Page 1 Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_1.htm[6/25/2012 12:33:36 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus The Lecture Contains: Complex Elastic Modulus of VEM Frequency and Temperature Dependence of VEM Page 2 Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_1.htm[6/25/2012 12:33:36 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus The Lecture Contains: Complex Elastic Modulus of VEM Frequency and Temperature Dependence of VEM Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_1a.htm[6/25/2012 12:33:36 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus There are about 23 VEMs frequently used for vibration damping. A few of these materials and their loss factors are listed below Table 14.1: Important VEM for damping Name of VEM Approx, Loss Factor PVA 2.5 Thiokol M-5 1.22 Butyl Rubber 1.5 3M tap 466 1.17 M 169A Butyl Gum 1.04 Polyisobutylene 0.8 Dupont Viton A 0.8 Silicone 0.6 Neoperene 0.5 PU 0.3 Filled Silicon Rubber 0.13 Natural Rubber 0.1 Page 3 Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_1.htm[6/25/2012 12:33:36 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus The Lecture Contains: Complex Elastic Modulus of VEM Frequency and Temperature Dependence of VEM Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_1a.htm[6/25/2012 12:33:36 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus There are about 23 VEMs frequently used for vibration damping. A few of these materials and their loss factors are listed below Table 14.1: Important VEM for damping Name of VEM Approx, Loss Factor PVA 2.5 Thiokol M-5 1.22 Butyl Rubber 1.5 3M tap 466 1.17 M 169A Butyl Gum 1.04 Polyisobutylene 0.8 Dupont Viton A 0.8 Silicone 0.6 Neoperene 0.5 PU 0.3 Filled Silicon Rubber 0.13 Natural Rubber 0.1 Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_2.htm[6/25/2012 12:33:37 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus Complex Modulus of Viscoelastic Materials Consider the generalised stress-strain relationship as follows: For harmonic excitation at steady state applying and We get Therefore This ratio could be denoted as complex Young's modulus such that where is the storage modulus and is the loss modulus. The loss factor is expressed as Hence, Similarly, the shear modulus of VEM and the bulk modulus of VEM The various modululli are interrelated as Page 4 Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_1.htm[6/25/2012 12:33:36 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus The Lecture Contains: Complex Elastic Modulus of VEM Frequency and Temperature Dependence of VEM Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_1a.htm[6/25/2012 12:33:36 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus There are about 23 VEMs frequently used for vibration damping. A few of these materials and their loss factors are listed below Table 14.1: Important VEM for damping Name of VEM Approx, Loss Factor PVA 2.5 Thiokol M-5 1.22 Butyl Rubber 1.5 3M tap 466 1.17 M 169A Butyl Gum 1.04 Polyisobutylene 0.8 Dupont Viton A 0.8 Silicone 0.6 Neoperene 0.5 PU 0.3 Filled Silicon Rubber 0.13 Natural Rubber 0.1 Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_2.htm[6/25/2012 12:33:37 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus Complex Modulus of Viscoelastic Materials Consider the generalised stress-strain relationship as follows: For harmonic excitation at steady state applying and We get Therefore This ratio could be denoted as complex Young's modulus such that where is the storage modulus and is the loss modulus. The loss factor is expressed as Hence, Similarly, the shear modulus of VEM and the bulk modulus of VEM The various modululli are interrelated as Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_3.htm[6/25/2012 12:33:37 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus Variation of the storage modulus and the loss factor of VEM with frequency and temperature are shown in Figs. 14.1a to 14.1d. Figure 14.1: Variation in storage modulus and the loss factor with frequency The figures depict the following facts: a. The shear modulus is low at low frequency and increase sharply beyond a critical frequency ? cr b. The loss modulus also reaches its maxima at the same frequency c. A reverse change is observed in the shear modulus with respect to temperature d. Here also, the loss modulus increases sharply at a critical temperature The critical frequency and temperature actually depict a phase change in the polymer. For frequency, the change occurs from rubbery to glassy phase and the reverse for temperature. Page 5 Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_1.htm[6/25/2012 12:33:36 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus The Lecture Contains: Complex Elastic Modulus of VEM Frequency and Temperature Dependence of VEM Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_1a.htm[6/25/2012 12:33:36 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus There are about 23 VEMs frequently used for vibration damping. A few of these materials and their loss factors are listed below Table 14.1: Important VEM for damping Name of VEM Approx, Loss Factor PVA 2.5 Thiokol M-5 1.22 Butyl Rubber 1.5 3M tap 466 1.17 M 169A Butyl Gum 1.04 Polyisobutylene 0.8 Dupont Viton A 0.8 Silicone 0.6 Neoperene 0.5 PU 0.3 Filled Silicon Rubber 0.13 Natural Rubber 0.1 Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_2.htm[6/25/2012 12:33:37 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus Complex Modulus of Viscoelastic Materials Consider the generalised stress-strain relationship as follows: For harmonic excitation at steady state applying and We get Therefore This ratio could be denoted as complex Young's modulus such that where is the storage modulus and is the loss modulus. The loss factor is expressed as Hence, Similarly, the shear modulus of VEM and the bulk modulus of VEM The various modululli are interrelated as Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_3.htm[6/25/2012 12:33:37 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus Variation of the storage modulus and the loss factor of VEM with frequency and temperature are shown in Figs. 14.1a to 14.1d. Figure 14.1: Variation in storage modulus and the loss factor with frequency The figures depict the following facts: a. The shear modulus is low at low frequency and increase sharply beyond a critical frequency ? cr b. The loss modulus also reaches its maxima at the same frequency c. A reverse change is observed in the shear modulus with respect to temperature d. Here also, the loss modulus increases sharply at a critical temperature The critical frequency and temperature actually depict a phase change in the polymer. For frequency, the change occurs from rubbery to glassy phase and the reverse for temperature. Objectives_template file:///D|/chitra/vibration_upload/lecture14/14_4.htm[6/25/2012 12:33:37 PM] Module 3: Dynamic Properties and Selection of Materials Lecture 14: Frequency and Temperature Dependence of Complex Elastic Modulus The frequency-dependence of the complex modulus we have just discussed can be explained through a linear viscoelastic model. For example, consider the simple, three-element model shown in the figure below: Figure 14.2: 3 Element model The stress-strain relation for this model is given by the following equation (14.1) where is a geometric parameter. Assuming a harmonic loading of frequency , we substitute ( ) for the operator in this equation. Then, we get the complex modulus as (14.2) Taking the real and imaginary parts of this equation, we obtain (14.3) It can be seen from eqns. (14.3) that the loss modulus has a maxima at , where is the relaxation parameter of the viscous branch.Read More

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