Applied explosives technology for construction and mining by Stig O. Olofsson

By Stig O. Olofsson

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38) We will investigate the influence of the damping ratio on the solution of the second-order linear homogeneous equation of motion, with f(t) = o. x(t) + 2~oonx(t) + oo~x(t) = O. 40) is "') ,2 = ron ( - t, ± Jt,2 -1) . 41) We consider three cases for the damping: 1. The system is underdamped, t, < 1 ; the damping ratio is less than the critical damping ratio, the sdof system will show oscillatory (periodic) behaviour (two conjugate complex roots). 2. The system is critically damped, t, = 1; the damping ratio is the critical damping ratio, the sdof system shows aperodic (nonoscillatory) behaviour (repeated real roots).

The creation of DTMs and ATMs is the same as the generation of LTMs. Two methods, fixed-free and free-free systems, of obtaining LTMs are discussed. Both methods are based upon the mode displacement method (MDM) in combination with the mode acceleration method (MAM). 1 Problem 1 Scan an available LN users manual with respect to the dynamic load specifications that must be applied in the design of spacecraft structure. com! 1 Introduction The single degree of freedom (sdof) system consists, in general, of a mass, a spring and a damper and is a very important dynamic element within the framework of mechanical vibration.

A 2 / solution becomes zl. 5061 . 2 Solution of the Damped Sdof System with Applied Forces The solution of a damped sdof system with applied forces can be divided into two categories: • Enforced motion; displacement, velocity and acceleration or combinations. In this book we will only consider sdof systems with enforced accelerations or base excitation. Enforced motion can be translated into applied forces. The sdof system is illustrated in Fig. • External forces applied to the sdof system. Enforced Accelerations An sdof system with a discrete mass m, a damper element c and a spring element k is placed on a moving base which is accelerated with an acceleration u(t) .

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