidence in an impact oscillator
resolves10.1016/0022-460X(92)90363-3
Cross-flow-induced chaotic vibrations of heat-exchanger tubes impacting on loose supports
resolves10.1016/S0889-9746(88)80023-9
Nonlinear and chaotic fluidelastic vibrations of a flexible pipe conveying fluid
resolves10.1115/1.2897220
Chaotic Motions of a Constrained Pipe Conveying Fluid: Comparison Between Simulation, Analysis, and Experiment
resolves10.1006/jfls.1993.1031
Nonlinear and Chaotic Dynamics of a Two-Degree-of-Freedom Analytical Model for a Rotated Triangular Array in Cross-Flow
resolves10.1080/00423119208969012
Investigation on Stability and Possible Chaotic Motions in the Controlled Wheel Suspension System
resolves10.1103/PhysRevA.46.2147
Homoclinic bifurcation sets of the parametrically driven Duffing oscillator
resolves10.1016/0020-7462(92)90083-J
Modal interactions in the non-linear response of elastic cables under parametric/external excitation
resolves10.1016/0022-460X(87)90535-9
An examination of initial condition maps for the sinusoidally excited buckled beam modeled by the Duffing's equation
resolves10.1016/0022-460X(91)90817-4
An examination of multi-frequency excitation of the buckled beam
resolves10.1115/1.3169123
A Study of Dynamic Instability of Plates by an Extended Incremental Harmonic Balance Method
resolves10.1115/1.3169175
Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method
resolves10.1016/S0022-460X(87)80235-3
Chaos in a mechanism with time delays under parametric and external excitation
resolves10.1016/0375-9601(84)90461-4
Absence of inversion-symmetric limit cycles of even periods and the chaotic motion of Duffing's oscillator
resolves10.1115/1.3176039
Order and Chaos in a Discrete Duffing Oscillator: Implications on Numerical Integration
resolves10.1007/BF02570610
On an approximate criterion for chaotic motion in a model of a buckled beam
resolves10.1016/0375-9601(83)90513-3
Transition from quasi-periodicity to chaos in a system of coupled nonlinear oscillators
resolves10.1103/PhysRevA.28.1654
Universal scaling property in bifurcation structure of Duffing's and of generalized Duffing's equations
resolves10.1007/BF00369977
Bifurcation sets and chaotic states of a gear system subjected to harmonic excitation
resolves10.1016/0375-9601(91)90930-7
The use of first return maps in the computation of basin boundaries in three-dimensional phase space
resolves10.1137/0720008
Estimating Regions of Existence of Unstable Periodic Orbits Using Computer-Based Techniques
resolves10.1016/0022-460X(88)90237-4
The dynamic response of a centrifugal pendulum vibration absorber with motion-limiting stops
resolves10.1115/1.3169068
The Dynamics of a Harmonically Excited System Having Rigid Amplitude Constraints, Part 1: Subharmonic Motions and Local Bifurcations
resolves10.1070/SM1970v010n01ABEH001588
A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE
resolves10.1061/(ASCE)0733-9399(1991)117:2(241)
Chaotic Motions of Self‐Excited Forced and Autonomous Square Prisms
resolves10.1016/0022-460X(92)90403-K
Empirical fluid-elastic models and chaotic galloping: A case study
resolves10.1115/1.2900856
Jumps to Resonance: Long Chaotic Transients, Unpredictable Outcome, and the Probability of Restabilization
resolves10.1016/0022-460X(89)90699-8
Integrity measures quantifying the erosion of smooth and fractal basins of attraction
resolves10.1098/rspa.1992.0170
Indeterminate trans-critical bifurcations in parametrically excited systems
resolves10.1016/0020-7462(89)90037-1
Non-linear dynamics of supported pipe conveying pulsating fluid—I. Subharmonic resonance
resolves10.1016/0020-7462(89)90038-3
Non-linear dynamics of supported pipe conveying pulsating fluid—II. Combination resonance
resolves10.1103/PhysRevLett.55.596
Fixed Winding Number and the Quasiperiodic Route to Chaos in a Convective Fluid
resolves10.1016/0375-9601(83)90785-5
Chaotic behaviour and limit cycle behaviour of anharmonic systems with periodic external perturbations
resolves10.1143/JPSJ.55.3279
Chaotic Behaviour of an Anharmonic Oscillator with Two External Periodic Forces
resolves10.1016/0045-7825(90)90146-D
Global analysis of nonlinear dynamical systems with fuzzy uncertainties by the cell mapping method
resolves10.1016/0020-7462(86)90023-5
The subharmonic resonance and its transition to chaotic motion in a non-linear oscillator
resolves10.1016/S0022-460X(87)81348-2
Secondary resonances and approximate models of routes to chaotic motion in non-linear oscillators
resolves10.1007/BF00534355
The refined approximate criterion for chaos in a two-state mechanical oscillator
resolves10.1016/0020-7462(88)90025-X
Bifurcations of harmonic solution leading to chaotic motion in the softening type Duffing's oscillator
resolves10.1016/0022-460X(92)90367-7
A discussion on necessary and sufficient conditions for steady state chaos
resolves10.1115/1.3176195
Period Doubling and Chaos in Unsymmetric Structures Under Parametric Excitation
resolves10.1016/0022-460X(92)90065-6
Local methods in predicting occurrence of chaos in two-well potential systems: Superharmonic frequency region
resolves10.1299/jsme1958.24.1616
Higher Approximation of Steady Oscillations in Nonlinear Systems with Single Degree of Freedom : Suggested Multi-Harmonic Balance Method
resolves10.1007/BF00034738
Cracks of fractal geometry with unilateral contact and friction interface conditions
resolves10.1016/0375-9601(87)90403-8
Fractal basins and chaotic bifurcations prior to escape from a potential well
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Fractal control boundaries of driven oscillators and their relevance to safe engineering design
resolves10.1098/rspa.1991.0007
Indeterminate jumps to resonance from a tangled saddle-node bifurcation
resolves10.1115/1.3169067
Period-Doubling Bifurcations and Modulated Motions in Forced Mechanical Systems
resolves10.1115/1.3424578
On Point Mappings for Mechanical Systems Possessing Homoclinic and Heteroclinic Points
resolves10.1007/BF01011512
Randomly transitional phenomena in the system governed by Duffing's equation
resolves10.1016/0020-7462(85)90024-1
Random phenomena resulting from non-linearity in the system described by duffing's equation
resolves10.1109/TCS.1981.1084975
Chaotically transitional phenomena in the forced negative-resistance oscillator
resolves10.1016/0022-247X(66)90066-7
Numerical computation of nonlinear forced oscillations by Galerkin's procedure
resolves10.1016/0020-7462(73)90007-3
Differential tones in a damped mechanical system with quadratic and cubic non-linearities
resolves10.1016/S0022-460X(88)80115-9
On the transition from regular to chaotic behaviour in the Duffing oscillator
resolves10.1016/0375-9601(87)90372-0
Simplicial approximation of Poincaré maps of differential equations
resolves10.1016/0141-1187(87)90011-3
The nonlinear rolling response of a vessel including chaotic motions leading to capsize in regular seas
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On the harmonic response of an oscillator with unsymmetric restoring force
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Effects of dry friction damping on the occurrence of localized forced vibrations in nearly cyclic structures
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The vibro-impact response of a harmonically excited and preloaded one-dimensional linear oscillator
resolves10.1016/0022-460X(91)90913-5
Periodic forced vibration of unsymmetrical piecewise-linear systems by incremental harmonic balance method
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Domains of attraction for multiple limit cycles of coupled van der pol equations by simple cell mapping
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Chaos in a Weakly Nonlinear Oscillator With Parametric and External Resonances
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Dynamics of a Weakly Nonlinear System Subjected to Combined Parametric and External Excitation
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Chaotic and stochastic dynamics for a nonlinear structural system with hysteresis and degradation
resolves10.1016/0022-460X(90)90541-7
Chaotic motions of an airfoil with non-linear stiffness in incompressible flow
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