Prabakaran Balasubramanian

Viscoelastic Characterization of Woven Dacron for Aortic Grafts by using Direction-Dependent Quasi-Linear Viscoelasticity

In case of direction-dependent viscoelasticity, a simplified formulation of the three-dimensional quasi-linear viscoelasticity has been obtained manipulating the original Fung equation. The experimental characterization of the static hyperelastic behaviour, the relaxation, the dynamic modulus and the loss factor of woven Dacron from a commercial aortic prosthesis has been performed. An 11% difference of the reduced relaxation (after infinite time) between axial and circumferential directions has been observed for the woven Dacron. A very large increase in stiffness is obtained in case of harmonic loading with respect to the static loading. These findings are particularly relevant for dynamic modelling of currently used aortic grafts.

A Paper-Based Piezoelectric Accelerometer

This paper presents the design and testing of a one-axis piezoelectric accelerometer made from cellulose paper and piezoelectric zinc oxide nanowires (ZnO NWs) hydrothermally grown on paper. The accelerometer adopts a cantilever-based configuration with two parallel cantilever beams attached with a paper proof mass. A piece of U-shaped, ZnO-NW-coated paper is attached on top of the parallel beams, serving as the strain sensing element for acceleration measurement. The electric charges produced from the ZnO-NW-coated paper are converted into a voltage output using a custom-made charge amplifier circuit. The device fabrication only involves cutting of paper and hydrothermal growth of ZnO NWs, and does not require the access to expensive and sophisticated equipment. The performance of the devices with different weight growth percentages of the ZnO NWs was characterized.

Identification of Non-Linear Parameters of a Nuclear Fuel Rod

In Pressurized Water Reactors (PWR), fuel assemblies are made up of fuel rods, long slender tubes filled with uranium pellets, bundled together using spacer grids. These structures are subjected to fluid-structure interactions, due to the flowing coolant surrounding the fuel assemblies inside the core, coupled with large-amplitude vibrations in case of external seismic excitation. Therefore, understanding the nonlinear response of the structure, and, particularly, its dissipation, is of paramount importance for the choice of safety margins, in the design of fuel assemblies, to ensure their functionality and safety in the worst external condition scenarios.To model the nonlinear dynamic response of fuel rods, the identification of the nonlinear stiffness and damping parameters is required. A tool based on harmonic balance method was developed to identify these parameters from the experimentally obtained force-response curves, considering one-to-one internal resonance phenomenon present in axisymmetric structures such as cylindrical tubes and shells. To validate the tool, it was applied to the reference case of circular cylindrical shell filled with water, which revealed an increase of damping with the excitation amplitude.In the following paper, the more realistic case of a single fuel rod with clamped-clamped boundary condition was investigated by applying harmonic excitation at various force levels. The nonlinear parameters including damping were extracted from experimental results by means of the adapted tool. An increase in damping with excitation amplitude has been shown according to earlier studies.Copyright

Experiments and Simulations in Travelling Wave and Non-Stationary Nonlinear Vibrations of Circular Cylindrical Shells

The nonlinear vibrations of a water-filled circular cylindrical shell subjected to radial harmonic excitation in the spectral neighborhood of the lowest resonances are investigated numerically and experimentally by using a seamless aluminum sample. The experimental boundary conditions are close to a simply supported circular cylindrical shell. Modal analysis reveals the presence of predominantly radial driven and companion modes in the low frequency range, implying the existence of a traveling wave phenomenon in the nonlinear field. Experimental studies previously carried out on cylindrical shells did not permit the complete identification of the characteristic traveling wave response and of its non-stationary nature. The added mass of the internal quiescent, incompressible and inviscid fluid results in an increase of the weakly softening behavior of the shell, as expected. The minimization of the added mass due to the excitation system and the negligible entity of the geometric imperfections of the shell allow the appearance of an exact one-to-one internal resonance between driven and companion modes. This internal resonance gives rise to a travelling wave response around the shell circumference and non-stationary, quasi-periodic vibrations, which are experimentally verified by means of stepped-sine testing with feedback control of the excitation amplitude. The same phenomenon is observed in the nonlinear response obtained numerically. The traveling wave is measured by means of state-of-the-art laser Doppler vibrometry applied to multiple points on the structure simultaneously. Previous studies present in literature did not show if this vibration can be chaotic for relatively small vibration amplitudes. Chaos is here observed in the frequency region where the travelling wave response is present for vibrations amplitudes smaller than the thickness of the shell. The relevant nonlinear reduced order model of the shell is based on the Novozhilov nonlinear shell theory retaining in-plane inertia and on an expansion of the displacements in terms of a properly chosen base of linear modes. An energy approach is used to obtain the nonlinear equations of motion, which are numerically studied (i) by using a code based on arc-length continuation and collocation method that allows bifurcation analysis in case of stationary vibrations, (ii) by a continuation code based on direct integration and Poincare maps, which also evaluates the maximum Lyapunov exponent in case of non-stationary vibrations. The comparison of experimental and numerical results is particularly satisfactory throughout the various excitation amplitude levels considered. The two methods concur in describing the progressive development of the companion mode into a fully developed traveling wave and the subsequent appearance of quasi-periodic and eventually chaotic vibrations.Copyright

Theoretical and Experimental Study on Large Amplitude Vibrations of Clamped Viscoelastic Plates

In this paper, the large amplitude vibrations of clamped-clamped thin viscoelastic rectangular plates due to a concentrated transversal harmonic load are investigated both theoretically and experimentally. Clamped boundary condition on all edges and von Karman nonlinear strain-displacement relationships are considered while rotary inertia, geometric imperfections, and shear deformation are neglected. In the theoretical study, the viscoelastic behaviour of the material is modelled using the Kelvin-Voigt model. In-plane loads applied during the assembly of the plate are taken into account and clamped boundary conditions are modelled using artificial rotational springs. The nonlinear ordinary differential equations for the considered Kelvin-Voigt model are obtained using the generalized energy approach. These equations contain quadratic and cubic nonlinear viscoelasticity terms in addition to quadratic and cubic stiffness terms. Non-dimensionalization of variables is carried out and each second order equation is converted into two first order equations. The resulting system of equations is solved using AUTO (software based on the arclength continuation method that allows bifurcation analysis), to get the frequency-response curves at various force levels. Moreover numerical time integration of equations was also performed using the fourth-order Runge-Kutta method to understand the time response of the structure. In the experimental study, two rubber plates with different material and thicknesses were considered; a silicone plate with 0.0015 m thickness and a neoprene plate with 0.003 m thickness. The plates were fixed on a heavy rectangular metal frame thereby ensuring the clamped boundary condition on all edges. Linear experimental modal analysis was carried out as a first step to estimate the mode shapes and natural frequencies. In the second step, the nonlinear vibration response of the plate around its first resonance was measured at various harmonic force levels. At each force level, the amplitude of the harmonic excitation was kept constant by LMS Data Acquisition System and Test.Lab Stepped Sine software module while slowly varying the frequency of excitation to get the frequency-response curves. Laser Doppler Vibrometry was used to measure the response from the plate as it eliminates the possible mass loading effect introduced by any contact type sensors. A maximum amplitude of more than three times the thickness of the plate was achieved. The nonlinear response curves showed a typical hardening type nonlinearity along with sudden jumps as expected for plates. Experimental frequency-response curves were compared with theoretical results and a good agreement was found. The influence of nonlinear viscoelastic damping terms was clearly noticed on the response curves of the plate. The retardation time, measured in seconds decreases with increasing excitation force and larger amplitude vibrations.Copyright

Nonlinear Damping on Large-Amplitude Vibrations of Plates

Large-amplitude (geometrically nonlinear) forced vibrations of completely free sandwich and steel rectangular plates are investigated experimentally. Harmonic excitation is applied by using an electro-dynamic exciter and the plate vibration is measured by using laser Doppler vibrometers. A scanning laser Doppler vibrometer is used for experimental modal analysis since it provides non-contact vibration measurements with very high spatial resolution. The large-amplitude vibration experiments are carried out by using a single point Laser Doppler Vibrometer and a stepped-sine testing procedure. The non-linear frequency response curves are obtained by increasing and decreasing the excitation frequency in very small steps at specific force amplitudes controlled in a closed-loop. The experimental results are compared to numerical simulations obtained by reduced-order models and show very good agreement. The nonlinear damping is experimentally obtained as a function of the vibration amplitude.Copyright