scholarly journals A Numerical Approach to Estimate Natural Frequency of Trees with Variable Properties

Forests ◽  
2020 ◽  
Vol 11 (9) ◽  
pp. 915
Author(s):  
Mojtaba Dargahi ◽  
Timothy Newson ◽  
John R. Moore
Keyword(s):  
Natural Frequency ◽  
Free Vibration Analysis ◽  
Numerical Approach ◽  
Benchmark Problems ◽  
The Finite Element Method ◽  
Closed Form Solutions ◽  
Circular Column ◽  
Longitudinal Stiffness ◽  
Problem Comparison ◽  
Case Validation

Free vibration analysis of a Euler-Bernoulli tapered column was conducted using the finite element method to identify the vibration modes of an equivalent tree structure under a specified set of conditions. A non-prismatic elastic circular column of height L was analysed, taking distributed self-weight into account. Various scenarios were considered: column taper, base fixity, radial and longitudinal stiffness (E) and density (ρ) and crown mass. The effect on the first natural frequency was assessed in each case. Validation against closed form solutions of benchmark problems was conducted satisfactorily. The results show that column taper, base fixity and E/ρ ratio are particularly important for this problem. Comparison of predictions with field observations of natural sway frequency for almost 700 coniferous and broadleaved trees from the published literature showed that the model worked well for coniferous trees, but less well for broadleaved trees with their more complicated crown architecture. Overall, the current study provides an in-depth numerical investigation of material properties, geometric properties and boundary conditions to create further understanding of vibration behaviour in trees.

Buckling behaviour of trees under self-weight loading

2019 ◽  
Vol 92 (4) ◽  
pp. 393-405 ◽  
Author(s):  
Mojtaba Dargahi ◽  
Timothy Newson ◽  
John Moore
Keyword(s):  
Management Strategies ◽  
Density Ratio ◽  
Benchmark Problems ◽  
Tree Stability ◽  
Closed Form Solutions ◽  
Circular Column ◽  
Instability Modes ◽  
Longitudinal Stiffness ◽  
Using Data ◽  
Case Validation

Abstract Understanding tree stability under self-weight and applied loads from wind and snow is important when developing management strategies to reduce the risk of damage from these abiotic agents. In this paper, linear buckling analysis was conducted using the finite element method to identify the instability modes of a tree structure under a specified set of loads. A non-prismatic elastic circular column of height H was analysed, taking self-weight into account. Various scenarios were considered: column taper, base rigidity, radial and longitudinal stiffness, ellipticity and crown weight. The effect on the critical buckling height was assessed in each case. Validation against closed form solutions of benchmark problems was conducted satisfactorily. The results indicate that column taper, base rigidity and the stiffness/density ratio are particularly important for this problem. Further comparison was made using data from a 15-year old Pinus radiata stand in New Zealand, which contained both buckled and non-buckled trees. While the model predicted factors of safety against buckling that were close to unity, it was unable to differentiate between buckled and non-buckled trees. Further investigation is needed to examine the reasons why this occurred. Despite this, the current study provides an in-depth numerical investigation, which has aided our understanding of the effects that material properties, geometric properties and boundary conditions have on buckling phenomenon in trees.

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

Frequency dependent resistance calculation of multiple conductors

2017 ◽  
Vol 36 (5) ◽  
pp. 1396-1410
Author(s):  
Tomislav Župan ◽  
Bojan Trkulja
Keyword(s):  
Design Methodology ◽  
Numerical Approach ◽  
Effective Resistance ◽  
Proximity Effects ◽  
The Finite Element Method ◽  
Frequency Range ◽  
Frequency Dependent ◽  
Content Type ◽  
Electromagnetic Devices ◽  
Practical Implications

Purpose The purpose of this paper is to present a method for calculating frequency-dependent resistance when multiple current-carrying conductors are present. Design/methodology/approach Analytical and numerical formulations are presented. Both skin- and proximity-effects are considered in the numerical approach, whereas only skin-effect can be taken into account in analytical equations. The calculation is done using a self-developed integral equation-based field solver. The results are benchmarked using professional software based on the finite element method (FEM). Findings Results from the numerical approach are in agreement with FEM-based software throughout the whole frequency range. Analytical formulations yield unsatisfactory results in higher frequency range. When multiple conductors are mutually relatively close, the proximity-effect has an impact on effective resistance and has to be taken into account. Research limitations/implications The methodology is presented using axially symmetrical conductors. However, the same procedure can be developed for straight conductors as well. Practical implications Presented fast and stable procedure can be used in most electromagnetic devices when frequency-dependent resistance needs to be precisely determined. Originality/value The value of the presented numerical methodology lies in its ability to take both skin- and proximity-effects into account. As conductors are densely packed in most electromagnetic devices, both effects influence the effective resistance. The method can be easily implemented using a self-developed solver and yields satisfactory results.

Residual strength of underground structures in service

2016 ◽  
Vol 53 (6) ◽  
pp. 988-999 ◽  
Author(s):  
Taous Kamel ◽  
Ali Limam ◽  
Claire Silvani
Keyword(s):  
Stress State ◽  
Residual Strength ◽  
Underground Structure ◽  
Numerical Approach ◽  
The Finite Element Method ◽  
Underground Structures ◽  
Weathering Processes ◽  
Working Face ◽  
Metro Tunnel ◽  
Loss Of Strength

Old tunnels suffer from deterioration and it is necessary to assess their residual strength to properly organize their repair and strengthen them. The stress state of underground structures evolves over time, firstly because of the advancement of the working face during construction, then due to gradual changes in soil properties and mechanical properties of materials composing the infrastructures, such as reduction of cohesion, loss of strength and (or) stiffness, etc. These changes are caused by combined actions such as creep and (or) weathering processes as well as the appearance of cracks that induce redistribution of stresses and therefore strains. This study investigates tunnels and galleries of the Paris underground. Macromodeling based on the finite element method allows consideration of different scenarios of tunnel-lining deterioration, specifically at the extrados of the galleries or tunnels. To understand changes in the stress state, and also damage occurrence and associated redistributions (stress and strain), it is necessary to model the delayed deformations. To model the infrastructure behavior, a time-dependency approach has been chosen. This approach can quantify the damage and predict the residual strength of this type of underground structure. An elastic–viscoplastic constitutive model with strain-softening is used to reproduce the appearance of the degraded zones and their behavior. The results obtained with the numerical approach reproduce Paris metro tunnel behavior, corroborate geoendoscopy results, clarify their interpretation, and improve the management of infrastructure repairs.

Uncertain Structural Free Vibration Analysis With Non-Probabilistic Spatially Varying Parameters

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Jinwen Feng ◽  
Qingya Li ◽  
Alba Sofi ◽  
Guoyin Li ◽  
Di Wu ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Spatial Dependency ◽  
The Finite Element Method ◽  
Engineering Structures ◽  
Spatially Varying ◽  
Computational Strategy ◽  
Bounded System

The uncertain free vibration analysis of engineering structures with the consideration of nonstochastic spatially dependent uncertain parameters is investigated. A recently proposed concept of interval field is implemented to model the intrinsic spatial dependency of the uncertain-but-bounded system parameters. By employing the appropriate discretization scheme, evaluations of natural frequencies for engineering structures involving interval fields can be executed within the framework of the finite element method. Furthermore, a robust, yet efficient, computational strategy is proposed such that the extreme bounds of natural frequencies of the structure involving interval fields can be rigorously captured by performing two independent eigen-analyses. Within the proposed computational analysis framework, the traditional interval arithmetic is not employed so that the undesirable effect of the interval overestimation can be completely eliminated. Consequently, both sharpness and physical feasibility of the results can be guaranteed to a certain extent for any discretized interval field. The plausibility of the adopted interval field model, as well as the feasibility of the proposed computational scheme, is clearly demonstrated by investigating both academic-sized and practically motivated engineering structures.

scholarly journals Study of the influence of the foundation and the reservoir on the dynamic response in a concrete gravity dam profile

2021 ◽  
Vol 14 (4) ◽  
Author(s):  
Iarly Vanderlei da Silveira ◽  
Lineu José Pedroso ◽  
Giuliano Santa Marotta
Keyword(s):  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Coupled System ◽  
Seismic Excitation ◽  
The Finite Element Method ◽  
Concrete Gravity Dam ◽  
Gravity Dams ◽  
Concrete Gravity Dams ◽  
Ansys Apdl ◽  
Maximum Stresses

abstract: This work aims to verify the influence of the foundation and the reservoir on the dynamic behavior of concrete gravity dams in terms of the natural frequencies, vibration modes for a free vibration analysis; and in terms of maximum displacements and maximum stresses at singular points of the structure for a seismic excitation. The dam-reservoir-foundation interaction was investigated through modal and transient analysis by the finite element method via ANSYS APDL software. For this study, we used a typical Brazilian dam profile and compatible data from a Brazilian earthquake for the seismic excitation. The results showed the influence of the reservoir and the foundation on the natural frequencies in the coupled system, as well as its repercussions on the response of the dam under seismic excitation.

scholarly journals Pounding Effects on the Earthquake Response of Adjacent Reinforced Concrete Structures Strengthened by Cable Elements

2014 ◽  
Vol 44 (2) ◽  
pp. 41-56 ◽  
Author(s):  
Angelos Liolios ◽  
Asterios Liolios ◽  
George Hatzigeorgiou ◽  
Stefan Radev
Keyword(s):  
Reinforced Concrete ◽  
Numerical Approach ◽  
Earthquake Response ◽  
Existing Buildings ◽  
The Finite Element Method ◽  
Time Step ◽  
Engineering Structures ◽  
Rc Structures ◽  
Incremental Approach ◽  
Rc Frames

Abstract A numerical approach for estimating the effects of pounding (seismic interaction) on the response of adjacent Civil Engineering structures is presented. Emphasis is given to reinforced concrete (RC) frames of existing buildings which are seismically strengthened by cable-elements. A double discretization, in space by the Finite Element Method and in time by a direct incremental approach is used. The unilateral behaviours of both, the cable-elements and the interfaces contact-constraints, are taken strictly into account and result to inequality constitutive conditions. So, in each time-step, a non-convex linear complementarity problem is solved. It is found that pounding and cable strengthening have significant effects on the earthquake response and, hence, on the seismic upgrading of existing adjacent RC structures.

Natural Frequencies of Rectangular Membrane With Boundary Perturbation

1995 ◽  
Vol 1 (2) ◽  
pp. 139-144 ◽  
Author(s):  
Jamal A. Masad
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Perturbation Approach ◽  
Boundary Perturbation ◽  
The Finite Element Method ◽  
Analytic Expression ◽  
Element Method

A perturbation approach, coupled with the adjoint concept, is used to derive an analytic expression for the natural frequencies of a nearly rectangular membrane. The method is applied for a rectangular membrane with a semicircle at one of the boundaries. The fundamental natural frequency results for this configuration are presented and compared with results from a finite-element method and results from an approximate Galerkin method. The agreement between the fundamental natural frequencies calculated with the perturbation approach and those calculated with the finite-element method improves as the radius of the semicircle decreases and as the semicircle location becomes more eccentric.

Failure Modeling of Hybrid Transition Structures

2016 ◽  
Vol 831 ◽  
pp. 44-53 ◽  
Author(s):  
Vitali Bitykov ◽  
Frank Jablonski
Keyword(s):  
Adhesive Bonding ◽  
Numerical Approach ◽  
The Finite Element Method ◽  
Metal Structures ◽  
Reinforced Plastics ◽  
Failure Modeling ◽  
Transition Structures ◽  
Failure Properties ◽  
Fiber Reinforced Plastics ◽  
Failure Tree

Metal structures and components made of fiber reinforced plastics are often tied using bolts, rivets or adhesive bonding methods. To avoid the disadvantages of these techniques, hybrid transition structures can be used. Two different concepts are investigated and a numerical approach to calculate the failure properties of such transition structures is proposed. This is done using cohesive zone models for a wire concept and probability functions in an extended failure tree analysis for a foil concept. Numerical results based on the finite element method are presented.

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