An approximate method for the transient response of nonlinear systems

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Virginia Polytechnic Institute

The analysis of engineering structures which are subjected to dynamic forces is an area of study which has received considerable attention in recent years. In some cases, an understanding of the behavior of a structure under its expected time-varying loads is imperative so that the designed facility fulfills its intended purpose. Such structures might be simple beams, columns, rigid frames, electrical, and mechanical equipment, etc.

In general, there are three types of motion which the design engineer might be required to investigate due to certain prescribed loads, namely, transient response, steady-state vibrations, and random vibrations. The motion studied usually depends upon the expected or predicted load which is sometimes called the input of the system. In what follows, only transient responses of systems subjected to short time-duration loads are considered. These impulsive-type forces might arise from sources such as earthquake tremors, wind gust forces and pressure, and pressure waves from explosions.

Of the various assumptions which the engineer must make when studying the dynamic response of structures, one of the most important is perhaps the model representation of the true structure. One method of representation is to judiciously idealize the structure into concentrated mass and to connect, each lumped mass to its neighbor by weightless springs and dashpots. The number of masses and the constraints or lack of them on each mass determine the number of degrees-of-freedom of the system. The differential equations which describe the motion of the model are either linear or nonlinear, depending upon the behavior of each mass, spring, and dashpot.