The analytical examination of mechanical systems in the aspect of their vibro-isolation can be limited to the construction of a computational system. The analytical description of the adopted appropriate computational model may be executed with the help of a set of differential equations of the second order, differential equations with partial derivatives or of both types at the same time. The latest description is associated with the so-called discrete-continuous systems. It is the most convenient to analyze the vibrations of the linear discrete-continuous systems in the class of functions generalized with the Fourier method of separation of variables. Until now it was possible to execute only for a small set of parameters of the system's structure. In the work the author presents a computational model that covers all the structural parameters of the system.
New models have been constructed for three physical systems. These models are characterized by a uniform and transparent mathematical description. The mathematical description belongs to the class of generalized functions, which means that all equations as well as their solutions are understood in the sense of weak topology. The elements of the set of generalized functions need not be dierentiable (in the classical sense) at each point domain of the function. Analyzing of actual systems in the class of generalized functions does not require a division into subsystems, which simplies signicantly execution of all mathematical operations. As compared with the classical methods, those presented in the study allow for a much faster achievement of the goal.
The research concerns analysis of transverse vibrations of power line transmission tower of variable cross section (changing on its length). Such constructions are subjected simultaneously to internal and external loads, which results in transverse and longitudinal vibrations. These vibrations are described by two partial differential equations of distributed parameters depending on two independent variables. If vibrations are small, the terms connecting equations of transverse and longitudinal vibrations can be neglected as infinitely small with respect to other quantities. Consequently, each vibration can be considered separately.
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