Designing a Dynamic Vibration Absorber System Dynamics Example

ABSORBERS, VIBRATION

V. SteffenJr., D. Rade , in Encyclopedia of Vibration, 2001

Introduction

Dynamic vibration absorbers (DVAs), also called Vibration Neutralizers or Tuned Mass Dampers, are mechanical appendages comprising inertia, stiffness, and damping elements which, once connected to a given structure or machine, named herein the primary system, are capable of absorbing the vibratory energy at the connection point. As a result, the primary system can be protected from excessively high vibration levels. In practice, DVAs can be included in the original system design or can be added to an existing system, often as part of a remedial course of action.

Since their invention by Frahm at the beginning of the twentieth century, dynamic vibration absorbers have been extensively used to mitigate vibrations in various types of mechanical systems. A very well-known application is the so-called Stockbridge damper, widely used to reduce wind-induced vibrations in overhead power transmission lines. In a remarkable engineering application, a 400-ton absorber has been designed for Citicorp Center, a 274-m high office building in New York City, for suppressing primarily the contribution of the first vibration mode in wind-induced oscillations. In a similar application, two 300-ton DVAs have been installed in the John Hancock Tower, in Boston, Massachussets. The dynamics of television towers are particularly favorable for the use of pendulum-like DVAs, which have been applied, for example, to the towers of Alma-Ata and Riga, in the former Soviet Union.

Due to their technological relevance both in the academic and industrial domains, DVAs are still a subject of permanent interest. New applications include devices used to stabilize ship roll motion, to improve the comfort of users when walking on pedestrian bridges, to attenuate vibrations transmitted from the main rotor to the cockpit of helicopters, and to improve machine tool operation conditions, to mention just a few examples. Military applications have also been developed. The use of DVAs to reduce the dynamic forces transmitted to an aircraft due to high rates of fire imposed on the canon motion can be mentioned as another example.

In practical applications, DVAs can be found in various configurations, intended for the attenuation of either rectilinear or angular motion. The simplest setup is that formed by a single mass attached to the primary system through a linear spring. This configuration is named the 'undamped dynamic vibration absorber'. As will be shown later, in designing an undamped DVA to attenuate harmonic vibrations, the values of its physical parameters (stiffness and inertia) must be chosen according to the value of the excitation frequency and it is then said that the DVA is tuned. The undamped DVA may become ineffective when the excitation frequency deviates, even slightly, from the nominal tuning frequency. In order to provide a mechanism for energy dissipation and to enlarge the effective bandwidth of the absorber, damping can be introduced into the DVA. In most applications, a viscous damping model is used, although viscoelastic and Coulomb-type dampers can be found in certain cases. In general, a DVA is designed to attenuate vibrations generated by a purely harmonic excitation. However, in several situations, vibrations are produced by periodic forces containing various harmonic components. In this case, multiple DVAs can be used, each one tuned to a specific frequency component. It is also possible to use distributed-parameter structural elements, such as beams or plates, as dynamic absorbers. Besides the ease of physical realization, the main interest in using these configurations is related to the fact that the DVA can be tuned to various frequency values simultaneously.

All the configurations mentioned above form the class of 'passive' DVAs, defined as those containing exclusively passive, time-independent, components. For this type of absorber, tuning can be achieved only by physically constructing inertia, stiffness and damping elements with adequate values. When the excitation frequency changes, which is likely to occur in many cases, the absorber becomes mistuned and less effective. To overcome this limitation, active DVAs have been developed. Besides the passive elements, they contain an actuator which applies a control force calculated according to an adequate control law. This strategy provides self-tuning capability to the DVA, over a finite frequency band.

In the following sections the basic theory of passive and active dynamic vibration absorbers are presented, as well as some special configurations.

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ABSORBERS, ACTIVE

G. Agnes , in Encyclopedia of Vibration, 2001

Controller Design

The design of a piezo-electric vibration absorber involves three factors: ${\tilde{K}}_{ij}$ , L and R. The value of ${\tilde{K}}_{ij}$ is maximized by locating the piezo-electric material in areas of high strain energy. This constant may be determined as a modal constant by considering either the open- and short-circuit resonant mode:

[6] ${\tilde{K}}_{ij}=\surd \left[\frac{{\left({\omega }^D\right)}^2-{\left({\omega }^E\right)}^2}{{\left({\omega }^E\right)}^2}\right]$

or analytically by:

[7] ${\tilde{K}}_{ij}=\surd \left[\frac{{\left({\omega }^E\right)}^2-{\left({\omega }^{*}\right)}^2}{{\left({\omega }^E\right)}^2}\frac{k_{ij}^2}{1-k_{ij}^2}\right]$

where ω ^* is the natural frequency with the mass of the piezo-electric device included, but its stiffness neglected.

Given the piezo-electric coupling coefficient, a broadband vibration absorber analagous to Den-Hartog's equal peak implementation can be formed by setting:

[8] ${\omega }_{\text{e}}={\omega }^E\surd \left(1+K_{ij}^2\right)={\omega }^D$

[9] $r=\surd \left(2\right)\frac{K_{ij}}{{\left(1+K_{ij}\right)}^{3/2}}$

For multimodal applications, numerical optimization must be used to determine the proper electrical network to suppress the vibration of the structure.

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OPTIMAL ACTIVE SUSPENSION WITH PREVIEW FOR A QUARTER-CAR MODEL INCORPORATING INTEGRAL CONSTRAINT AND VIBRATION ABSORBER

Z.S. Abduljabbar , M.M. ElMadany , in Current Advances in Mechanical Design and Production VII, 2000

5 CONCLUSIONS

Optimal multivariable controllers with and without preview, with and without passive vibration absorber have been designed for the ride control of road vehicles. The performance characteristics of such suspension systems are evaluated and compared with a passive suspension system.

In case of no preview, the actively controlled suspension equipped with vibration absorber may be designed to provide excellent ride comfort without diverse effect on suspension travel or tire deflection. The presence of preview control allows significant improvements in the vehicle performance in terms of ride comfort, suspension travel, and road-holding ability. The active systems with and without vibration absorber give similar performance characteristics.

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HYBRID CONTROL

J. Tang , K.W. Wang , in Encyclopedia of Vibration, 2001

Introduction

Traditionally, structural vibration control techniques have been categorized into two categories, namely, passive and active. Classical passive methods include material damping enhancement, viscoelastic dampers, frictional dampers and joints, and various vibration absorbers and isolation schemes. The advantages of the passive approach are that the devices are relatively simple and cheap, and the system will always be stable since the control is realized by energy dissipation and/or energy redistribution with no external power being added to the system. However, since it produces fixed designs, such schemes might not be optimal or even effective when the system or the operating condition changes. In addition, these schemes usually work well at the high-frequency region or within a narrow frequency range, but often have poor low-frequency performance. Due to the rapid progress in modern electronics and digital signal-processing technique, active systems with feedback/feedforward control schemes have become a viable means for vibration suppression. A typical active control system consists of the plant, actuator(s), sensor(s), and the control electronics. The vibration control is achieved by applying a secondary input to the structure, thereby modifying the system dynamic response to a desirable pattern. While active systems are generally more effective than passive methods, they have the disadvantages such as being complicated and expensive, having the potential to destabilize the system, and being sensitive to system modeling error and uncertainties.

It is clear that the passive and active vibration suppression approaches both have respective strength and weaknesses. This gives rise to the idea of active–passive hybrid vibration controls. In a hybrid system, the active and passive components are synthesized in an integrated manner such that their combined effect would be superior to that of the individual active or passive actions. If properly designed, hybrid controls could outperform the purely passive and active approaches while requiring much less control power input than active systems. Also, since energy is almost always being dissipated/redistributed by the passive components, they are much more robust and stable than the active approach. In other words, they could have the advantages of both the passive (stability, failsafe, lower power consumption, good high-frequency performance) and active (high performance, especially in the low-frequency range, feedback/feedforward actions) schemes.

In general, the design of a hybrid vibration control system involves the selection/determination of the active and passive components. It is a natural thought first to identify the relations and performance tradeoffs between the active and passive control mechanisms, and then to have the two complement each other such that a system with the best control performance and least control effort can be achieved. There are two schools of thoughts in designing a hybrid system. One is to integrate individual active and passive devices on to the host structure to synthesize a global hybrid control. The other is to design hybrid devices at a local level, such that the actuators will have self-contained active–passive hybrid actions. For both approaches, design strategies need to be developed such that the active and passive actions can be integrated in an optimal manner. A discussion of the design methodologies is presented in the following section. These strategies are generic and are not tied to specific passive control mechanisms and active control actuator/sensor selections. Lastly, some representative self-contained hybrid actuator configuration will be presented.

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Detailed accounts of thermoset resins for moulding and composite matrices

Michel Biron , in Thermosets and Composites, 2004

Mechanical industry

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Seals cast in situ, high-temperature seals, tight and flexible joints.

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Cables for chemical plants, wire coatings for control circuits.

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Cast moulding parts in small series and prototypes, shock and vibration absorbers.

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Roller covering for handling of hot products such as coating machines, soft covering for wheels of packing machines.

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Hot air sheaths.

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Bellows, diaphragms.

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Flexible keyboards for machine control panels.

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Binders of refractory fillers for the manufacture of ablative materials.

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Foamed seals for handling vacuum pads.

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Silicone foam coated adhesive tapes.

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Protection in silicone foam coated glass fibre or aluminium sheets.

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Vibration analysis of a shafting system for a marine diesel generator set including dynamic characteristics between shell and housing of generator bearing

W.H. Kim , ... W.H. Joo , in 10th International Conference on Vibrations in Rotating Machinery, 2012

1 INTRODUCTION

Diesel generator sets are widely used in modern industry for high energy density and dynamic stability. A marine diesel generator set is shown in figure 1 . For many years, design technology of diesel generator sets has been used to achieve high power efficiency and environment-friendly operation. As compact design technology has been developed, diesel generator sets were exposed to noise and vibration problems. Accordingly, many studies on low noise and vibration have been performed. For example, the optimal design of vibration absorber on base structure was attempted to decrease the structural vibration of a diesel generator set. To reduce the vibration of rotor system, which is mainly exerted by crankshaft, theoretical prediction methods have been developed focusing on the torsional and axial vibration of a crankshaft. However, the existing prediction methods of a crankshaft system are difficult to enhance the vibration characteristics of a diesel generator set since crankshaft systems have a complex three-dimensional coupled vibration under operating conditions, including the torsional, axial and lateral vibrations. Additionally, the importance of rotor and structure vibration of the generator induced by an engine part is increasing due to the the low vibration requirement of customers. The analytical model of the entire rotor system including a crankshaft, coupling and generator rotor is not fully developed yet.

Figure 1. Marine diesel generator set

In this paper, a rotordynamic analysis model of a marine diesel generator set is developed including the generator rotor and bearing. The engine crankshaft was idealized by Timoshenko beam elements with rotational inertia and linearized main engine bearings. The torsional damper and flywheel are idealized by a set of masses and moments of inertia. The Timoshenko beam model of generator rotor is added in the crankshaft model through laminated plate coupling model. To accurately computational model, dynamic characteristics of the laminated plate coupling are extracted by impact tests. By calculation of the entire rotor system, shaft vibrations of the generator rotor under cylinder firing forces are evaluated. To validate the calculated results, the shaft vibration of generator was measured. The comparison data are presented to assess the reliability of the developed model. These results may be used to improve the vibration characteristics of a marine diesel generator set.

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Characteristics of elastomer materials

Maziar Ramezani , Zaidi M. Ripin , in Rubber-Pad Forming Processes, 2012

3.1 Introduction

Elastomers or rubber-like materials have been used as an engineering material for nearly 150   years. The term elastomer, which is derived from elastic polymer, is a polymer which has the property of viscoelasticity, with low Young's modulus and high yield strain. It consists of monomers which are linked together to form the polymer and are usually made of carbon, hydrogen, oxygen and/or silicon. At temperatures above the glass transition temperature, the elastomers are amorphous polymers with the possibility of segmental motion.

Rubbers are widely used as seals, adhesives, tires, springs, shock isolators, noise and vibration absorbers, corrosion and abrasion protection, and electrical and thermal insulators. Rubber materials possess high damping and large extensibility, which are very useful in suspending resonant vibrations. Due to their large elastic deformability they are widely used as impact absorption in the marine industries and even for blast protection. Panels and reinforced concrete walls coated with rubber can provide some level of protection to the occupants when the walls are subjected to airblast or explosive loading. The low modulus of the rubber made it an ideal material for building isolator bearings for earthquake protection.

According to ASTM D 1566, an elastomer is a material that can recover from large deformations quickly without the need for applying external force and is capable of withstanding high per cent of elongation before fracture. Under tension, elastomers can generally stretch 300–500 per cent before breaking, behaving as hyperelastic materials. They also have low thermal conductivity and show significant hysteresis under cyclic loading.

Elastomer parts are mostly fabricated using a molding process. With this process inexpensive molds can be used to mold large or intricate shaped pairs at relatively low costs and the material characteristics can be optimized to suit the requirement of the application. The rubber to be used in the molding process is mixed with other chemicals (known as additives) and then heated, melted and processed into a mold. The molding process is based on the controlled temperature–pressure–time cycle. Once the chemical process is completed ('cured') the rubber is vulcanized and cooled.

In order to give rubber its shape, the polymer chains in rubber are tied together in a process known as 'crosslinking' or 'vulcanization'. Vulcanization is the process of adding sulphur or other equivalent curing chemicals which will modify the polymer mechanical characteristics by forming crosslinks. Table 3.1 listed the mechanical properties of general elastomers in comparison with other engineering materials. What characterizes elastomers are the low elastic modulus, Poisson's ratio of about 0.5 (incompressible) and high values of percentage of elongation to fracture. The deformation of elastomers are non-linear and as such the value of the Young's modulus can only serve as a guideline with little use in design evaluation. Since the modulus is strain dependent, analysis of rubber components must use rubber material models such as Mooney-Rivlin, Ogden and Arruda-Boyce which are based on strain energy function, as discussed later.

Table 3.1. Comparison of properties of elastomers and some engineering materials

Material	Modulus of elasticity (GPa)	Poisson's ratio	Ultimate tensile stress (MPa)	Percentage of elongation to fracture (%)	Thermal conductivity (W/m   K)
Elastomers	0.0007–0.0004	0.47-0.5	7-20	100-800	0.13-0.16
Aluminum alloys	70-79	0.33	100-550	1-45	177-237
High strength steels	190-210	0.27-0.3	550-1200	5-25	35-60
Titanium alloys	100-120	0.33	900-1200	10	7-7.5
Nylon plastic	2.1-3.4	0.4	40-80	20-100	0.3

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Highly Responsive Magnetoactive Elastomers

Mikhail Shamonin , Elena Yu. Kramarenko , in Novel Magnetic Nanostructures, 2018

7.5 Prospects of Research and Development

The subject of MAEs is flourishing now. What are the reasons for that success? MAEs come into the focus of research interest from engineering not from fundamental science. The Oxford Dictionary defines engineering as "the branch of science and technology concerned with the design, building, and use of engines, machines, and structures."[108] This is the reason. MAEs can do something useful. They have been developed as an alternative to MR fluids, because MR elastomers are eventually free of their disadvantages, such as deposition, sealing issues, and environmental contamination [3] . Therefore, most of applied research has concentrated on utilization of magnetomechanical properties of these materials. Most current applications utilize the MR or field-stiffening properties of MAEs. Examples are vibration absorbers and isolators. Soft actuators (e.g., controllable valve [109] or Kashima's [110] actuators) relying on magnetodeformation have been proposed as well. The review [3] provides a comprehensive overview of MAE devices. However, one can observe that not many magnetomechanical devices relying on MAEs have found their way into industrial applications or daily life. One reason is probably that there exist alternative technologies, which can solve similar problems in a more effective way. Two such disadvantages of MAEs are relatively large power consumption, from tens watts to hundreds watts, and large device size due to necessity of magnetic circuit [3]. It seems to be challenging to overcome these limitations in conventional applications. So what is our subjective opinion? First, we believe that MAEs may find their unique place in "niche" applications, where there are no alternative technical solutions. One such field could be biomedical engineering [111,112]. Second, more progress has to be done in understanding the material behavior. It turns out that the behavior of MAEs is more complex than it appeared at the beginning—e.g., explanation of the sign of magnetostriction, or prediction of how to design a sample with given sign and value of magnetostriction, remains a great challenge.

In this Chapter, we practically did not touch a wide field of theoretical research in the area of MAE. For >   15   years, various theoretical approaches have been developed; however, they have mainly proposed either too simplified models based on dipole-dipole interactions and linear approximations, which do not work for highly filled MAEs where maximum effects are observed, or they are too complex for the practice. Furthermore, there is still a need for development of controlled strategies [4] for successful implementation of MAE-based devices. The effective medium approach has not been fully explored yet [10].

Hitherto, most of research is done on bulk properties of MAEs. Structuring of magnetic filler along magnetic field lines takes place not only within the bulk of MAEs but also on the surface resulting in formation of needle-like "mountains" [113,114]. The characteristic height of these mountains and their separation depend on the MAE composition and external magnetic field. Thus, application of the field could tune not only the rigidity of MAE films, but also the structure of their surface profile providing a new way to control its wettability and adhesion properties. It is plausible that new interesting application will emerge from the high surface responsivity of MAEs.

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Magnetostrictive Actuators

Seda Aksoy , in Encyclopedia of Smart Materials, 2022

Vibration/Noise Control

Vibration absorption reduces undesired vibration in a structure. The new actuation technologies extend vibration control from narrowband to broadband. Active vibration control has two strategies: feedback and feed-forward control. Feed-forward control can be only implemented with known disturbances. The idea is to generate a second disturbance to cancel the primary known one. Feedback control has different types. Modal feedback control provides perfect tracking of the reference value while rejecting disturbance. However, it has some difficulties in reducing damping. Active damping control simply increases the damping of vibration modes of a structure. In practice, an active damping system limits the actuator dynamics as a result of its bandwidth. A tuned vibration absorber is limited to single-frequency vibration attenuation. The resonance frequency of the tuned absorber matches the frequency of a structure, and the vibration is absorbed by a mechanical system (a spring-mass-damper system). Magnetostrictive actuators are used to for both feedback and feed-forward active vibration control. By applying the magnetic field and changing the magnetization state of the magnetostrictive material, the resonance frequency of the mechanical system can be changed and any resonance amplification prevented. Active vibration control using linear magnetostrictive actuators have been exploited with an induced strain of 27 µm and a blocked force of up to 4000 N in the linear range ( Moon et al., 2007). Another application is related to performance improvement for tooling machines such as lathe machines or boring bars. Vibrations are mainly related to the self-excited vibration – Chatter – That occurs during machining. Many studies have been performed of chatter suppression. Stability in machining can be achieved by using actuators that apply a desired force at the point where the machining force, such as cutting or opening a hole, is applied. For low-frequency applications, a magnetostrictive actuator has been modeled using a Terfenol-D rod, and it successfully operates from 1260 down to 167 Hz (Braghin et al., 2012). Terfenol-D and FSMA-based actuators are also used in the active vibration control unit of helicopter blades. Manufactured sonic actuators have been used to test vibration reduction; when they work far from their resonant frequencies, the resulting reduction of vibration is in the range up to 400 Hz (Zucca et al., 2015).

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Continuum Physics of Materials with Time-Dependent Properties

Mokarram Hossain , Paul Steinmann , in Advances in Applied Mechanics, 2015

4.1 Introduction

So-called magnetorheological elastomers (MREs) or magnetoactive polymers (MAPs) are a relatively new group of smart materials that have recently obtained considerable attention. The mechanical properties such as the shear modulus of MREs can be enhanced by the application of a magnetic field. MREs are prepared using magnetically permeable particles, mainly iron particles which are embedded in a nonmagnetically active polymeric matrix. One of the reasons for mechanical property enhancements in the entire MREs system is due to mutual interactions between particles and between the particles and the bulk matrix. An external magnetic load to MREs results in significant changes in their macroscopic properties, i.e., such excitation can vary the material stiffness and damping properties that make MREs attractive candidates for various technical applications. Applications include different components in automotive industry, civil engineering devices, e.g., suspension bushing, brakes, smart springs in dynamic vibration absorber, building vibration isolation, noise barrier systems, and sensors ( Boczkowska & Awietjan, 2009; Borbath et al., 2012; Danas et al., 2012; Xu et al., 2011). The application of an external magnetic field as well as the dispersion of iron particles in the polymeric matrix can be achieved in two ways (L. Chen, Gong, & Li, 2007; Kaleta, Krolewicz, & Lewandowski, 2011; Zhou, 2003). Firstly, when the bulk polymer matrix is exposed to a magnetic field during curing, the ferromagnetic particles are magnetized and form chain-like structures in the direction of the applied magnetic field. This results in anisotropic elastomers where the magnetic particles are aligned in a particular orientation (Jolly, Carlson, & Munoz, 1996). Secondly, if there is no application of the magnetic load during the entire curing process, especially just after the start of the curing process, the iron particles will have a random isotropic distribution in the composite, cf. Varga, Filipcsei, and Zrsquoteinyi (2006), Kaleta et al. (2011), and Kankanala and Triantafyllidis (2004).

Some papers (Danas et al., 2012; Jolly et al., 1996; Kaleta et al., 2011) report experimental works both on isotropic and anisotropic magnetosensitive polymeric composites. Moreover, a considerable amount of literature can be found mainly discussing modeling and simulation of isotropic and anisotropic magnetoactive elastomers in the framework of large deformation, cf. Bustamante et al. (R. Bustamante, 2009a, 2009b, 2010; R. Bustamante, Dorfmann, & Ogden, 2007; B. Bustamante, Dorfmann, & Ogden, 2009; R. Bustamante & Shariff, 2015; Shariff, Bustamante, Hossain, & Steinmann, 2015), Dorfmann and Ogden (2003, 2004), and Brigadnov and Dorfmann (2003). Some papers deal with numerical methods for magnetomechanical coupled problems, cf. Miehe and Göktepe (2005), Miehe, Kiefer, and Rosato (2011), Miehe, Rosato, and Kiefer (2011), Vogel, Bustamante, and Steinmann (2013), Vogel, Bustamante, and Steinmann (2012), and Vogel, Goektepe, Kuhl, and Steinmann (2014). However, there is no constitutive model, to the best of the authors' knowledge, that can predict the material parameter evolution as well as the stiffness gain during the curing process in the presence of a magnetic field (or a magnetic induction). During the preparation of particle-filled MREs, residual stresses might generate due to an uneven or differential curing (well known as warpage phenomenon) of the composites, particularly if the thickness of a sample becomes large. Moreover, if the mould is constrained to disallow motions in some directions, there will be shrinkage-generated stresses that can eventually debond composites from the mould. Therefore, modeling and simulation tools can be optimal ways to predict and minimize these pathological phenomena. Since the elastomeric matrix can undergo large deformations when excited by an external magnetic induction, a finite strain framework is essential to predict the curing process behavior under the application of a magnetomechanically coupled load. To extend the approach to a magnetomechanically coupled load, a phenomenologically motivated convolution integral type total energy function is proposed that consists of three parts, i.e., a pure mechanical part, a pure magnetic part and a magnetomechanically coupled part (Hossain, 2010). The total energy function is formulated considering some physical observations that are reported to happen during curing processes, cf. Kiasat (2000) and Gillen (1988). One of the important physical phenomena is that a curing material does not change its stress state as resulted from previous deformations—even though its material properties continue to evolve until it changes the current state of deformation. This observation is extended for the magnetic loading also, see Hossain (2010). Another assumption is considered herein which was adapted earlier for a purely mechanical curing model development that during the curing process all relevant material parameters are simultaneously experiencing temporal evolutions.

The section is organized as follows: Section 4.2 will briefly review a compressible magneto-viscoelastic model for fully cured elastomers. In Section 4.3, the main mathematical foundation that leads to a constitutive relation for the polymer curing process in the presence of a magnetomechanically coupled load is discussed in detail. A viscoelastic extension of the elastic framework developed in Section 4.3 is presented in Section 4.4. A novel approach to model the curing-induced volume shrinkage is proposed that is based on a multiplicative decomposition of the deformation gradient into mechanical and magnetic induction-produced shrinkage parts in Section 4.5 while the evolution of the various time-dependent material parameters appearing in the total energy function are discussed in Section 4.6. The final Section 4.7 presents some numerical examples which illustrate that the proposed model can capture relevant phenomena of polymer curing in the presence of a magnetomechanically coupled field.

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Designing a Dynamic Vibration Absorber System Dynamics Example

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