The harmonic balance (HB) method is one of the most commonly used methods for solving
periodic solutions of both weakly and strongly nonlinear dynamical systems. However, it is …

Through the previous three editions, Handbook of Differential Equations has proven an
invaluable reference for anyone working within the field of mathematics, including …

In this paper, the formulation of the incremental harmonic balance (IHB) method is derived
for a general system of differential equations with cubic non-linearity, which governs a wide …

Vibrating structures, such as gas turbine engines, are assemblages of multiple components
interfaced with each other through physical contact. The friction produced at these contact …

For the many different deterministic non-linear dynamic systems (physical, mechanical,
technical, chemical, ecological, economic, and civil and structural engineering), the …

Based on the granular diatomic lattice chain model, the band gap properties and
nonreciprocal transmission of elastic wave metamaterials with the nonlinearity are studied …

A single-degree-of-freedom non-linear system subjected to periodic excitation is considered.
The non-linearity is in the restoring force and is represented by unsymmetrical piecewise …

In this paper we analyze the vibrations of nonlinear structures by means of the novel
approach of isogeometric finite elements. The fundamental idea of isogeometric finite …

A multiharmonic frequency domain analysis combined with a Craig-Bampton component
mode synthesis is presented to compute the dry friction damped forced response of blades …

The shooting, Newton and p-version, hierarchical finite element methods are applied to
study geometrically non-linear periodic vibrations of elastic and isotropic, beams and plates …