Two principal concepts of nonlinear normal vibrations modes (NNMs), namely the Kauderer–
Rosenberg and Shaw–Pierre concepts, are analyzed. Properties of the NNMs and methods …

This survey is devoted to recent achievements in the field of asymptotic approaches. Here
we consider the asymptotics in relation to completely new and sometimes unexpected …

In this book a detailed and systematic treatment of asymptotic methods in the theory of plates
and shells is presented. The main features of the book are the basic principles of …

Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions
comprehensively covers the theoretical background of asymptotic approaches and their use …

The asymptotic development method is applied to analyze the free vibration of non-uniform
axially functionally graded (AFG) beams, of which the governing equations are differential …

Based on the Taylor expansion, we propose a renormalization method (TR method, for
simplicity) for asymptotic analysis. The standard renormalization group (RG) method for …

В последнее время в механике весьма популярным стал так называемый
гомотопический метод возмущений [142, 148, 150–152, 154–157, 163, 164]. Суть его …

An asymptotic perturbation method is proposed to investigate stability of an axially
accelerating viscoelastic beam. The material time derivative is used in the viscoelastic …

An asymptotic approach is proposed to investigate nonlinear parametric vibration of axially
accelerating viscoelastic strings. The string is constituted by the Kelvin model with the …

In this paper He's homotopy perturbation method has been adopted for solving non-linear
partial differential equations. An approximate solution of the differential equation which …