scholarly journals Electrical analogs of curved beams and application to piezoelectric network damping

2021 ◽  
pp. 108128652110276
Author(s):  
Robin Darleux ◽  
Boris Lossouarn ◽  
Ivan Giorgio ◽  
Francesco dell’Isola ◽  
Jean-François Deü
Keyword(s):  
Finite Number ◽  
Analog Circuit ◽  
Mode Shapes ◽  
Curved Beam ◽  
Curved Beams ◽  
Lumped Element ◽  
Lumped Elements ◽  
Electric Analog ◽  
Frequency Coherence ◽  
Micro Structures

In this paper, the method of electric analog synthesis is applied to design a piezo-electro-mechanical arch able to show the capacity of multimodal damping. An electric-analog circuit is designed by using a finite number of lumped elements representing the equivalent of a curved beam. Spatial and frequency coherence conditions are proven to be verified for the modes to be damped: in fact, lumped-element circuit can damp only a finite number of vibration modes. Analogous boundary conditions are ensured, so that natural frequencies and mode shapes of both the curved beam and the analog circuit are equal. The instance considered here is the vibration mitigation of a piezo-electro-mechanical arch. Having a view towards prototypical applications, all simulations consider values of physically feasible passive circuital elements. It is believed that the present results may represent a step towards the design of multi-physics metamaterials based on micro-structures exploiting the principle of multimodal damping.

Earthquake response of linear-elastic arch-frames using exact curved beam formulations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Baran Bozyigit
Keyword(s):  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Opening Angle ◽  
Earthquake Response ◽  
Response Analysis ◽  
Curved Beam ◽  
Curved Beams ◽  
Base Shear ◽  
Content Type

PurposeThis study aims to obtain earthquake responses of linear-elastic multi-span arch-frames by using exact curved beam formulations. For this purpose, the dynamic stiffness method (DSM) which uses exact mode shapes is applied to a three-span arch-frame considering axial extensibility, shear deformation and rotational inertia for both columns and curved beams. Using exact free vibration properties obtained from the DSM approach, the arch-frame model is simplified into an equivalent single degree of freedom (SDOF) system to perform earthquake response analysis.Design/methodology/approachThe dynamic stiffness formulations of curved beams for free vibrations are validated by using the experimental data in the literature. The free vibrations of the arch-frame model are investigated for various span lengths, opening angle and column dimensions to observe their effects on the dynamic behaviour. The calculated natural frequencies via the DSM are presented in comparison with the results of the finite element method (FEM). The mode shapes are presented. The earthquake responses are calculated from the modal equation by using Runge-Kutta algorithm.FindingsThe displacement, base shear, acceleration and internal force time-histories that are obtained from the proposed approach are compared to the results of the finite element approach where a very good agreement is observed. For various span length, opening angle and column dimension values, the displacement and base shear time-histories of the arch-frame are presented. The results show that the proposed approach can be used as an effective tool to calculate earthquake responses of frame structures having curved beam elements.Originality/valueThe earthquake response of arch-frames consisting of curved beams and straight columns using exact formulations is obtained for the first time according to the best of the author’s knowledge. The DSM, which uses exact mode shapes and provides accurate free vibration analysis results considering each structural members as one element, is applied. The complicated structural system is simplified into an equivalent SDOF system using exact mode shapes obtained from the DSM and earthquake responses are calculated by solving the modal equation. The proposed approach is an important alternative to classical FEM for earthquake response analysis of frame structures having curved members.

scholarly journals Stochastic Modal Models of Slender Uncertain Curved Beams Preloaded Through Clamping

2012 ◽  
Author(s):  
Javier Avalos ◽  
Lanae A. Richter ◽  
X. Q. Wang ◽  
Raghavendra Murthy ◽  
Marc P. Mignolet
Keyword(s):  
Stochastic Model ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Simulated Data ◽  
Mode Shapes ◽  
Curved Beams ◽  
Shape Information ◽  
Final Shape ◽  
Modal Model ◽  
Clamped Beams

This paper addresses the stochastic modeling of the stiffness matrix of slender uncertain curved beams that are forced fit into a clamped-clamped fixture designed for straight beams. Because of the misfit with the clamps, the final shape of the clamped-clamped beams is not straight and they are subjected to an axial preload. Both of these features are uncertain given the uncertainty on the initial, undeformed shape of the beams and affect significantly the stiffness matrix associated with small motions around the clamped-clamped configuration. A modal model using linear modes of the straight clamped-clamped beam with a randomized stiffness matrix is employed to characterize the linear dynamic behavior of the uncertain beams. This stiffness matrix is modeled using a mixed nonparametric-parametric stochastic model in which the nonparametric (maximum entropy) component is used to model the uncertainty in final shape while the preload is explicitly, parametrically included in the stiffness matrix representation. Finally, a maximum likelihood framework is proposed for the identification of the parameters associated with the uncertainty level and the mean model, or part thereof, using either natural frequencies only or natural frequencies and mode shape information of the beams around their final clamped-clamped state. To validate these concepts, a simulated, computational experiment was conducted within Nastran to produce a population of natural frequencies and mode shapes of uncertain slender curved beams after clamping. The application of the above concepts to this simulated data led to a very good to excellent matching of the probability density functions of the natural frequencies and the modal components, even though this information was not used in the identification process. These results strongly suggest the applicability of the proposed stochastic model.

Exact Solutions of Dynamic Characteristics for Curved Beams with Pinned-Pinned Ends

2013 ◽  
Vol 405-408 ◽  
pp. 702-705
Author(s):  
Xiao Fei Li ◽  
Wei Ming Yan ◽  
Hao Xiang He
Keyword(s):  
Exact Solutions ◽  
Dynamic Characteristics ◽  
Analytical Solutions ◽  
Stiffness Matrix ◽  
Virtual Work ◽  
Analytic Method ◽  
Curved Beam ◽  
Curved Beams ◽  
Curved Bridges ◽  
Scientific Base

Based on the theory of virtual work and principle of thermal elasticity, exact solutions for in-plane displacements of curved beams with pinned-pinned ends are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. Basing on the stiffness matrix of statically indeterminate curved beams at three freedom direction, the dynamic characteristics are derived explicitly. The analytic method of dynamic characteristics for curved beam performed in this paper would provide a scientific base for further study and design of the curved bridges.

Rayleigh–Bloch surface waves along periodic gratings and their connection with trapped modes in waveguides

1999 ◽  
Vol 386 ◽  
pp. 233-258 ◽  
Author(s):  
R. PORTER ◽  
D. V. EVANS
Keyword(s):  
Finite Number ◽  
Surface Waves ◽  
Cross Section ◽  
Electromagnetic Waves ◽  
Mode Shapes ◽  
Special Choice ◽  
Trapped Mode ◽  
Uniform Cross Section ◽  
New Type ◽  
Incident Waves

Rayleigh–Bloch surface waves are acoustic or electromagnetic waves which propagate parallel to a two-dimensional diffraction grating and which are exponentially damped with distance from the grating. In the water-wave context they describe a localized wave having dominant wavenumber β travelling along an infinite periodic array of identical bottom-mounted cylinders having uniform cross-section throughout the water depth. A numerical method is described which enables the frequencies of the Rayleigh–Bloch waves to be determined as a function of β for an arbitrary cylinder cross-section. For particular symmetric cylinders, it is shown how a special choice of β produces results for the trapped mode frequencies and mode shapes in the vicinity of any (finite) number of cylinders spanning a rectangular waveguide or channel. It is also shown how one particular choice of β gives rise to a new type of trapped mode near an unsymmetric cylinder contained within a parallel-sided waveguide with locally-distorted walls. The implications for large forces due to incident waves on a large but finite number of such cylinders in the ocean is discussed.

Eigenstructure Calculation for Mixed Vibratory Systems Composed of a Continuous Beam and Concentrated Actuators

2001 ◽  
Author(s):  
Michael J. Panza
Keyword(s):  
Active Vibration Control ◽  
Open Loop ◽  
Mode Shapes ◽  
Mixed System ◽  
Continuous Beam ◽  
Actuator Dynamics ◽  
Asymmetric System ◽  
Lumped Element ◽  
Active Vibration ◽  
Parameter Values

Abstract A calculation of the eigenstructure for mixed vibratory systems composed of a continuous beam and concentrated actuators is presented. The combined distributed and lumped element systems include actuators for active vibration control. The focus of this paper is on open loop models where with zero voltage input to the actuators. The continuous beam is isolated and discretized via modal analysis and combined with the actuator dynamics to form an asymmetric system. The resulting system is cast into a generalized nondimensional form suitable for studying system behavior for a broad range of system parameters. The solution is expressed as a series using the isolated beam mode eigenfunctions as a basis. The coefficients in the series are obtained from the complex eigensolution of the asymmetric system. Two examples are used to show a comparison of the complex mixed system and real isolated beam natural frequencies and mode shapes. The effect of beam and actuator parameter values are investigated via a key dimensionless parameter.

Isogeometric Free Vibration Analysis of Curved Euler–Bernoulli Beams With Particular Emphasis on Accuracy Study

2020 ◽  
pp. 2150011
Author(s):  
Zhuangjing Sun ◽  
Dongdong Wang ◽  
Xiwei Li
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Convergence Rates ◽  
Harmonic Wave ◽  
Free Vibration Analysis ◽  
Curved Beam ◽  
Curved Beams ◽  
Stiffness Matrices ◽  
Accuracy Measure ◽  
Accuracy Study

An isogeometric free vibration analysis is presented for curved Euler–Bernoulli beams, where the theoretical study of frequency accuracy is particularly emphasized. Firstly, the isogeometric formulation for general curved Euler–Bernoulli beams is elaborated, which fully takes the advantages of geometry exactness and basis function smoothness provided by isogeometric analysis. Subsequently, in order to enable an analytical frequency accuracy study, the general curved beam formulation is particularized to the circular arch problem with constant radius. Under this circumstance, explicit mass and stiffness matrices are derived for quadratic and cubic isogeometric formulations. Accordingly, the coupled stencil equations associated with the axial and deflectional displacements of circular arches are established. By further invoking the harmonic wave assumption, a frequency accuracy measure is rationally attained for isogeometric free analysis of curved Euler–Bernoulli beams, which theoretically reveals that the isogeometric curved beam formulation with [Formula: see text]th degree basis functions is [Formula: see text]th order accurate regarding the frequency computation. Numerical results well confirm the proposed theoretical convergence rates for both circular arches and general curved beams.

A Finite Element Modeling Framework for Planar Curved Beam Dynamics Considering Nonlinearities and Contacts

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Tianheng Feng ◽  
Soovadeep Bakshi ◽  
Qifan Gu ◽  
Dongmei Chen
Keyword(s):  
Finite Element ◽  
Beam Dynamics ◽  
Curved Beam ◽  
Shape Functions ◽  
Curved Beams ◽  
Modeling Framework ◽  
External Wall ◽  
Beam Elements ◽  
High Compression ◽  
Assumed Strain

Motivated by modeling directional drilling dynamics where planar curved beams undergo small displacements, withstand high compression forces, and are in contact with an external wall, this paper presents an finite element method (FEM) modeling framework to describe planar curved beam dynamics under loading. The shape functions of the planar curved beam are obtained using the assumed strain field method. Based on the shape functions, the stiffness and mass matrices of a planar curved beam element are derived using the Euler–Lagrange equations, and the nonlinearities of the beam strain are modeled through a geometric stiffness matrix. The contact effects between curved beams and the external wall are also modeled, and corresponding numerical methods are discussed. Simulations are carried out using the developed element to analyze the dynamics and statics of planar curved structures under small displacements. The numerical simulation converges to the analytical solution as the number of elements increases. Modeling using curved beam elements achieves higher accuracy in both static and dynamic analyses compared to the approximation made by using straight beam elements. To show the utility of the developed FEM framework, the post-buckling condition of a directional drill string is analyzed. The drill pipe undergoes spiral buckling under high compression forces, which agrees with experiments and field observations.

Curved Beams

1964 ◽  
Vol 68 (638) ◽  
pp. 134-137
Author(s):  
C. G. B. Mitchell
Keyword(s):  
Curved Beam ◽  
Curved Beams ◽  
Torsional Strength ◽  
Strength And Stiffness ◽  
General Method

A type of structure for which no general method of analysis appears to be available is that of a curved beam of low torsional strength and stiffness supported by a torque box. This note outlines ways of analysing two simple cases.

Natural Vibrations of a Clamped-Clamped Arch With an Open Transverse Crack

1997 ◽  
Vol 119 (2) ◽  
pp. 145-151 ◽  
Author(s):  
M. Krawczuk ◽  
W. Ostachowicz
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Edge Crack ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Curved Beam ◽  
Natural Vibrations ◽  
Crack Location ◽  
Cracked Arch

The paper presents a finite element model of the arch with a transverse, one-edge crack. A part of the cracked arch is modelled by a curved beam finite element with the crack. Parts of the arch without the crack are modelled by noncracked curved beam finite elements. The crack occurring in the arch is nonpropagating and open. It is assumed that the crack changes only the stiffness of the arch, whereas the mass is unchanged. The method of the formation of the stiffness matrix of a curved beam finite element with the crack is presented. The effects of the crack location and its length on the changes of the in-plane natural frequencies and mode shapes of the clamped-clamped arch are studied.

In-Plane Free Vibration of Curved Beams Using Finite Element Method

2007 ◽  
Author(s):  
F. Yang ◽  
R. Sedaghati ◽  
E. Esmailzadeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Central Line ◽  
Circular Ring ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Element Method

Curved beam-type structures have many applications in engineering area. Due to the initial curvature of the central line, it is complicated to develop and solve the equations of motion by taking into account the extensibility of the curve axis and the influences of the shear deformation and the rotary inertia. In this study the finite element method is utilized to study the curved beam with arbitrary geometry. The curved beam is modeled using the Timoshenko beam theory and the circular ring model. The governing equation of motion is derived using the Extended-Hamilton principle and numerically solved by the finite element method. A parametric sensitive study for the natural frequencies has been performed and compared with those reported in the literature in order to demonstrate the accuracy of the analysis.

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