zbMath0840.34001MaRDI QIDQ4857776
Ronald E. Mickens
Publication date: 6 December 1995
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dynamics of nonlinear transversely vibrating beams: parametric and closed-form solutions,
Exploring oscillations with a nonlinear restoring force,
Approximate solutions and chaotic motions of a piecewise nonlinear-linear oscillator,
Existence of a period two solution of a delay differential equation,
Application of a modified Lindstedt-Poincaré method in coupled TDOF systems with quadratic nonlinearity and a constant external excitation,
Exact and approximate solutions for the anti-symmetric quadratic truly nonlinear oscillator,
Application of a modified He's homotopy perturbation method to obtain higher-order approximations to a nonlinear oscillator with discontinuities,
Newton-harmonic balancing approach for accurate solutions to nonlinear cubic-quintic duffing oscillators,
Accurate analytical approximate solutions to general strong nonlinear oscillators,
Haar wavelet solutions of nonlinear oscillator equations,
A new exact solution of a damped quadratic non-linear oscillator,
Nonlinear vibration of a two-mass system with nonlinear stiffnesses,
Iteration calculations of periodic solutions to nonlinear jerk equations,
Growth and performance of the periodic orbits of a nonlinear driven oscillator,
Construction of approximate analytical solutions to strongly nonlinear damped oscillators,
Calculation of single-mode approximation to the limit-cycle solution of a nonlinear wave equation,
Exact solution for the unforced Duffing oscillator with cubic and quintic nonlinearities,
Modified solutions of some oscillators by iteration procedure,
Accurate analytical solutions to oscillators with discontinuities and fractional-power restoring force by means of the optimal homotopy asymptotic method,
Periodic solutions for Hamiltonian equation associated with Gaussian potential,
Analytical solutions of a generalized Duffing-harmonic oscillator by a nonlinear time transformation method,
Application of modified Mickens iteration procedure to a pendulum and the motion of a mass attached to a stretched elastic wire,
Nonlinear oscillations of a point charge in the electric field of charged ring using a particular He's frequency-amplitude formulation,
Numerical solutions of Duffing van der Pol equations on the basis of hybrid functions,
Application of a generalized senator-bapat perturbation technique to nonlinear dynamical systems with an irrational restoring force,
Notes on ``Application of the Hamiltonian approach to nonlinear oscillators with rational and irrational elastic terms, Exploring the non-linear oscillation of a rigid sphere on an elastic half-space, Parametric disorder effects on a subcritical stationary bifurcation under nonlinear gradient term, An optimal iteration method for strongly nonlinear oscillators, On asymptotic approximations of first integrals for second order difference equations, Rational harmonic balance based method for conservative nonlinear oscillators: application to the Duffing equation, Qualitative analysis and simulation of a 10 degrees of freedom model of an electrically operated vehicle, Relativistic potential energy of a non-dissipative classical harmonic oscillator, A note on the two-variable expansion method, Approximations for period-1 rotation of vertically and horizontally excited parametric pendulum, Zero-Hopf bifurcation for van der Pol's oscillator with delayed feedback, Truly nonlinear oscillator with limit cycles and harmonic solutions, Exact time-integral inversion via Čebyšëv quintic approximations for nonlinear oscillators, Cubic quintic septic Duffing oscillator: an analytical study, Triple-zero bifurcation in van der Pol's oscillator with delayed feedback, Nonlinear oscillator with power-form elastic-term: Fourier series expansion of the exact solution, Some issues on HPM and HAM methods: a convergence scheme, On the determination of approximate periodic solutions of some non-linear ODE, Systematic designing of bi-rhythmic and tri-rhythmic models in families of Van der Pol and Rayleigh oscillators, On the mathematical modelling of complex dynamical systems of an electrically operated vehicle, An optimal approach to study the nonlinear behaviour of a rotating electrical machine, Application of He's parameter-expansion method for oscillators with smooth odd nonlinearities, A piecewise variational iteration method for treating a nonlinear oscillator of a mass attached to a stretched elastic wire, Reduction of kinetic equations to Liénard-Levinson-Smith form: counting limit cycles, Nonlinear dynamics of a RLC series circuit modeled by a generalized Van der Pol oscillator, Uniform global asymptotic stability for oscillators with nonlinear damping and nonlinear restoring terms, On the determination of the limit cycles using the harmonic balance method, Spectro-spatial wave features as detectors and classifiers of nonlinearity in periodic chains, Bifurcation analysis in van der Pol's oscillator with delayed feedback, The period function and the harmonic balance method, Analytical approximate solutions for the cubic-quintic Duffing oscillator in terms of elementary functions, Accurate approximation to the double sine-Gordon equation, An analytical approach to investigate the response and stability of Van der Pol-Mathieu-Duffing oscillators under different excitation functions, Multiple-parameters technique for higher accurate numerical solution of Duffing-harmonic oscillation, Reanalysis of a Castor model limit cycle calculation, Iterative solution of some nonlinear differential equations, Approximate solutions for nonlinear oscillation of a mass attached to a stretched elastic wire, Analysis of the nonlinear vibration of a two-mass-spring system with linear and nonlinear stiffness, Analytical approximate solutions for conservative nonlinear oscillators by modified rational harmonic balance method, Approximate solutions to Van der Pol damped nonlinear oscillators by means of He's energy balance method, An easy trick to a periodic solution of relativistic harmonic oscillator, On nonlinear oscillation response of a negatively dissipated oscillator and its analogy to long Josephson junction, A new method based on the harmonic balance method for nonlinear oscillators, Accurate higher-order analytical approximate solutions to large-amplitude oscillating systems with a general non-rational restoring force, Comparing the direct normal form and multiple scales methods through frequency detuning, Perturbation method for periodic solutions of nonlinear jerk equations, A multiple times scale solution for non-linear vibration of mass grounded system, Approximate periodic solutions for the non-linear relativistic harmonic oscillator via differential transformation method, Relationship between the homotopy analysis method and harmonic balance method, Parametric excitation and Hopf bifurcation analysis of a time delayed nonlinear feedback oscillator, Solution for the nonlinear relativistic harmonic oscillator via Laplace-Adomian decomposition method, A note on iterative solutions of an iterative functional differential equation, Exact solutions for a Wick-type stochastic reaction Duffing equation, Solution for an anti-symmetric quadratic nonlinear oscillator by a modified He's homotopy perturbation method, Free vibration analysis of a structural system with a pair of irrational nonlinearities, Bifurcations in Twinkling Patterns for the Lengyel–Epstein Reaction–Diffusion Model, Closed-form exact solutions for the unforced quintic nonlinear oscillator, The spreading residue harmonic balance study on the vibration frequencies of tapered beams, Asymptotic analysis and accurate approximate solutions for strongly nonlinear conservative symmetric oscillators, Periodic bifurcation of Duffing-van der Pol oscillators having fractional derivatives and time delay, Higher-Order Approximate Solutions to a Strongly Nonlinear Duffing Oscillator, Analytical approximate solutions to oscillation of a current-carrying wire in a magnetic field, Duffing equations with cubic and quintic nonlinearities, Higher-order solutions of coupled systems using the parameter expansion method, Parametrically excited oscillations of second-order functional differential equations and application to Duffing equations with time delay feedback, Comparison of energy balance period with exact period for arising nonlinear oscillator equations. (He's energy balance period for nonlinear oscillators with and without discontinuities.), Solution of nonlinear cubic-quintic Duffing oscillators using He's energy balance method, A new approach to approximate solutions for nonlinear differential equation, Periodic solution of the strongly nonlinear asymmetry system with the dynamic frequency method, Piecewise-linearized methods for oscillators with limit cycles, A new analytical approach to the Duffing-harmonic oscillator