Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators
-
M.M. Fatih Karahan
and
Mehmet Pakdemirli
Abstract
Strongly nonlinear cubic-quintic Duffing oscillatoris considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.
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Articles in the same Issue
- Frontmatter
- First Principle DFT Study of Electric Field Effects on the Characteristics of Bilayer Graphene
- Darboux Transformation for Coupled Non-Linear Schrödinger Equation and Its Breather Solutions
- Molecular Interactions in Particular Van der Waals Nanoclusters
- Neimark-Sacker Bifurcation and Chaotic Behaviour of a Modified Host–Parasitoid Model
- First-Principles Investigations on Structural, Elastic, Dynamical, and Thermal Properties of Earth-Abundant Nitride Semiconductor CaZn2N2 under Pressure
- Quantum-Phase-Field Concept of Matter: Emergent Gravity in the Dynamic Universe
- Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators
- Electronic Polarisability of NaNO2–NaNO3 and NaOH–NaNO3 Ionic Melts and Effective Ionic Radius of OH－
- Upon Generating Discrete Expanding Integrable Models of the Toda Lattice Systems and Infinite Conservation Laws
- Preparation, Structural, Optical, Electrical, and Magnetic Characterisation of Orthorhombic GdCr0.3Mn0.7O3 Multiferroic Nanoparticles
