Engineering Projects

Introduction to Forced Frequency Dependent Exciting Force with Viscous Damping Some machines like Turbo-generators produce unbalanced force which imparts into the foundation-soil system frequency dependent exciting force. In Turbo generators two counteracting masses are placed at an eccentricity, e. This is shown in Figs. 1(a) and (b). The masses are so placed that they reach the top simultaneously. The rotating force of each mass is given by,  ———-(1) Referring to the figure and resolving the force horizontally and vertically we got the total vertical force as:    ———-(2) And horizontal forces…

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In foundation soil system damping is always present in one form or another. For this case fig. 1 (a), the equation of motion is:   ———-(1)   ———-(2) The solution of equation (2) is done by applying the concept of rotating vector. In the figure 1 the exciting force vector Q­0 is placed with a phase angle ahead of the displacement vector A. The equation of displacement may be expressed as:   ———-(3) In figure 1 (b) the position of motion vector is shown. In figure 1 (c) the position…

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In the case forced vibration of a mass spring system without damping the mass spring system is acted by a periodic oscillation force and the damping is absent. Unbalanced rotating machinery such as compressor piston produces such type of motion. This is shown in fig.1 (a). For this case the equation of motion can be written as: ———-(1) The solution of equation includes the solution for free vibration and solution satisfying the right hand side. Concept of rotating vector is used to solve the equation (1). s per the vector…

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Fig.1 (a) shows the free vibration of a system with damping. A device known as damper is shown in the figure below. The damping force acts in the opposite direction to that of oscillating mass. The equation of motion for this case can be written as:   ———-(1) Where, c = coefficient of viscous damping Or,   ———-(2)   Or,   ———-(3)   Put then     And   ———-(4) By substituting the value in equation (3) we have,   ———-(5) The solution for can be written as:   ———-(6)…

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Fig.1 gives the different stages of a freely vibrating system without damping. In Fig.1(c) the displacement ‘z’ from the position of static equilibrium at a certain time ‘t’ is shown. The static deflection is given by, ———-(1) Fig.1 (f) shows the free body diagram of the system. Applying Newton’s second law we get, ———- (2) Or, ———- (3) Or, ———- (4) Or, ———- (5) Put ———- (6) Then ———- (7) By substation the value from equation (6) and (7) in equation (5), = 0 ———- (8) Or, = 0 ———-…

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