There are various methods of analysis for machine foundation. They include: Empirical methods Elastic half space method Lumped parameter method Barkan’s method Among these methods lumped parameter method and barkan’s method are most popular widely used. Empirical methods: – The empirical methods suggested by Tschebotarioff and Alpan can be used for preliminary design purpose for the different soil types. However, these methods can Read more […]

## 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 Read more […]

## Forced Vibration of a Mass Spring System with Damping

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 Read more […]

## Forced Vibration of a Mass Spring System without Damping

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 Read more […]

## Free Vibration of a Mass Spring System with Damping

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 Read more […]

## Free Vibration of a Mass Spring System Without Damping

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 Read more […]

## Theory of Vibration | Simple Harmonic Motion

Theory of Vibration The response of a machine foundation is generally analyzed by Lumped Parameter Approach. In this approach the foundation is represented quite well by a mass, spring and a dash-pot and the problems are usually studied under following headings. Free vibration of a mass spring system without damping Free Vibration of a mass spring system with damping Forced vibration of a mass spring system without damping Forced vibration Read more […]

## Types of Machines and Machines Foundation

Types of Machines Machines are categorized into three major groups. They are high speed machines, low speed machines and impact machines. Low speed machines – Compressors and reciprocating engines come under this category. They produce unbalanced forces. The speed of such machines is usually smaller than 600 rpm. High speed machines – Turbo rotary compressors fall in this category of machines. These machines may have speeds ranging from 3000 to Read more […]

## Types of Machines | Types of Machine Foundation

Types of Machines Machines are categorized into three major groups. They are high speed machines, low speed machines and impact machines. Low speed machines – Compressors and reciprocating engines come under this category. They produce unbalanced forces. The speed of such machines is usually smaller than 600 rpm. High speed machines – Turbo rotary compressors fall in this category of machines. These machines may have speeds ranging from 3000 Read more […]

## Design Criteria of Machine Foundation

In the design a rigid block is assumed to rest directly in the soil. When acted by dynamic loads the rigid block as shown in Fig. 2 may vibrate in any one of six degrees of freedom and the complete evaluation of the response of the block is very complex. However many researchers have conformed from various studies that freedom of vibration in order to arrive at reasonable solution. A vibrating foundation fails when velocity or acceleration or displacement Read more […]