An analytical approach for detecting isolated periodic solution branches in weakly nonlinear structures

AbstractThis paper considers isolated responses in nonlinear systems; both in terms of isolas in the forced responses, and isolated backbone curves (i.e. the unforced, undamped responses). As isolated responses are disconnected from other response branches, reliably predicting their existence poses a significant challenge. Firstly, it is shown that breaking the symmetry of a two-mass nonlinear oscillator can lead to the breaking of a bifurcation on the backbone curves, generating an isolated backbone. It is then shown how an energy-based, analytical method may be used to compute the points at which the forced responses cross the backbone curves at resonance, and how this may be used as a tool for finding isolas in the forced responses. This is firstly demonstrated for a symmetric system, where an isola envelops the secondary backbone curves, which emerge from a bifurcation. Next, an asymmetric configuration of the system is considered and it is shown how isolas may envelop a primary backbone curve, i.e. one that is connected directly to the zero-amplitude solution, as well as the isolated backbone curve. This is achieved by using the energy-based method to determine the relationship between the external forcing amplitude and the positions of the crossing points of the forced response. Along with predicting the existence of the isolas, this technique also reveals the nature of the responses, thus simplifying the process of finding isolas using numerical continuation

adhesion of functional layer on polymeric substrates for optoelectronic applications

The use of plastic film substrates for organic electronic devices promises to enable new applications, such as flexible displays. Plastic substrates have several distinct advantages, such as ruggedness, robustness, ultra lightness, conformability and impact resistance over glass substrates, which are primarily used in flat panel displays (FPDs) today. However, high transparency, proper surface roughness, low gas permeability and high transparent electrode conductivity of the plastic substrate are required for commercial applications. Polyesters, both amorphous and semicrystalline, are a promising class of commercial polymer for optoelectronic applications. Surface modification of polyester films was performed via chemical solution determining hydrolysis or oxidation. Hydrolysis was carried out by means of sodium hydroxide solution and oxidation by using standard clean 1 (SC-1) of RCA procedure [1]. For this work we have used commercial polymer films of 100µm in thickness: AryLite™ [2], supplied by Ferrania Imaging Technologies S.p.A. and characterised by very high glass transition temperature, Mylar™ (Polyethylene Terephthalate PET) and Teonex™ (Polyethylene Naphthalate PEN) both supplied by Dupont. More over, a bioriented and semicrystalline PET have been used. The aim of this study is modifying the polymer surface to improve the adhesion between organic-inorganic layer. It was found that the NaOH and SC-1 treatment cause a decrease of contact angles. In the present study we have deposited a thin films of amorphous hydrogenated silicon (a-Si:H) and its oxide (SiO2) on a new high temperature polymer substrate, AryLite™, by plasma enhanced chemical vapour deposition (PECVD) [3], with a radio frequency plasma system

An optimized tuned mass damper/harvester device

Much work has been conducted on vibration absorbers, such as tuned mass dampers (TMD), where significant energy is extracted from a structure. Traditionally, this energy is dissipated through the devices as heat. In this paper, the concept of recovering some of this energy electrically and reuse it for structural control or health monitoring is investigated. The energy-dissipating damper of a TMD is replaced with an electromagnetic device in order to transform mechanical vibration into electrical energy. That gives the possibility of controlled damping force whilst generating useful electrical energy. Both analytical and experimental results from an adaptive and a semi-active tuned mass damper/harvester are presented. The obtained results suggest that sufficient energy might be harvested for the device to tune itself to optimise vibration suppression

The Significance of Nonlinear Normal Modes for Forced Responses

Nonlinear normal modes (NNMs) describe the unforced and undamped periodic responses of nonlinear systems. NNMs have proven to be a valuable tool, and are widely used, for understanding the underlying behaviour of nonlinear systems. They provide insight into the types of behaviour that may be observed when a system is subjected to forcing and damping, which is ultimately of primary concern in many engineering applications. The definition of an NNM has seen a number of evolutions, and the contemporary definition encompasses all periodic responses of a conservative system. Such a broad definition is essential, as it allows for the wide variety of responses that nonlinear systems may exhibit. However, it may also lead to misleading results, as some of the NNMs of a system may represent behaviour that will only be observed under very specific forcing conditions, which may not be realisable in any practical scenario. In this paper, we investigate how the significance of NNMs may differ and how this significance may be quantified. This is achieved using an energy-based method, and is validated using numerical simulations

Thermochemical interpretation of one-dimensional seismic reference models for the upper mantle: Evidence for bias due to heterogeneity

A 1-D reference model for the mantle that is physically meaningful would be invaluable both in geodynamic modelling and for an accurate interpretation of 3-D seismic tomography. However, previous studies have shown that it is difficult to reconcile the simplest possible 1-D physical model—1300°C adiabatic pyrolite—with seismic observations. We therefore generate a set of alternative 1-D thermal and chemical mantle models, down to 900 km depth, and compare their properties with seismic data. We use several different body and surface wave data sets that provide complementary constraints on mantle structure. To assess the agreement between our models and seismic data, we take into account the large uncertainties in both the elastic/anelastic parameters of the constituent minerals, and the thermodynamic procedures for calculating seismic velocities. These uncertainties translate into substantial differences in seismic structure. However, in spite of such differences, subtle trends remain. We find that models which attain (1) higher velocity gradients between 250 and 350 km; (2) higher velocity gradients in the lower transition zone; and (3) higher average velocities immediately beneath the 660-discontinuity, than 1300°C adiabatic pyrolite—either via a temporary shift to lower temperatures, and/or a change to a seismically faster chemical composition—provide a significantly better fit to the seismic data than adiabatic pyrolite. This is compatible with recent thermochemical dynamic models by Tackley et al. in which average thermal structure is smooth and monotonous, but average chemical structure deviates substantially from pyrolite above, in, and below the transition zone. Our results suggest that 1-D seismic reference models are being systematically biased by a complex 3-D chemical structure. This bias should be taken into account when attempting quantitative interpretation of seismic anomalies, since those very anomalies contribute to the 1-D average signa

Lateral load effects on tall shear wall structures of different height

A three-dimensional formulation is proposed to analyze the lateral loading distribution of external actions in high-rise buildings. The method is extended to encompass any combination of bracings, including bracings with open thin-walled cross-sections, which are analyzed in the framework of Timoshenko-Vlasov’s theory of sectorial areas. More in detail, the proposed unified approach is a tool for the preliminary stages of structural design. It considers infinitely rigid floors in their own planes, and allows to better understand stress and strain distributions in the different bearing elements if compared to a finite element analysis. Numerical examples, describing the structural response of tall buildings characterized by bracings with different cross-section and height, show the effectiveness and flexibility of the proposed method. The accuracy of the results is investigated by a comparison with finite element solutions, in which the bracings are modelled as three-dimensional structures by means of shell elements