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.

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).

On the Cauchy problem of the standard linear solid model with Cattaneo heat conduction

In the present paper we consider the Standard Linear Solid model in R N coupled with the Cattaneo law of heat conduction. We show the well-posedness and asymptotic stability of the problem, giving decay rates for a norm related to the solution. These results are compared with those given for the Fourier problem in (Pellicer and Said-Houari (2020)) and the ones of the problem without heat conduction (see previous work (Appl Math. Optim 80 (2019) 447–478)). The main difference is that the Cattaneo system exhibits the well-known regularity-loss phenomenon. The methods used to prove these results are the energy method in the Fourier space and the eigenvalues expansion method.