Structural Dynamics Concepts

The static method (exact) is based on the use of the equations of dynamic equilibrium, which additionally include (according to the d’Alembert principle) the inertial forces of the moving masses. When calculating complex systems, the use of the static method can cause significant difficulties due to the cumbersomeness of the calculations, and in these cases approximate methods and techniques are often used. The energy method (approximate) is based on the law of conservation of energy, according to which, in the absence of resistance forces, the sum of the potential and kinetic energies of an oscillating elastic system remains constant at any moment in time. When using this method, the main task is to find such a deformed state of the system that is closest in form to its actual state during oscillations. The equations of the bent axes of the rods of the deformed system are taken approximately, and this is the approximation of the energy method. In the dynamics of structures, the main characteristic of a system is the number of its degrees of freedom – the number of independent geometric parameters that determine the position of all masses at any moment in time for any deformations of the system.

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