Dynamic Calculation of Nonlinear Oscillations of Flat Trusses Part 1: Mathematical Model of Nonlinear Structural Oscillations

摘要

The article deals with the application of the analytical method - the method of time analysis - to the problems of dynamic discrete dissipative systems, taking into account the physical and structural nonlinearity. Here are the equations of the mathematical model of nonlinear oscillations of discrete systems that allow representing the vector of dynamic restoring force as the algebraic sum of the linear and nonlinear components. This makes it possible to realize a diagram of a deformation piecewise linear form with consolidation and unloading. In this system of differential equations of motion at a certain time interval has the form of ODE with constant coefficients. This allows modeling of a common position to determine the dynamic response of the system for these types of non-linearity. Analytical expressions of jumps of the designed dynamic response parameters are also given during their transition to a new state in a nonlinear operation, showing that the value of the jump depends on the change in stiffness and damping matrices.