Nonlinear Vibrations and Instability of Shallow Pyramidal Trusses

2015 ◽  
Author(s):  
Carlos Henrique L. de Castro ◽  
Paulo B. Gonçalves ◽  
Diego Orlando
Keyword(s):  
Carbon Nanostructures ◽  
Nonlinear Vibrations ◽  
Nonlinear Behavior ◽  
Basins Of Attraction ◽  
Dynamic Loads ◽  
Phase Portraits ◽  
Major Influence ◽  
Non Linear ◽  
Static And Dynamic Loads ◽  
Von Mises

Pyramidal space trusses are a basic component of several structures, from carbon nanostructures to large geodesic domes. These structures, such as the classical Von Mises truss, have a highly non-linear response in the presence of static and dynamic loads. The geometric nonlinearity is particularly significant, even at low load levels when these structures are shallow, that is, has a small height to base ratio. This paper presents an exact non-linear formulation for a shallow pyramidal truss composed of n equally spaced bars. Based on this formulation, the loss of stability and nonlinear vibrations of these structures under static and dynamic loads is analyzed. To understand its nonlinear behavior, time responses, phase portraits, bifurcation diagrams, energy profiles and basins of attraction are obtained. The results highlight the complex nonlinear dynamics of this class of structures and its major influence in design.

The Effects of a Constant Excitation Force on the Dynamics of an Infinite-Equilibrium Chaotic System Without Linear Terms: Analysis, Control and Circuit Simulation

2020 ◽  
Vol 30 (15) ◽  
pp. 2050234
Author(s):  
L. Kamdjeu Kengne ◽  
Z. Tabekoueng Njitacke ◽  
J. R. Mboupda Pone ◽  
H. T. Kamdem Tagne
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Nonlinear Behavior ◽  
Basins Of Attraction ◽  
Phase Portraits ◽  
Unique Contribution ◽  
Chaotic Signals ◽  
Excitation Force

In this paper, the effects of a bias term modeling a constant excitation force on the dynamics of an infinite-equilibrium chaotic system without linear terms are investigated. As a result, it is found that the bias term reduces the number of equilibrium points (transition from infinite-equilibria to only two equilibria) and breaks the symmetry of the model. The nonlinear behavior of the system is highlighted in terms of bifurcation diagrams, maximal Lyapunov exponent plots, phase portraits, and basins of attraction. Some interesting phenomena are found including, for instance, hysteretic dynamics, multistability, and coexisting bifurcation branches when monitoring the system parameters and the bias term. Also, we demonstrate that it is possible to control the offset and amplitude of the chaotic signals generated. Compared to some few cases previously reported on systems without linear terms, the plethora of behaviors found in this work represents a unique contribution in comparison with such type of systems. A suitable analog circuit is designed and used to support the theoretical analysis via a series of Pspice simulations.

Influence of Modal Coupling on the Nonlinear Dynamics of Augusti’s Model

2011 ◽  
Vol 6 (4) ◽  
Author(s):  
Diego Orlando ◽  
Paulo B. Gonçalves ◽  
Giuseppe Rega ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Behavior ◽  
Dynamic Responses ◽  
Phase Portraits ◽  
Modal Interactions ◽  
Structural Problems ◽  
Lumped Parameter ◽  
Modal Coupling ◽  
Post Buckling ◽  
Static And Dynamic Loads

The nonlinear behavior and stability under static and dynamic loads of an inverted spatial pendulum with rotational springs in two perpendicular planes, called Augusti’s model, is analyzed in this paper. This 2DOF lumped-parameter system is an archetypal model of modal interaction in stability theory representing a large class of structural problems. When the system displays coincident buckling loads, several post-buckling paths emerge from the bifurcation point (critical load) along the fundamental path. This leads to a complex potential energy surface. Herein, we aim to investigate the influence of nonlinear modal interactions on the dynamic behavior of Augusti’s model. Coupled/uncoupled dynamic responses, bifurcations, escape from the pre-buckling potential well, stability, and space-time-varying displacements; attractor-manifold-basin phase portraits are numerically evaluated with the aim of enlightening the system complex response. The investigation of basins evolution due to variation of system parameters leads to the determination of erosion profiles and integrity measures which enlighten the loss of safety of the structure due to penetration of eroding fractal tongues into the safe basin.

New Research on the Use of Hardening Plastics for Aircraft Construction

1940 ◽  
Vol 44 (349) ◽  
pp. 44-73
Author(s):  
Wilhelm Kuech
Keyword(s):  
Strength Properties ◽  
Dynamic Loads ◽  
Absorbed Energy ◽  
Good Strength ◽  
Different Temperatures ◽  
Bonding Properties ◽  
Static And Dynamic Loads ◽  
Impact Bending ◽  
New Research ◽  
Laminated Materials

Laminated materials incorporating plastics seem to be especially well suited lor highly stressed aircraft components, by reason of their good strength properties. Paper, fabric and wood veneers treated with plastics on a phenolic basis were tested with regard to their strength, especially in bending, shear, absorbed energy in impact bending, notching strength and in their resistance against moisture. Further, the behaviour of compressed plastics was studied at different temperatures under static and dynamic loads. A part of the research was extended to pure phenol resin and to thermoplastics based on methacrylate and polyvinylchloride. The bonding properties of laminated compressed plastics were established. Concluding, some experiments relating to the practical manufacture of aeroplane components are communicated.

scholarly journals Preliminary investigation of use of flexible folding wing tips for static and dynamic load alleviation

2016 ◽  
Vol 121 (1235) ◽  
pp. 73-94 ◽  
Author(s):  
A. Castrichini ◽  
V. Hodigere Siddaramaiah ◽  
D.E. Calderon ◽  
J.E. Cooper ◽  
T. Wilson ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Preliminary Investigation ◽  
Aircraft Design ◽  
Dynamic Loads ◽  
Induced Drag ◽  
Aeroelastic Model ◽  
Static And Dynamic Loads ◽  
Folding Wing ◽  
Wing Tips ◽  
Wing Tip

ABSTRACTA recent consideration in aircraft design is the use of folding wing-tips with the aim of enabling higher aspect ratio aircraft with less induced drag while also meeting airport gate limitations. This study investigates the effect of exploiting folding wing-tips in flight as a device to reduce both static and dynamic loads. A representative civil jet aircraft aeroelastic model was used to explore the effect of introducing a wing-tip device, connected to the wings with an elastic hinge, on the load behaviour. For the dynamic cases, vertical discrete gusts and continuous turbulence were considered. The effects of hinge orientation, stiffness, damping and wing-tip weight on the static and dynamic response were investigated. It was found that significant reductions in both the static and dynamic loads were possible. For the case considered, a 25% increase in span using folding wing-tips resulted in almost no increase in loads.

Nonlinear Dynamics of an Imperfect Microbeam Under an Axial Load and Electric Excitation

2011 ◽  
Author(s):  
Laura Ruzziconi ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Microelectromechanical Systems ◽  
Complex Dynamics ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Theoretical Point ◽  
Initial Shape ◽  
Electric Excitation

This study is motivated by the growing attention, both from a practical and a theoretical point of view, toward the nonlinear behavior of microelectromechanical systems (MEMS). We analyze the nonlinear dynamics of an imperfect microbeam under an axial force and electric excitation. The imperfection of the microbeam, typically due to microfabrication processes, is simulated assuming the microbeam to be of a shallow arched initial shape. The device has a bistable static behavior. The aim is that of illustrating the nonlinear phenomena, which arise due to the coupling of mechanical and electrical nonlinearities, and discussing their usefulness for the engineering design of the microstructure. We derive a single-mode-reduced-order model by combining the classical Galerkin technique and the Pade´ approximation. Despite its apparent simplicity, this model is able to capture the main features of the complex dynamics of the device. Extensive numerical simulations are performed using frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior charts. We investigate the overall scenario, up to the inevitable escape, obtaining the theoretical boundaries of appearance and disappearance of the main attractors. The main features of the nonlinear dynamics are discussed, stressing their existence and their practical relevance. We focus on the coexistence of robust attractors, which leads to a considerable versatility of behavior. This is a very attractive feature in MEMS applications. The ranges of coexistence are analyzed in detail, remarkably at high values of the dynamic excitation, where the penetration of the escape (dynamic pull-in) inside the double well may prevent the safe jump between the attractors.

The Mechanical Properties Comparative Analysis for Socked and Non-Socketed Composite Pile

2014 ◽  
Vol 1061-1062 ◽  
pp. 748-750
Author(s):  
Heng Chen ◽  
Ke Sheng Ma
Keyword(s):  
Mechanical Properties ◽  
Comparative Analysis ◽  
Seismic Performance ◽  
Dynamic Loads ◽  
Vertical Load ◽  
Interlayer Thickness ◽  
Static Loads ◽  
Soil Stress ◽  
Composite Pile ◽  
Static And Dynamic Loads

For socked and non-socketed piles in the different mechanical behavior under static and dynamic loads, the paper use ABAQUS to model, simulate the pile , the soil interlayer thickness between the bottom of the pile and bedrock are 2m, 4m under vertical load and Earthquake, cushion cap, pile and pile soil stress situation found non-socketed piles when the soil interlayer thickness within a certain range, the composite pile small subside under dynamic, static loads, the non-socketed piles can better take advantage of the pile soil has a good seismic performance in the earthquake.

Manufacturing of Bellows Compensator by Pulsed-Magnetic Field Pressure

2022 ◽  
Vol 1049 ◽  
pp. 108-113
Author(s):  
Nikolay Kurlaev ◽  
Ahmed Soliman Mohamed Sherif ◽  
Nikolay Ryngach
Keyword(s):  
Relative Elongation ◽  
Operating Time ◽  
Dynamic Loads ◽  
Pulse Field ◽  
Magnetic Pulse ◽  
System Operation ◽  
Effective Protection ◽  
Expansion Joints ◽  
Static And Dynamic Loads ◽  
Tubular Billet

Bellows are a cylindrical shell with a corrugated part, widely used in aviation engineering as a movable sealing element to balance pressure and temperature differences, which ensure continuous and accurate system operation. The use of bellows expansion joints provides reliable and effective protection of pipelines from static and dynamic loads arising from deformations and vibration. Welded-edge bellows are a popular choice for regulating and controlling fuel supply in aircraft devices. The ability of the compensator to perceive deformations is determined by its assigned operating time, which describes how many cycles, and with what amplitude, the bellows compensator perceives without damage. A method for stamping bellows from tubular billets by using magnetic-pulse field in rigid dies, including sequential shaping of corrugations by distributing the internal magnetic pressure with axial movement of the free end of a tubular billet, characterized in that the material of the tubular billet for shaping corrugations is selected in accordance with its relative elongation.

ISUM: Its Birth, Growth and Future

2016 ◽  
Author(s):  
Sherif Rashed
Keyword(s):  
Nonlinear Behavior ◽  
Impact Loads ◽  
Coarse Mesh ◽  
Structural Units ◽  
Large Size ◽  
Linear Behavior ◽  
Large Ship ◽  
Non Linear ◽  
Recent Developments ◽  
Future Potential

ISUM (The Idealized Structural Unit Method) was born in 1972 to efficiently and accurately analyze the behavior of large size structures up to and beyond their ultimate strength. In this method a structure is divided into large elements, basically its structural units (members). Geometric and material non-linear behavior inside the element is formulated and expressed at a limited number of nodal points at the element boundaries. In this way a large structure can be modeled using a coarse mesh while still being able to consider the nonlinear behavior until the collapse of the structure. Several ISUM elements have been formulated and used to analyze the non-linear behavior of large ship structures. In further developments, more elements with more accurate formulations have been developed and more types of structures have been analyzed using this method. The same ISUM concept has been applied to the analysis of welding deformation of large welded structures and to failure analysis of structural and mechanical components subjected to impact loads. In this paper, the basic ISUM concept is outlined, and several elements are presented. Examples of applications to ships and marine structures are presented demonstrating the effectiveness of the method. Recent developments are also reviewed and future potential is explored.

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