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Extra info for Ashrae Pocket Guide for Air Conditioning, Heating, Ventilation, Refrigeration: Inch-Pound Edition

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14 when the forcing functions FE1 = 16 sin(Ωt)N and FE2 = 0 are applied. 45 rad/s. 45 rad/s the masses are almost π out of phase, with a ratio given by x02 (note that in the figure the maximum positive amplitudes per period are shown, so the sign difference in x02 is not evident). 45 rad/s there is a 2π jump down in the phase of mass two as it lags more than 2π behind the forcing frequency. Superposition does not generally hold for nonlinear systems, and so this powerful technique cannot be extended from linear directly to nonlinear.

2003). There are also texts which discuss the vibration and control of smart structures such as Clark et al. (1998), Srinivasan and McFarland (2001), Preumont (2002), Worden et al. (2003) and Leo (2007). A good overview of linear control is given by Goodwin et al. (2000). A good introduction to nonlinear control can be found in Slotine and Li (1991). 34 1 Introduction to Nonlinear Vibration and Control References Beards, C. F. (1981). Vibration analysis and control system dynamics. Chichester: Ellis Horwood.

The signs of λ1,2 are significant in determining the type of equilibrium points. 1 Equilibrium Points for Linear Harmonic Oscillator Now consider the linear harmonic oscillator defined by m x¨ + c x˙ + kx = F(t), Eq. 3). First set the forcing parameter, F(t), to zero so that the state space representation, Eq. 4), becomes x˙1 x˙2 = 0 1 − mk − mc x1 . 16) Provided that all the parameters are non-zero, this system has a single equilibrium point at x1 = x2 = 0. Physically this is because, for an unforced, but damped, linear oscillator, releasing the mass from any non-zero displacement and velocity values results in the system gradually losing energy until it reaches the ‘at rest’ (zero displacement and velocity) point.

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Ashrae Pocket Guide for Air Conditioning, Heating, Ventilation, Refrigeration: Inch-Pound Edition by Mildred Geshwiler (Editor)


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