14.1 Fundamental Concepts 519members AB and BC with distributed massesmand absolutely rigid member CD
.EID1/. The simplest form of vibration is shown by the dotted line.Fig. 14.6 Frame with
distributed and concentrated
parametersEI, m EI=•EI, m=0AB C DFEI, m14.1.4 Purpose of Structural Dynamics.............................
The two fundamental problems of dynamical analysis are the following:1.Determine the internal forces and deflections of a structure caused by dynamical
loads
2.Determine the dynamical displacements, velocities, and accelerations. These
quantities are transferred onto the equipment operators and other types of special
equipment, which are located on the structure, and must not exceed allowable
quantities
The solution of these problems is based on determining the very important char-
acteristic of a structure – its frequencies and shapes of free vibration.
Free vibration of a structure occurs with some frequencies. These frequencies
depend on only the parameters of the structure (boundary conditions, distribution of
masses and stiffnesses within the members, etc.) and does not depend on the rea-
son of vibration. Therefore, these frequencies are often called as eigenfrequencies,
because these frequencies are inherent tothe given structure. The number of fre-
quency vibrations coincides with the number of degrees of freedom. The structure
with distributed parameters has infinitynumber of degrees of freedom. The set of
frequency vibration presents the frequencies spectrum of a structure. Each mode
shape of vibration shows the form of elastic curve, which corresponds to specific
frequency.
This chapter contains only free vibration analysis.
14.1.5 Assumptions..................................................
Free vibration analysis presented in this textbook is based on the following
assumptions:1.Only linear vibrations are considered
2.Damping effects are ignored
3.Stiffness and inertial effects of the structure are time independent