Planar Finite Forced Dynamics of a Double Hinged Circular Arch: Theory and Experiments

1997 ◽  
Author(s):  
Francesco Benedettini
Keyword(s):  
Theoretical Models ◽  
Instability Region ◽  
Vertical Force ◽  
Circular Arch ◽  
Analytical Approximations ◽  
Modal Coupling ◽  
Simplifying Assumptions ◽  
Antisymmetric Component ◽  
Principal Region ◽  
Theory And Experiments

Abstract The planar dynamics of an elastic circular arch undergoing large displacements under a sinusoidally varying, concentrated, vertical force at its tip is analyzed. First, a revision of theoretical models found in the literature and an analysis on different analytical approximations consistent with different simplifying assumptions is done; then, the analytical results are compared with those of an experimental steel model of a double hinged circular arch. The principal region of instability of the unimodal symmetric solution in which the nonlinear modal coupling excites the antisymmetric component is studied; moreover, inside this principal instability region, subregions of instability of any periodic solution are found and the corresponding increased complexity of the time laws is analyzed by using time series analysis tools.

scholarly journals Interconnections Accelerate Collapse in a Socio-Ecological Metapopulation

2019 ◽  
Vol 11 (7) ◽  
pp. 1852 ◽  
Author(s):  
Zachary Dockstader ◽  
Chris Bauch ◽  
Madhur Anand
Keyword(s):  
Theoretical Models ◽  
Ecological Sustainability ◽  
Human Populations ◽  
Metapopulation Model ◽  
Single Population ◽  
Metapopulation Structure ◽  
Model Dynamics ◽  
Simplifying Assumptions ◽  
Over Exploitation ◽  
The Impact

Over-exploitation of natural resources can have profound effects on both ecosystems and their resident human populations. Simple theoretical models of the dynamics of a population of human harvesters and the abundance of a natural resource being harvested have been studied previously, but relatively few models consider the effect of metapopulation structure (i.e., a population distributed across discrete patches). Here we analyze a socio-ecological metapopulation model based on an existing single-population model used to study persistence and collapse in human populations. Resources grow logistically on each patch. Each population harvests resources on its own patch to support population growth, but can also harvest resources from other patches when their own patch resources become scarce. We show that when populations are allowed to harvest resources from other patches, the peak population size is higher, but subsequent population collapse is significantly accelerated and across a broader parameter regime. As the number of patches in the metapopulation increases, collapse is more sudden, more severe, and occurs sooner. These effects persist under scenarios of asymmetry and inequality between patches. Our model makes simplifying assumptions in order to facilitate insight and understanding of model dynamics. However, the robustness of the model prediction suggests that more sophisticated models should be developed to ascertain the impact of metapopulation structure on socio-ecological sustainability.

A Study of Unsteady Pressures Near the Tip of a Transonic Fan in Unstalled Supersonic Flutter

1984 ◽  
Vol 106 (2) ◽  
pp. 198-203 ◽  
Author(s):  
D. G. Halliwell ◽  
S. G. Newton ◽  
K. S. Lit
Keyword(s):  
Pressure Ratio ◽  
Theoretical Models ◽  
Complex Motion ◽  
Blade Passage ◽  
Unsteady Aerodynamic ◽  
Supersonic Flutter ◽  
Simplifying Assumptions ◽  
Blade Section ◽  
Transonic Fan ◽  
Theoretical Results

A comparison of experimental and theoretical results is presented for a modern transonic research fan, vibrating in a coupled flutter mode. The measurement of steady and unsteady pressures on the aerofoil surface is described, as also is the derivation of the accompanying blade motion using casing-mounted frequency modulated grids. This complex motion is made use of to calculate unsteady pressures from various unsteady aerodynamic theories. These theoretical models are reviewed in turn and compared against the experimental data at a reference blade section. Considering the complexity of the flow and the inherent simplifying assumptions, the comparisons on both amplitude and phase are generally favorable. The position of the shock in the blade passage is shown to be important. The comparison is extended to unsteady work and again the results are favorable if allowance is made for the differences in blade pressure ratio between the various theories and the experiment.

Revisiting the Cattaneo-Mindlin Concept of Interfacial Slip in Tangentially Loaded Compliant Bodies

2009 ◽  
Author(s):  
Izhak Etsion
Keyword(s):  
Failure Mode ◽  
Experimental Verification ◽  
Failure Criterion ◽  
Basic Problem ◽  
Theoretical Models ◽  
Interfacial Slip ◽  
Numerical Techniques ◽  
Plastic Yield ◽  
Alternative Approach ◽  
Simplifying Assumptions

The Cattaneo-Mindlin concept of interfacial slip in tangentially loaded compliant bodies is revisited and its basic simplifying assumptions are critically examined. It is shown that these assumptions, which, in the absence of modern numerical techniques, were essential in 1949 to enable an elegant quantitative solution of the basic problem of presliding between contacting bodies, are actually non physical. An alternative approach to the same problem that is based on treating sliding inception as a failure mode involving material plastic yield is discussed. This alternative approach was suggested even before 1949 but for the same lack of modern numerical techniques could only be promoted qualitatively. Some recent theoretical models, that are based on this earlier alternative approach, and in which the simplifying assumptions of the Cattaneo-Mindlin concept were completely relaxed are described along with their experimental verification. It is shown that the pre-sliding problem between contacting bodies can be accurately solved by these models using realistic physical assumptions and failure criterion.

Revisiting the Cattaneo–Mindlin Concept of Interfacial Slip in Tangentially Loaded Compliant Bodies

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Izhak Etsion
Keyword(s):  
Failure Mode ◽  
Experimental Verification ◽  
Failure Criterion ◽  
Basic Problem ◽  
Theoretical Models ◽  
Interfacial Slip ◽  
Numerical Techniques ◽  
Plastic Yield ◽  
Alternative Approach ◽  
Simplifying Assumptions

The Cattaneo–Mindlin concept of interfacial slip in tangentially loaded compliant bodies is revisited and its basic simplifying assumptions are critically examined. It is shown that these assumptions, which, in the absence of modern numerical techniques, were essential in 1949 to enable an elegant quantitative solution of the basic problem of presliding between contacting bodies, may be nonphysical. An alternative approach to the same problem that is based on treating sliding inception as a failure mode involving material plastic yield is discussed. This alternative approach was suggested even before 1949 but for the same lack of modern numerical techniques could only be promoted qualitatively. Some recent theoretical models, which are based on this earlier alternative approach, and in which the simplifying assumptions of the Cattaneo–Mindlin concept were completely relaxed, are described along with their experimental verification. It is shown that the presliding problem between contacting bodies can be accurately solved by these models using realistic physical assumptions and failure criterion.

scholarly journals Theoretical Models for Magnetic Properties of Iron Pnictides Part II: Boson Formalism

2011 ◽  
Vol 35 (1) ◽  
pp. 45-54 ◽  
Author(s):  
M. Vujinović ◽  
M. Pantić ◽  
M. Pavkov-Hrvojević ◽  
P. Mali
Keyword(s):  
Magnetic Properties ◽  
Spin Wave ◽  
Random Phase ◽  
Wave Theory ◽  
Theoretical Models ◽  
Wave Dispersion ◽  
Iron Pnictides ◽  
Satisfactory Description ◽  
Model Hamiltonian ◽  
Theory And Experiments

Theoretical Models for Magnetic Properties of Iron Pnictides Part II: Boson FormalismWe analyze theJ1-J2-JcHeisenberg model Hamiltonian by using the Dyson-Maleev representation for spin operators and keeping the terms quadratic in Bose operators (linear spin wave theory). From the resulting Hamiltonian we find the ground state magnetisation and spin wave dispersion by employing the Green's function method. We compare the results with those of random phase approximation analysis from Part I and with experimental data for parent pnictide compounds. Neither of the two approaches gives a completely satisfactory description of the magnetic properties of iron pnictides. We conclude that alterations of the model Hamiltonian are needed to get a better agreement between the theory and experiments.

The Use of Experimental Tests in the Formulation of Analytical Models for the Finite Forced Dynamics of Planar Arches

2001 ◽  
Author(s):  
Rocco Alaggio ◽  
Francesco Benedettini
Keyword(s):  
Experimental Analysis ◽  
Experimental Tests ◽  
Analytical Models ◽  
Shape Functions ◽  
Concentrated Force ◽  
Modal Coupling ◽  
Principal Region ◽  
Continuous Problem ◽  
Discretization Procedure

Abstract The role of the experimental analysis in the formulation of reduced analytical models of planar arches under a vertical, sinusoidally varying, concentrated force on the tip is analyzed in this work. After recalling the theory describing the continuous problem for different initial geometries, using a standard Galerkin procedure, two ode’s are derived and used to enlighten all the interesting phenomena exhibited by different prototypes tested in a companion experimental analysis whose results are also used to validate the shape functions used in the discretization procedure. The principal region of instability of the unimodal symmetric solution in which the nonlinear modal coupling excites antisymmetric components is studied analyzing the bifurcation conditions and the post-critical behavior.

Theoretical and Experimental Finite Forced Dynamics of a Cantilever Beam: Dynamic Instability and Modal Coupling

1999 ◽  
Author(s):  
Francesco Benedettini ◽  
Angelo Di Egidio
Keyword(s):  
Cantilever Beam ◽  
Dynamic Instability ◽  
Path Following ◽  
Analysis Tool ◽  
Vertical Force ◽  
Chaotic Motions ◽  
Beam Dynamic ◽  
Global Dynamic ◽  
Modal Coupling ◽  
Linearized Model

Abstract The 3-d dynamics of a cantilever beam undergoing large displacements under a sinusoidally varying, concentrated, vertical force at its free end is analyzed. The pde’s of the motion are obtained by using the Hamilton principle and then a reduced 3 degree-of-freedom model is obtained using in a Galerkin discretization, three eigenfunctions of the linearized model. A path following procedure is used to describe the global dynamic behavior in the excitation control parameter plane. The results obtained using the simple 3 d.o.f. analytical model are then compared with those of an experimental steel model of the cantilever. The regions of instability of the unimodal planar solution in which the nonlinear modal coupling excites the torsional component are studied; the planar motion usually looses stability via Hopf bifurcations after which quasi-periodic and/or chaotic motions are found. Inside the regions in which the system shows a complex time-evolution the complexity-level of the response is analyzed using, for the experimental model, a time series analysis tool.

scholarly journals Controlling Normal Stiffness in Droplet-Based Linear Bearings

Micromachines ◽  
2018 ◽  
Vol 9 (10) ◽  
pp. 525 ◽  
Author(s):  
Qi Ni ◽  
Nathan Crane
Keyword(s):  
Closed Form ◽  
Normal Load ◽  
Vertical Force ◽  
Design Strategies ◽  
Supporting Surface ◽  
Moving Plate ◽  
Positioning Accuracy ◽  
Analytical Approximations ◽  
Load Carrying ◽  
Stiffness Characteristics

While capillary forces are negligible relative to gravity at the macroscale, they provide adequate force to effectively manipulate millimeter to micro meter objects. The fluidic actuation can be accomplished using droplets that also act as bearings. While rotary droplet bearings have been previously demonstrated, this paper addresses the positioning accuracy of a droplet-based bearing consisting of a droplet between a moving plate and a stationary substrate with constrained wetting region under a normal load. Key wetting cases are analyzed using both closed form analytical approximations and numerical simulations. The vertical force and stiffness characteristics are analyzed in relation to the wetting boundaries of the supporting surface. Case studies of different wetting boundaries are presented and summarized. Design strategies are presented for maximizing load carrying capability and stiffness. These results show that controlled wetting and opposing droplet configurations can create much higher stiffness fluidic bearings than simple droplets.

scholarly journals Fabrication and microfluidic analysis of graphene-based molecular communication receiver for Internet of Nano Things (IoNT)

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Murat Kuscu ◽  
Hamideh Ramezani ◽  
Ergin Dinc ◽  
Shahab Akhavan ◽  
Ozgur B. Akan
Keyword(s):  
Theoretical Models ◽  
Theoretical Work ◽  
Practical Implementation ◽  
Graphene Field Effect Transistor ◽  
Simplifying Assumptions ◽  
Information And Communication ◽  
Microfluidic Analysis ◽  
Time Varying Channel ◽  
Communication Methods ◽  
Efficiency And Reliability

AbstractBio-inspired molecular communications (MC), where molecules are used to transfer information, is the most promising technique to realise the Internet of Nano Things (IoNT), thanks to its inherent biocompatibility, energy-efficiency, and reliability in physiologically-relevant environments. Despite a substantial body of theoretical work concerning MC, the lack of practical micro/nanoscale MC devices and MC testbeds has led researchers to make overly simplifying assumptions about the implications of the channel conditions and the physical architectures of the practical transceivers in developing theoretical models and devising communication methods for MC. On the other hand, MC imposes unique challenges resulting from the highly complex, nonlinear, time-varying channel properties that cannot be always tackled by conventional information and communication tools and technologies (ICT). As a result, the reliability of the existing MC methods, which are mostly adopted from electromagnetic communications and not validated with practical testbeds, is highly questionable. As the first step to remove this discrepancy, in this study, we report on the fabrication of a nanoscale MC receiver based on graphene field-effect transistor biosensors. We perform its ICT characterisation in a custom-designed microfluidic MC system with the information encoded into the concentration of single-stranded DNA molecules. This experimental platform is the first practical implementation of a micro/nanoscale MC system with nanoscale MC receivers, and can serve as a testbed for developing realistic MC methods and IoNT applications.

Generating Structural Models of Amorphous Tetrahedral Carbon: Basis set Dependencies

1997 ◽  
Vol 498 ◽  
Author(s):  
Peter A. Schultz ◽  
E. B. Stechel
Keyword(s):  
Density Functional ◽  
Structural Model ◽  
Structural Models ◽  
Theoretical Models ◽  
Basis Set ◽  
Minimal Basis ◽  
Functional Theory ◽  
Atomic Orbitals ◽  
Coordination Numbers ◽  
Simplifying Assumptions

ABSTRACTWe present the results of a systematic first-principles investigation of the requirements for developing realistic and reliable structural models for amorphous tetrahedral carbon (a-tC) and relate those structural models to the physical properties of this material. Within a linear combination of atomic orbitals formulation of density functional theory, we show that a large variational flexibility is required to accurately treat the highly defected and strained structures that can exist in a-tC. The average strain in the a-tC lattice is predicted to be roughly twice the strain of having all carbon atoms in three-member rings. A key figure of merit of a structural model, the proportion of three-fold bonded atoms, is shown to triple in going from a minimal basis description of a structure to a high quality basis. The basis-converged calculations agree well with experimental observables, such as the presence of four-member rings, lack of dangling bonds, and a significant gap. The simulations predict a much larger proportion of three-fold atoms than estimated in simple analyses of EELS and neutron scattering experiments. We show that the larger three-fold fraction is indeed consistent with the properties of a-tC, and imply that there are flaws in the simplifying assumptions that go into constructing experimental estimates of coordination numbers. These results highlight the perils of applying highly simplified theoretical models for a-tC before the correct physics has been identified and built into the models.

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