Glossary

Active constrained layer damping (ACLD)
ACLD is a damping treatment consisting of a viscoelastic layer sandwiched between two piezoelectric layers. The bottom layer acts as a sensor bonded to the structure and the top layer acts as an actuator to enhance the shear strain in response to structural vibration.
Active piezoelectric damping composites (APDC)
APDC is a damping treatment consisting of a viscoelastic (VEM) layer with embedded matrix of piezoelectric fibers. The fibers are embedded either perpendicularly or obliquely to the surface of the VEM to enhance compression damping or compression and shear damping, respectively when the piezo‐fibers are activated.
Attenuation parameter ( α )
It is the real part of the propagation parameter (μ) which represents the logarithmic decay of the state vector as the wave propagates between adjacent cells.
Augmented temperature field (ATF)
The ATF method is a physically‐based approach that models the VEM by introducing a temperature field to interact with the structural field of a vibrating structure. The augmented field is described by a first order differential equation in an internal degree of freedom of the VEM.
Burgers model
It consists of a Maxwell VEM model in series with a Kelvin–Voigt VEM model.
Constrained layer damping (CLD)
It is a damping treatment consisting of a VEM sandwiched between a base structure and a constraining layer in order to introduce shear deformation in the VEM. This shear deformation enhances significantly the energy dissipation characteristics of the damping treatment.
Cole–Cole plot
It is a plot of the storage modulus (E′ or G′) versus the loss modulus (E″ or G″) or versus the loss factor (η or tan δ). This plot is also called a “Wicket Plot.”
Complex modulus ( E *, G * )
It is a description of the VEM elastic and viscoelastic properties in a complex number format such that: E * = E′(1 + ηi) with E′ and η denoting the storage modulus and loss factor, respectively. Also, i denote the unit imaginary number which is equal to b3-i0001. This is the classical description of VEM when subject to different sinusoidal excitations and temperatures.
Creep
It is the physical phenomenon associated with monitoring the continuous drop of the strain of a VEM when subjected to a constant applied stress. Measuring the time history of the strain is used to determine the time‐dependent “Creep compliance.”
Creep compliance
The creep modulus J(t) is determined by measuring the time history of the strain ε(t) when a VEM is subjected to a step‐stress of σ 0, such that: J(t) = ε(t)/σ 0.
Damping
It is a mechanism for dissipating the energy of a vibrating structure whether in viscous, viscoelastic, or structural manner.
Damping composite
It is a damping treatment which is formed by an assembly of viscoelastic material, arranged or mixed with multiple ingredients, layers, particle fillings, and/or fiber mats in order to achieve desirable damping characteristics.
Damping factor
It is a quantitative measure of the energy dissipation characteristics of a VEM.
Dynamic mechanical thermal analysis (DMTA)
It is a measuring instrument for measuring the storage and loss factor of a VEM at different temperatures and frequencies using sinusoidal excitations in bending, shear, or tension.
Elastomers
Elastomers are damping materials that are present in the rubbery phase at room temperature.
Fading memory phenomenon
A material exhibits a fading memory phenomenon if the effect of an action on the material response deteriorates and fades away as the time goes by.
Fractional derivatives
Fractional calculus, introduced in 1695 by Leibniz, to generalize the meaning of derivatives from integer order to non‐integer order derivatives.
Free volume ( v f )
The free volume defines the space between the molecules of a viscoelastic material.
Golla–Hughes–McTavish model (GHM)
The model describes the shear modulus of viscoelastic materials with a second order differential equation unlike the first order differential equations used to describe the Maxwell, Kelvin–Voigt, Poynting–Thomas, and Zener models. Such a distinction makes it easy to incorporate the dynamics of the viscoelastic materials into finite element models of vibrating structures.
Glass transition temperature (T g )
The glass transition temperature is an important physical property of the VEM at which significant changes in mechanical properties of the VEM takes place. Below T g the VEM exists in a glassy phase and above T g it exists in a rubbery state.
Jeffery model
It consists of a Kelvin–Voigt VEM model in series with a damping element.
Kelvin–Voigt model
A classical model of VEM consisting of a spring and viscous damper in a parallel arrangement.
Loss modulus (E″ or G″)
This modulus quantifies the dissipative component of the “Complex Modulus” of a VEM. It is commonly denoted also as the “Out of‐Phase” and/or “Imaginary Modulus.”
Loss factor (or tan δ )
It is the ratio of loss modulus to the storage modulus of VEM. It quantifies the energy dissipation characteristics of the VEM.
Master curve
The master curve is a universal plot of the storage modulus E ' (or G′) and the loss factor η of a polymer as a function of the reduced frequency α T ω and temperature based on the application of the principle of “temperature‐frequency” superposition.
Maxwell model
A classical model of VEM consisting of a spring and viscous damper in a series arrangement.
Morlet wavelet
Morlet wavelet is a sinusoidal function, oscillating at the frequency ω w , modulated by a Gaussian envelope of unit variance.
Pass band
It is a specific frequency band within which waves can propagate along the periodic structures.
Percolation zone
It is the zone, where clustering of conductive particles embedded in an insulating matrix are enough to initiate the formation of continuous conductive networks throughout the matrix. In this zone, the conductivity of the composite experiences a significant increase of several orders of magnitude.
Periodic structure
It is a structure, whether passive or active, that consists of identical substructures, or cells, which are repeated and connected in an identical manner in 1, 2, and 3D.
Phase parameter ( β )
It is the imaginary part of the propagation parameter (μ) that defines the phase difference between the adjacent cells.
Poisson's ratio ( ν )
It is the ratio of the transverse strain to the axial strain of a VEM. This ratio is typically equal to 0.5.
Poynting–Thomson model
It consists of a Kelvin–Voigt VEM model in series with an elastic element (spring).
Propagation parameter ( μ )
It is a complex number whose real part (α) represents the logarithmic decay of the state vector and its imaginary part (β) defines the phase difference between the adjacent cells.
Relaxation
It is the physical phenomenon associated with monitoring the continuous drop of the stress of a VEM when subjected to a constant applied strain. Measuring the time history of the stress is used to determine the time‐dependent “Relaxation Modulus.”
Relaxation modulus
The relaxation modulus E(t) is determined by measuring the time history of the stress σ(t) when a VEM is subjected to a step‐strain of ε0, such that: E(t) = σ(t)/ε 0.
Rayleigh damping model
It is a damping model that describes the equivalent viscous damping coefficient of a damping material as linear combination of its mass and stiffness through the use of appropriate mass and stiffness damping parameters.
Static condensation method (Guyan reduction)
It is a method that reduces (or condenses) the DOF of the system to include only the primary set of DOF only without eliminating them.
Stop band
It is a frequency band within which the wave propagation is completely blocked.
Strain energy
It is the energy stored in a structure as it deforms under the influence of an external load.
Storage modulus (Young's ( E′), shear ( G′))
This modulus quantifies the elastic storage component of the “Complex Modulus” of a VEM that is subjected to sinusoidal in tension or shear loading, respectively. It is also denoted as the “In‐Phase” and “Real Modulus.”
Viscoelastic material (VEM)
Viscoelastic materials have a time‐dependent response, even if the loading is constant. Many polymers and biological tissues exhibit such a behavior. Linear viscoelasticity is a commonly used approximation where the stress depends linearly on the strain and its time derivatives.
Viscous damping
It is the class of damping in which the damping force is linearly proportional to the velocity of deformation.
Zener model
It consists of a Maxwell VEM model in parallel with a damping element.
..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.
Reset