scholarly journals Fuzzy Stochastic Vibrations of Double-Beam Complex System as Model Sandwich Beam with Uncertain Parameters

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Krystyna Mazur-Śniady ◽  
Katarzyna Misiurek ◽  
Olga Szyłko-Bigus ◽  
Paweł Śniady
Keyword(s):  
Sandwich Beam ◽  
Uncertain Parameters ◽  
Fuzzy Random Variables ◽  
Bernoulli Beam ◽  
Beam System ◽  
Double Beam ◽  
Stochastic Load ◽  
Euler Bernoulli Beam ◽  
Two Parameter ◽  
Fuzzy Random

The dynamic behavior of a double Euler-Bernoulli beam system with uncertain parameters (fuzzy random variables) under a fuzzy stochastic excitation and axial compression is being considered. The beams are identical and parallel, one is above the other, and they are continuously coupled by a linear two-parameter (Pasternak subsoil) elastic element. This double Euler-Bernoulli beam system can be also treated as a theoretical model of a sandwich beam. The load process is fuzzy random both in space and time. The top beam carries a fuzzy stochastic load. The solution of the problem was found thanks to the fuzzy random dynamic influence function. The aim of the paper is to find the solution for the membership function of the probabilistic characteristics of the response of the structure.

LMI-based hybrid temporal-spatial differential control design for a class of Euler-Bernoulli beam system

2021 ◽  
pp. 095440622110036
Author(s):  
Jiaqi Zhong ◽  
Xiaolei Chen ◽  
Yupeng Yuan ◽  
Jiajia Tan
Keyword(s):  
Vibration Suppression ◽  
Direct Method ◽  
Recursive Algorithm ◽  
Linear Matrix ◽  
Bernoulli Beam ◽  
Hybrid Controller ◽  
Beam System ◽  
Active Vibration ◽  
Differential Control ◽  
Euler Bernoulli Beam

This paper addresses the problem of active vibration suppression for a class of Euler-Bernoulli beam system. The objective of this paper is to design a hybrid temporal-spatial differential controller, which is involved with the in-domain and boundary actuators, such that the closed-loop system is stable. The Lyapunov’s direct method is employed to derive the sufficient condition, which not only can guarantee the stabilization of system, but also can improve the spatial cooperation of actuators. In the framework of the linear matrix inequalities (LMIs) technology, the gain matrices of hybrid controller can obtained by developing a recursive algorithm. Finally, the effectiveness of the proposed methodology is demonstrated by applying a numerical simulation.

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.

scholarly journals Analysis of static forces generated in-track on a railway sleeper resting on an elastic foundation due to structural imperfections using the PONTOS system

2019 ◽  
Vol 262 ◽  
pp. 11001
Author(s):  
Włodzimierz Andrzej Bednarek
Keyword(s):  
Theoretical Calculations ◽  
Railway Track ◽  
Bernoulli Beam ◽  
Main Concept ◽  
Field Investigations ◽  
Railway Sleeper ◽  
Foundation Parameters ◽  
Euler Bernoulli Beam ◽  
Structural Imperfections ◽  
Two Parameter

In the paper a considered railway sleeper was analysed as an Euler-Bernoulli beam and a Timoshenko beam of finite length resting on a oneand two-parameter foundation. The foundation parameters were determined based on a modified and analogue Vlasov soil model and field investigations. The main concept for the executed investigations was to induce an intentional imperfection in an actual railway track, propose a way of appropriate measurement (e.g. the PONTOS system by GOM mbh), and utilize author’s field investigations results to calibrate necessary parameters for theoretical calculations. An experimental formula describing the value of the force transferred from the rail to the railway sleeper on the grounds of the survey site caused by a locomotive was given. Furthermore, the deflection of the chosen railway sleeper due to the generated imperfection was analysed. Finally the objective of the present analysis was to resolve the calculations into the beam element such that the results can be utilised in computational railway practice. In the presented paper also the computational examples, diagrams and tables reflecting influence of analyzed parameters on obtained a CWR track’s displacements are enclosed.

Variational Approach to Beams Resting on Two-Parameter Tensionless Elastic Foundations

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
A. Nobili
Keyword(s):  
Variational Formulation ◽  
Variational Approach ◽  
Multiple Solutions ◽  
Numerical Solutions ◽  
Bernoulli Beam ◽  
Scaling Invariance ◽  
Two Parameters ◽  
Euler Bernoulli Beam ◽  
Two Parameter ◽  
Nonlinear Nature

This paper presents a Hamiltonian variational formulation to determine the energy minimizing boundary conditions (BCs) of the tensionless contact problem for an Euler–Bernoulli beam resting on either a Pasternak or a Reissner two-parameters foundation. Mathematically, this originates a free-boundary variational problem. It is shown that the BCs setting the contact loci, which are the boundary points of the contact interval, are always given by second order homogeneous forms in the displacement and its derivatives. This stands for the nonlinear nature of the problem and calls for multiple solutions in the displacement, together with the classical result of multiple solutions in the contact loci position. In particular, it is shown that the Pasternak soil possesses an extra solution other than Kerr’s, although it is proved that such solution must be ruled out owing to interpenetration. The homogeneous character of the BCs explains the well-known load scaling invariance of the contact loci position. It is further shown that the Reissner foundation may be given two mechanical interpretations, which lead to different BCs. Comparison with the established literature is drawn and numerical solutions shown which confirm the energy minimizing nature of the assessed BCs.

Analytical and experimental investigation of cable–beam system dynamics

2019 ◽  
Vol 25 (19-20) ◽  
pp. 2678-2691 ◽  
Author(s):  
Mohammad Hadi Jalali ◽  
Geoff Rideout
Keyword(s):  
Transmission Lines ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Bending Stiffness ◽  
Bernoulli Beam ◽  
Cable System ◽  
Beam System ◽  
Pole Structure ◽  
Euler Bernoulli Beam ◽  
Reduced Scale

Interactions between cables and structures affect the design and nondestructive testing of electricity transmission lines, guyed towers, and bridges. An analytical model for an electricity pole beam–cable system is presented, which can be extended to other applications. A cantilever beam is connected to two stranded cables. The cables are modeled as tensioned Euler–Bernoulli beams, considering the sag due to self-weight. The pole is also modeled as a cantilever Euler–Bernoulli beam and the equations of motion are derived using Hamilton’s principle. The model was validated with a reduced-scale system in the laboratory and a setup was designed to accurately measure the bending stiffness of the stranded cable under tension. It is concluded that the bending stiffness and sag of the cable have a significant effect on the dynamics of beam–cable structures. By adding the cable to the pole structure, some hybrid modes emerge in the eigenvalue solution of the system. Modes with antisymmetric cable motion are sag-independent and the modes with symmetric cable motion are dependent on the cable sag. The effect of sag on the natural frequencies is more significant when the bending stiffness of the cables is higher.

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