FORCE DRIVEN VIBRATIONS OF NONLINEAR PLATES ON A VISCOELASTIC WINKLER FOUNDATION UNDER THE HARMONIC MOVING LOAD

In the present paper, the forced driven nonlinear vibrations of an elastic plate in a viscoelastic medium and resting on a viscoelastic Winkler-type foundation are studied. The damping features of the surrounding medium and foundation are described by the Kelvin-Voigt model and standard linear solid model with fractional derivatives, respectively. The dynamic response of the plate is described by the set of nonlinear differential equations with due account for the fact that the plate is being under the conditions of the internal resonance accompanied by the external resonance. The expressions for the stress function and nonlinear coefficients for different types of boundary conditions are presented.

Bending of a Viscoelastic Timoshenko Cracked Beam Based on Equivalent Viscoelastic Spring Models

Considering the transverse crack as a massless viscoelastic rotational spring, the equivalent stiffness of the viscoelastic cracked beam is derived by Laplace transform and the generalized Dirac delta function. Using the standard linear solid constitutive equation and the inverse Laplace transform, the analytical expressions of the deflection and rotation angle of the viscoelastic Timoshenko beam with an arbitrary number of open cracks are obtained in the time domain. By numerical examples, the bending results of the analytical expressions are verified with those of the FEM program. Additionally, the effects of the time, slenderness ratio, and crack depth on the bending deformations of the different cracked beam models are revealed.

Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid

Parallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models. The first one is the standard linear solid model implemented in ABAQUS/CAE. The second one is the new model for 3D viscoelastic free surface fluid flow, which combines the Oldroyd-B incompressible fluid model and the incompressible neo-Hookean solid model via incorporation of an additional elastic tensor and a dynamic equation for it. The simulation results indicate that either approach can be applied to model the MCS compression with reasonable accuracy. Future application of the viscoelastic free surface fluid model is the MCSs fusion highly-demanded in bioprinting.

Experimental identification of the material standard linear solid model parameters by means of dynamical measurements

A procedure for the experimental identification of the material standard linear solid model parameters by means of dynamic mechanical analysis test instrument measurements is presented. Since the standard linear solid material stress–strain functional D( ω) relationship in the frequency domain formally depends on the standard linear solid material parameters, a procedure able to identify these parameters from test measurement estimates is proposed in this work. Nevertheless, a critical, nonlinear and non-parametric approach is to be followed since the number of the material standard linear solid block components is generally unknown, and the material D( ω) shows a highly nonlinear dependency on the unknown standard linear solid material parameters. For these reasons, measurement and test model noise is expected to strongly influence the accuracy of the identification results. A multi-step procedure is presented, consisting first in the non-parametric identification of a frequency dependent, two degrees of freedom model instrument frame by means of a polynomial rational function, where polynomial order and parameters, such as polynomial coefficients and pole-residue couples, are optimally identified by means of an algebraic numerical technique and of an iterative stabilization procedure. Another procedure able to identify the material D( ω) polynomial rational functional relationship in the frequency domain is also proposed, taking into account the dynamic contribution of the instrument frame, of the inertial contribution of the distributed mass of the beam and of the lumped mass of the instrument force measuring system. An effective procedure, able to identify the standard linear solid material model parameters in the time domain from the identified material physical poles, is finally proposed. Some application examples, concerning the identification of the standard linear solid model of a known material and of an unknown composite material, are shown and discussed as well.

Identifying the parameters of viscoelastic model for a gel-type material as representative of cardiac muscle in dynamic tests

In this paper, mechanical parameters of a calf heart muscle are identified and a gel-type material as the representative of the cardiac muscle in dynamic tests is introduced. The motivation of this study is to introduce a replacement material of the heart muscle to use in experimental studies of the leadless pacemaker. A particular test setup is developed to capture the experimental data based on the stress relaxation test method where its outputs are time histories of the force and displacement. The standard linear solid model is used for mathematical modeling of the heart muscle sample and a gel-type material specimen namely α-gel. Five tests with different strain history [Formula: see text] are performed by regarding and disregarding the influence of the initial ramp of the loading. The mechanical parameters of the standard linear solid model were identified with precise curve fitting. Consideration of the initial ramp significantly influences the consequences and they are so close to their experimental counterparts. The identified parameters of the standard linear solid model by regarding the influence of the initial ramp for the gel-type material are within an acceptable range for the viscoelastic properties of the calf heart tissue. These results show that the gel-type material has the potential to represent the cardiac muscle in the leadless pacemaker experimental studies. Dynamic mechanical analysis is used to characterize the dynamic viscoelastic properties for the gel by utilizing the identified parameters with taking into account the initial ramp in the frequency domain. Results show that Storage modulus, Loss modulus, and Loss tangent are strongly frequency-dependent especially at low-frequency around the heartbeat frequency range (0–2 Hz).

Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators

A waveguide model for a pre-compressed cylindrical natural rubber vibration isolator is developed within a wide frequency range—20 to 2000 Hz—and for a wide pre-compression domain—from vanishing to the maximum in service, that is 20%. The problems of simultaneously modeling the pre-compression and frequency dependence are solved by applying a transformation of the pre-compressed isolator into a globally equivalent linearized, homogeneous, and isotropic form, thereby reducing the original, mathematically arduous, and complex problem into a vastly simpler assignment while using a straightforward waveguide approach to satisfy the boundary conditions by mode-matching. A fractional standard linear solid is applied as the visco-elastic natural rubber model while using a Mittag–Leffler function as the stress relaxation function. The dynamic stiffness is found to depend strongly on the frequency and pre-compression. The former is resulting in resonance phenomena such as peaks and troughs, while the latter exhibits a low-frequency magnitude stiffness increase in addition to peak and trough shifts with increased pre-compressions. Good agreement with nonlinear finite element results is obtained for the considered frequency and pre-compression range in contrast to the results of standard waveguide approaches.

Nearly constant Q models of the generalized standard linear solid type and the corresponding wave equations

Time-domain seismic forward and inverse modeling for a dissipative medium is a vital research topic to investigate the attenuation structure of the Earth. Constant Q, also called frequency independence of the quality factor, is a common assumption for seismic Q inversion. We propose the first- and second-order nearly constant Q dissipative models of the generalized standard linear solid type, using a novel Q-independent weighting function approach. The two new models, which originate from the Kolsky model (a nearly constant Q model) and the Kjartansson model (an exactly constant Q model), result in the corresponding wave equations in differential form. Even for extremely strong attenuation (e.g., Q = 5), the quality factor and phase velocity for the two new models are close to those for the Kolsky and Kjartansson models, in a frequency range of interest. The wave equations for the two new models involve explicitly a specified Q parameter and have compact and simple forms. We provide a novel perspective on how to build a nearly constant Q dissipative model which is beneficial for time-domain large scale wavefield forward and inverse modeling. This perspective could also help obtain other dissipative models with similar advantages. We also discuss the extension beyond viscoacousticity and other related issues, for example, extending the two new models to viscoelastic anisotropy.