Vibrational mechanics is a new, intensively developing section of nonlinear dynamics and of the theory of nonlinear oscillations. It presents a general approach to the study of the effects of vibration on nonlinear systems. This approach is characterized by simplicity of application and by physical clearness.In recent years a number of new, essential results have been obtained both on the development of the mathematical apparatus of vibrational mechanics and on the solution of certain applied problems. This book reflects those results through the ingenious presentation of the authors — well-known scientists from Germany, Denmark and Russia. For the convenience of readers, the main content is preceded by a brief description of the main theses of vibrational mechanics.