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EG260 Stiffness - A.K Slone EG-260 Dynamics(1 EG-260...

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A.K. Slone EG-260 Dynamics (1) ©a.k.slone 2006 1 of 11 EG-260 DYNAMICS I – Stiffness 1. Introduction ...................................................... 2 2. Material Properties .......................................... 2 3. Examples of spring constants .......................... 2 3.1. Longitudinal vibration. .................................... 3 3.2. Transverse vibration. ....................................... 5 3.3. Torsional vibration. .......................................... 6 3.4. Summary of spring constants .......................... 7 4. Combination of springs .................................... 9 4.1. Springs in parallel ............................................ 9 4.2. Springs in series .............................................. 10
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A.K. Slone EG-260 Dynamics (1) ©a.k.slone 2006 2 of 11 1. Introduction The stiffness of a body is directly related to the geometry and material properties of the body. The relationships between stiffness, material properties including elastic modulus and geometries of various types of springs are set out below. 2. Material Properties Table 1 shows some material properties for a number of common materials. Material Young’s Modulus E (N/m 2 ) Shear modulus G (N/m 2 ) Density r (kg/m 3 ) Steel 2.0 x 10 11 8.0 x10 10 7.8 x 10 3 Aluminium 7.1 x 10 10 2.67 x 10 10 2.7 x 10 3 Brass 10.0 x 10 10 3.68 x 10 10 8.5 x 10 3 Copper 6.0 x 10 10 2.22 x 10 10 2.4 x 10 3 Rubber 2.3 x 10 9 8.21 x 10 8 1.1 x 10 3 Concrete 3.8 x 10 9 - 1.3 x 10 3 Plywood 5.4 x 10 9 - 6.0 x 10 2 Table 1 Material Properties Young’s modulus, E, commonly called the elastic modulus, has units of pascal (Pa), which are newtons per square metre, N/m 2 , as does G, the shear modulus or modulus of rigidity. 3. Examples of spring constants
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