Forced Vibrations of Strongly Nonlinear Systems with Multiple Scales Lindstedt Poincaré Method

Application of the method of multiple scales for nonlinear vibration analysis of mechanical systems with dry and lubricated clearance joints

In this study, the method of multiple scales is used to perform a nonlinear vibration analysis of a mechanical system in two cases; with dry and lubricated clearance joints. In the dry contact case, the Lankarani-Nikravesh model is used to represent the contact force between the joined bodies. The surface elasticity is modeled as a nonlinear spring-damper element. Primary resonance is discussed...

Stability Analysis of a Strongly Displacement Time-Delayed Duffing Oscillator Using Multiple Scales Homotopy Perturbation Method

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

Forced Vibrations for a Nonlinear Wave Equation

Analysing Forced Oscillators with Multiple Time Scales

We present a novel formulation, called the WaMPDE, for solving systems with forced autonomous components. An important feature of the WaMPDE is its ability to capture frequency modulation (FM) in a natural and compact manner. This is made possible by a key new concept: that of warped time, related to normal time through separate time scales. Using warped time, we obtain a completely general for...

Initialization of Homoclinic Solutions near Bogdanov-Takens Points: Lindstedt-Poincaré Compared with Regular Perturbation Method

To continue a branch of homoclinic solutions starting from a Bogdanov–Takens (BT) point in parameter and state space, one needs a predictor based on asymptotics for the bifurcation parameter values and the corresponding small homoclinic orbits in the phase space. We derive two explicit asymptotics for the homoclinic orbits near a generic BT point. A recent generalization of the Lindstedt–Poinca...