Martin Schagerl

On the paradox of the free falling folded chain

SummaryIt is shown both by experiment and also by numerical simulation that for a vertically hanging folded chain the free part, if released, is falling faster than a free falling body under gravitational acceleration. A qualitative explanation of thisparadoxical phenomenon is given by showing that a downpulling force at the fold is created. In the simulation this force is also calculated quantitatively.

Stability of Relative Equilibria. Part I: Comparison of Four Methods

In this first part of the paper, we review methods for the investigation of stability of relative equilibria of symmetric Hamiltonian systems and explain them by means of the model problem of a rotating pendulum. For this example the modern approaches, known as energy momentum methods are compared with stability assessment by linearization and by the classical method of Routh.

Dynamical Analysis of the Deployment Process of Tethered Satellite Systems

The equations of motion describing the deployment process of a sub-satellite from a main satellite are derived from Hamilton’s principle. The dynamics of the drum on which the tether is stored is included. Both free and controlled deployments are numerically simulated.

Propagation of small waves in inextensible strings

Abstract The model of an inextensible uniform string subject to constant gravitation is used to study the propagation of transversal waves in one-dimensional continua. Perturbation analysis of the equations of motion yields as a result the local representation of small waves in terms of a normalized Riemann function. By means of the latter, shape and speed of propagating waves may be discussed. A refined analysis confirms that on first order, small waves travel along characteristics of the unperturbed equilibrium configuration. An explicit power law for the waves’ amplitudes is given, and the findings are supported by the numerical results.

Analytical formulas for the effective width caused by bulging and flattening of curved aircraft panels

The skin of a curved aircraft panel flattens, if it is subjected to circumferential tension, and bulges, if it is subjected to compression. These deformations distort the hoop stress distribution, which further leads to a reduced load-carrying width of the skin in circumferential direction. The book Roarks Formulas for Stress and Strain (W. C. Young and R. G. Budynas, 2002) presents a method to calculate the effective width of wide flanges of curved beams under tension. Although often used, it is shown in the current article that this method is not applicable to assess the effects of flattening and bulging of aircraft panels. As a reason, the support provided by the longitudinal stringers is identified. The current article consists of two parts. The first part presents the derivation of an analytical method to calculate the effective width caused by bulging and flattening of curved aircraft panels. The underlying model uses standard theories for straight and curved beams and is thus consistent with the assumptions made for Roarks formula. For improving the accuracy of this analytical result, the second part presents a simple procedure to fit this analytical approach to results from parametric Finite Element studies.

Characterizing the Conductivity and Enhancing the Piezoresistivity of Carbon Nanotube-Polymeric Thin Films

The concept of lightweight design is widely employed for designing and constructing aerospace structures that can sustain extreme loads while also being fuel-efficient. Popular lightweight materials such as aluminum alloy and fiber-reinforced polymers (FRPs) possess outstanding mechanical properties, but their structural integrity requires constant assessment to ensure structural safety. Next-generation structural health monitoring systems for aerospace structures should be lightweight and integrated with the structure itself. In this study, a multi-walled carbon nanotube (MWCNT)-based polymer paint was developed to detect distributed damage in lightweight structures. The thin film’s electromechanical properties were characterized via cyclic loading tests. Moreover, the thin film’s bulk conductivity was characterized by finite element modeling.

An Inkjet-Printed Carbon Nanotube Strain Distribution Sensor for Quasi Real-Time Strain Monitoring of Lightweight Design Materials

Carbon fiber-reinforced polymer (CFRP) composites are lightweight, durable, and corrosionresistive materials that are popular for constructing automotive bodies and aircraft structures. However, their heterogeneous composition and anisotropic mechanical behavior make design of their service lives challenging. To address challenges in monitoring CFRP’s structural behavior, a cheap, weightless, and reliable sensor shall be developed for CFRPs to monitor their damage-to-failure mode. In this study a carbon nanotube (CNT)-embedded thin film is inkjet-printed onto a flexible substrate and applied over a tensile testing coupon. Coupled with the algorithm of electrical impedance tomography, the sensor with 16 electrodes is able to reconstruct the strain distribution of a surface under 8 sec. Non-uniform strain distribution can also be reconstructed at strain levels down to 0.001%.

Optimal Placement of Fiber Optical Sensors along Zero-strain Trajectories to Detect Damages in Thin-walled Structures with Highest Sensitivity

This article discusses the optimal placement of fiber optical sensors to detect damages in thin-walled lightweight structures. Both, measurement sensitivity and data management indicate that strain sensors are optimally placed if they measure no signal if the structure is undamaged. Such locations are found by in-depth structure analysis, particularly by analysis of the strain state of the deformed structure. Although the fundamental principle and numerical algorithm is demonstrated by means of a simple metallic plate it is shown that the results are in general applicable to both, fiber optical sensors attached on the surface and also sensors embedded between the plies of laminated composite materials. doi: 10.12783/SHM2015/138

Numerically Efficient Formulation of The Equations of Motion of Tethered Satellite Systems

Simulation of tethered satellite systems requires the numerical solution of a coupled system of nonlinear partial and ordinary differential equations.

In situ spatial strain monitoring of a single-lap joint using inkjet-printed carbon nanotube embedded thin films

Adhesive bonds are particularly favored by lightweight structures due to their weight efficiency and insulating property regarding contact corrosion. However, it is challenging to interrogate directly over the bonding area due to its sandwiched structure. In this study, an inkjet-printed carbon nanotube (CNT) strain distribution sensing film is embedded at the interface between an adherend and the adhesive in a single-lap joint configuration to monitor the spatial strain distribution over the bonding area. The conductivity distribution reconstructed by an algorithm of electrical impedance tomography (EIT) results in similar trend to the correlated conductivity distribution numerically calculated from a three-dimensional (3D) finite element model. Moreover, the EIT result of a defect-embedded testing specimen shows a different conductivity distribution compared to the healthy specimen, indicating the existence of the debonding region.