Coupled Bending, Torsion and Axial Vibrations of a Cable-Harnessed Beam With Periodic Wrapping Pattern

2018 ◽  
Author(s):  
Karthik Yerrapragada ◽  
Armaghan Salehian
Keyword(s):  
Coupled System ◽  
Mode Shapes ◽  
Element Analysis ◽  
Varying Coefficients ◽  
Equivalent Continuum Model ◽  
Spatially Varying ◽  
Analysis Models ◽  
Euler Bernoulli Beam ◽  
Equivalent Continuum ◽  
Fixed Boundary Condition

This paper presents an equivalent continuum model to study the bending-torsion-axial coupled vibrations of a cable-harnessed beam. The pre-tensioned cable is wrapped periodically around the beam in a diagonal manner. The host structure is assumed to behave as a Euler-Bernoulli beam. The system is modeled using energy methods. The diagonal wrapping pattern results in variable coefficient strain and kinetic energies. Homogenization technique is used to convert spatially varying coefficients into a constant coefficient one. Coupled partial differential equations representing the bending, torsion and the axial modes are derived using Hamilton’s principle. The free vibration characteristics such as the natural frequencies and the mode shapes of the coupled system are analyzed for a fixed-fixed boundary condition and compared to results from the uncoupled and finite element analysis models.

scholarly journals Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams

2018 ◽  
Vol 2018 ◽  
pp. 1-25 ◽  
Author(s):  
Blake Martin ◽  
Armaghan Salehian
Keyword(s):  
Reference Values ◽  
Natural Frequencies ◽  
Unit Length ◽  
Reference Value ◽  
Bending Stiffness ◽  
Mode Shapes ◽  
Beam Model ◽  
Continuous Bending ◽  
Spatially Varying ◽  
Euler Bernoulli Beam

The Lindstedt-Poincaré method is applied to a nonuniform Euler-Bernoulli beam model for the free transverse vibrations of the system. The nonuniformities in the system include spatially varying and piecewise continuous bending stiffness and mass per unit length. The expression for the natural frequencies is obtained up to second-order and the expression for the mode shapes is obtained up to first-order. The explicit dependence of the natural frequencies and mode shapes on reference values for the bending stiffness and the mass per unit length of the system is determined. Multiple methods for choosing these reference values are presented and are compared using numerical examples.

Dynamic Analysis and Experiment of Beamlike Space Deployable Lattice Truss

2011 ◽  
Vol 199-200 ◽  
pp. 1273-1280
Author(s):  
Hong Wei Guo ◽  
Rong Qiang Liu ◽  
Zong Quan Deng
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Continuum Model ◽  
Model Simulation ◽  
Element Model ◽  
Mode Shapes ◽  
Equivalent Continuum Model ◽  
Simulation Results ◽  
Equivalent Continuum ◽  
The Finite Element Model

The dynamic equivalent continuum model of beamlike space deployable lattice truss which is repetition of the basic truss bay is established based on the energy equivalence. The finite element model of the lattice truss is also developed. Free vibration frequencies and mode shapes are calculated and simulated based on equivalent continuum model and discrete finite element model. The analytical solutions calculated by equivalent continuum model match well with the finite element model simulation results. A prototype of deployable lattice truss consist of 20 truss bays is manufactured. The dynamic response of lattice truss with different truss bays are tested by dynamic vibration experiment, and natural frequencies of lattice truss with different length are obtained from acceleration response curves. The experiment results are compared with simulation results which verifies that the correctness of finite element model, which also validate the effectiveness of equivalent continuum model indirectly.

scholarly journals Boundary Control for a Kind of Coupled PDE-ODE System

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yuanting Wang ◽  
Fucheng Liao ◽  
Yonglong Liao ◽  
Zhengwei Shen
Keyword(s):  
Differential Equation ◽  
State Feedback ◽  
Coupled System ◽  
Backstepping Method ◽  
Closed Loop System ◽  
Stabilizing Controller ◽  
Varying Coefficients ◽  
Ode System ◽  
Exponentially Stable ◽  
Spatially Varying

A coupled system of an ordinary differential equation (ODE) and a heat partial differential equation (PDE) with spatially varying coefficients is discussed. By using the PDE backstepping method, the state-feedback stabilizing controller is explicitly constructed with the assumptionsλ(x)∈P[x]nandλ(x)∈C[0, l]∞, respectively. The closed-loop system is proved to be exponentially stable by this controller. A simulation example is presented to illustrate the effectiveness of the proposed method.

Output Feedback Stabilization of the Linearized Bilayer Saint-Venant Model

2016 ◽  
Author(s):  
Ababacar Diagne ◽  
Shuxia Tang ◽  
Mamadou Diagne ◽  
Miroslav Krstic
Keyword(s):  
Output Feedback ◽  
Control Method ◽  
Coupled System ◽  
Backstepping Control ◽  
Feedback Stabilization ◽  
Feedback Controller ◽  
Varying Coefficients ◽  
The One ◽  
Spatially Varying ◽  
Constant System

We consider the problem of output feedback exponentially stabilizing the 1-D bilayer Saint-Venant model, which is a coupled system of two rightward and two leftward convecting transport partial differential equations (PDEs). The PDE backstepping control method is employed. Our designed output feedback controller is based on the observer built in this paper and the state feedback controller designed in [1], where the backstepping control design idea can also be referred to [2] and can be treated as a generalization of the result for the system with constant system coefficients [2] to the one with spatially-varying coefficients. Numerical simulations of the bilayer Saint-Venant problem are also provided to verify the result.

Rotor-Dynamics of Different Shaft Configurations for a 6 kW Micro Gas Turbine for Concentrated Solar Power

2016 ◽  
Author(s):  
A. Arroyo ◽  
M. McLorn ◽  
M. Fabian ◽  
M. White ◽  
A. I. Sayma
Keyword(s):  
Gas Turbines ◽  
High Speed ◽  
Dynamic Models ◽  
Solar Power ◽  
Critical Issue ◽  
Rotor Dynamics ◽  
Mode Shapes ◽  
Concentrated Solar Power ◽  
Element Analysis ◽  
Rotor Dynamic

Rotor-dynamics of Micro Gas Turbines (MGTs) under 30 kW have been a critical issue for the successful development of reliable engines during the last decades. Especially, no consensus has been reached on a reliable MGT arrangement under 10 kW with rotational speeds above 100,000 rpm, making the understanding of the rotor-dynamics of these high speed systems an important research area. This paper presents a linear rotor-dynamic analysis and comparison of three mechanical arrangements of a 6 kW MGT intended for utilising Concentrated Solar Power (CSP) using a parabolic dish concentrator. This application differs from the usual fuel burning MGT in that it is required to operate at a wider operating speed range. The objective is to find an arrangement that allows reliable mechanical operation through better understanding of the rotor dynamics for a number of alternative shaft-bearings arrangements. Finite Element Analysis (FEA) was used to produce Campbell diagrams and to determine the critical speeds and mode shapes. Experimental hammer tests using a new approach based on optical sensing technology were used to validate the rotor-dynamic models. The FEA simulation results for the natural frequencies of a shaft arrangement were within 5% of the measurements, while the deviation for the shaft-bearings arrangement increased up to 16%.

Vibration of Beam with Elastically Restrained Ends and Rotational Spring-Lumped Rotary Inertia System at Mid-Span

2015 ◽  
Vol 15 (02) ◽  
pp. 1450040 ◽  
Author(s):  
Seyed Mojtaba Hozhabrossadati ◽  
Ahmad Aftabi Sani ◽  
Masood Mofid
Keyword(s):  
Technical Note ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Mass System ◽  
Rotational Spring ◽  
Beam System ◽  
Sample Frequency ◽  
Elastically Restrained ◽  
Euler Bernoulli Beam

This technical note addresses the free vibration problem of an elastically restrained Euler–Bernoulli beam with rotational spring-lumped rotary inertia system at its mid-span hinge. The governing differential equations and the boundary conditions of the beam are presented. Special attention is directed toward the conditions of the intermediate spring-mass system which plays a key role in the solution. Sample frequency parameters of the beam system are solved and tabulated. Mode shapes of the beam are also plotted for some spring stiffnesses.

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