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Additional info for Piping Engineering
Simple harmonic motion A single-degree-of-freedom system is one for which only one coordinate is required to define completely the configuration of the system at any instant. ) A snubber is a device used to increase the stiffness of an elastic system (usually by a large factor) whenever the displacement becomes larger than a specified value. snubber A spectrum is a definition of the magnitude of the frequency components that constitute a quantity. , the square root of the mean of the squares of the deviations from the mean value of a vibrating quantity.
13 Response factors for a viscous-damped single-degree-of-freedom system excited in forced vibration by a force acting on the mass. The velocity response factor shown by horizontal lines is defined by Eq. 36), the displacement response factor shown by diagonal lines of positive slope is defined by Eq. 33), and the acceleration response factor shown by diagonal lines of negative slope is defined by Eq. 37). The velocity and acceleration response factors defined by Eqs. 37) are shown graphically in Fig.
Then Eq. 9 According to Eq. 29), the amplitude x increases continuously with time, reaching an infinitely great value only after an infinitely great time. 11 Undamped single-degree-offreedom system excited in forced vibration by motion of foundation. Motion of Foundation. The differential equation of motion for the system of Fig. 11 excited by a continuing motion u = u0 sin ωt of the foundation is m x¨ = −k(x − u0 sin ωt) The solution of this equation is u0 sin ωt x = A1 sin ωnt + B2 cos ωnt + ᎏᎏ 1 − ω2/ωn2 where ωn = k/m and the coefficients A1, B1 are determined by the velocity and displacement of the mass, respectively, at time t = 0.