Kabak V. Asymptotic - numerical method of research of the forced nonlinear oscillations of mechanical systems, which parameters depend on time

Mechanical systems with time dependent parameters. Development of the new asymptotic -numerical approach for solving the problem of the forced oscillations of nonlinear mechanical systems properties of which are functions of time. A method of research is the method of double asymptotic expansion. The new approached analytical method for research of the forced nonlinear oscillations of elastic systems with variable parameters is created. The asymptotic solutions of the nonlinear non-uniform differential equations of the second order with small parameter and variable in time of coefficients, which describe the nonlinear forced oscillations of mechanical systems with parameters, time dependent, are constructed. The solution received is important for practical use of the problem of forced nonlinear oscillations of rectangular plate with variable in time rigidity. The developed technique can be used with for implementation of the dynamic analysis of design elements of rocket and aircraft constructions.