scholarly journals A Linearised Hybrid FE-SEA Method for Nonlinear Dynamic Systems Excited by Random and Harmonic Loadings

Vibration ◽  
2020 ◽  
Vol 3 (3) ◽  
pp. 304-319
Author(s):  
Fiorenzo A. Fazzolari ◽  
Puxue Tan
Keyword(s):  
Dynamic Systems ◽  
Ad Hoc ◽  
Plate Theory ◽  
Ritz Method ◽  
Random Loading ◽  
Hybrid Finite Element ◽  
Thin Plate Theory ◽  
Different Types ◽  
New Formulation ◽  
Nonlinear Joints

The present paper proposes a linearised hybrid finite element-statistical energy analysis (FE-SEA) formulation for built-up systems with nonlinear joints and excited by random, as well as harmonic, loadings. The new formulation was validated via an ad-hoc developed stochastic benchmark model. The latter was derived through the combination of the Lagrange-Rayleigh-Ritz method (LRRM) and the Monte Carlo simulation (MCS). Within the build-up plate systems, each plate component was modelled by using the classical Kirchhoff’s thin-plate theory. The linearisation processes were carried out according to the loading-type. In the case of random loading, the statistical linearisation (SL) was employed, while, in the case of harmonic loading, the method of harmonic balance (MHB) was used. To demonstrate the effectiveness of the proposed hybrid FE-SEA formulation, three different case studies, made-up of built-up systems with localized cubic nonlinearities, were considered. Both translational and torsional springs, as joint components, were employed. Four different types of loadings were taken into account: harmonic/random point and distributed loadings. The response of the dynamic systems was investigated in terms of ensemble average of the time-averaged energy.

scholarly journals Forced Response of Polar Orthotropic Tapered Circular Plates Resting on Elastic Foundation

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
A. H. Ansari
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Ritz Method ◽  
Forced Response ◽  
Bending Moments ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Different Types ◽  
Foundation Parameter ◽  
Polar Orthotropic

Forced axisymmetric response of polar orthotropic circular plates of linearly varying thickness resting on Winkler type of elastic foundation has been studied on the basis of classical plate theory. An approximate solution of problem has been obtained by Rayleigh Ritz method, which employs functions based upon the static deflection of polar orthotropic circular plates. The effect of transverse loadings has been studied for orthotropic circular plate resting on elastic foundation. The transverse deflections and bending moments are presented for various values of taper parameter, rigidity ratio, foundation parameter, and flexibility parameter under different types of loadings. A comparison of results with those available in literature shows an excellent agreement.

Lessons Not Learned: Why is There Still a Crisis-Level Shortage of Accounting Ph.D.s?

2014 ◽  
Vol 28 (2) ◽  
pp. 313-330 ◽  
Author(s):  
R. David Plumlee ◽  
Philip M. J. Reckers
Keyword(s):  
Student Perceptions ◽  
Structural Changes ◽  
Ad Hoc ◽  
Doctoral Programs ◽  
Cumulative Impact ◽  
Program Administrators ◽  
Accounting Faculty ◽  
Present Information ◽  
Different Types

SYNOPSIS: In 2005, an ad hoc committee appointed by the American Accounting Association (AAA) documented a crisis-level shortage of accounting Ph.D.s and recommended significant structural changes to doctoral programs (Kachelmeier, Madeo, Plumlee, Pratt, and Krull 2005). However, subsequent studies show that the shortage continues and the cumulative costs grow (e.g., Fogarty and Holder 2012; Brink, Glasscock, and Wier 2012). The Association to Advance Collegiate Schools of Business (AACSB) recently called for renewed attention to the problem (AACSB 2013b). We contribute to the literature by providing updated information regarding responses by doctoral programs and, from the eyes of potential candidates, of continuing impediments to solving the doctoral shortage. In this paper, we present information gathered through surveys of program administrators and master's and Accounting Doctoral Scholars Program (ADS) students. We explore (1) the cumulative impact of the Ph.D. shortage as of 2013, including its impact on accounting faculty composition, across different types of institutions, (2) negative student perceptions of Ph.D. programs and academic accounting careers, which discourage applicants from pursuing Ph.D. programs, and (3) impediments facing institutions in expanding doctoral programs.

scholarly journals Semi-analytical static analysis of nonlocal strain gradient laminated composite nanoplates in hygrothermal environment

2021 ◽  
Vol 43 (5) ◽  
Author(s):  
Giovanni Tocci Monaco ◽  
Nicholas Fantuzzi ◽  
Francesco Fabbrocino ◽  
Raimondo Luciano
Keyword(s):  
Thin Plate ◽  
Strain Gradient ◽  
Plate Theory ◽  
Laminated Composite ◽  
Equilibrium Equations ◽  
Thin Plate Theory ◽  
Bending Behavior ◽  
Hygrothermal Environment ◽  
Load Types ◽  
Novel Applications

AbstractIn this work, the bending behavior of nanoplates subjected to both sinusoidal and uniform loads in hygrothermal environment is investigated. The present plate theory is based on the classical laminated thin plate theory with strain gradient effect to take into account the nonlocality present in the nanostructures. The equilibrium equations have been carried out by using the principle of virtual works and a system of partial differential equations of the sixth order has been carried out, in contrast to the classical thin plate theory system of the fourth order. The solution has been obtained using a trigonometric expansion (e.g., Navier method) which is applicable to simply supported boundary conditions and limited lamination schemes. The solution is exact for sinusoidal loads; nevertheless, convergence has to be proved for other load types such as the uniform one. Both the effect of the hygrothermal loads and lamination schemes (cross-ply and angle-ply nanoplates) on the bending behavior of thin nanoplates are studied. Results are reported in dimensionless form and validity of the present methodology has been proven, when possible, by comparing the results to the ones from the literature (available only for cross-ply laminates). Novel applications are shown both for cross- and angle-ply laminated which can be considered for further developments in the same topic.

Sinusoidal Torsional Buckling of Bars of Angle Section Under Bending Loads, as a Problem in Plate Theory

1951 ◽  
Vol 18 (3) ◽  
pp. 285-292
Author(s):  
H. J. Plass
Keyword(s):  
Infinite Series ◽  
Plate Theory ◽  
Ritz Method ◽  
Compressive Load ◽  
Series Solutions ◽  
Torsional Buckling ◽  
Bending Load ◽  
Angle Section ◽  
Bending Loads

Abstract Timoshenko has applied plate theory to each leg of an angle-section bar to determine the critical compressive load needed to cause sinusoidal torsional buckling. In this paper his idea is used to calculate the critical bending load needed to cause sinusoidal torsional buckling of an angle bar. The bending is assumed to be applied so that the extreme fibers of the angle are in compression, the vertex in tension. Approximate results are first obtained by means of the Rayleigh-Ritz method. The approximate deflection functions from which the energy terms are computed are based upon certain infinite-series solutions. After having obtained approximate results, exact values are obtained, using the approximate values as a guide to limit the amount of calculation. The results of this calculation are shown in Fig. 5, where they are compared with those predicted by bar theory. Differences between the two theories become more noticeable as the bar becomes short compared to its flange width. It is found that the critical bending load becomes larger very rapidly as the ratio of length to width of the flanges decreases. Bar theory predicts no such increase. The reason for this difference is explained.

Study on Gradual Deformation and Prediction Model of the Mined Overburden

2012 ◽  
Vol 524-527 ◽  
pp. 699-704
Author(s):  
Xiao Gang Xia ◽  
Yun Feng Yang
Keyword(s):  
Boundary Condition ◽  
Plate Theory ◽  
Surface Expression ◽  
Rock Deformation ◽  
Double Trigonometric Series ◽  
Mechanics Model ◽  
Thin Plate Theory ◽  
Gradual Deformation ◽  
Exchange Condition ◽  
Gradual Transformation

Based on the overburden three caving feature, the deformation of mining rock process was devided and the criterion of gradual transformation of each stages deformation were given. Then , combined the thin-plate theory, the differential models were derived for rock deformation in level and similar to level bured condition. The boundary condition of each models and exchange condition between different models were put forward and the gradual mechanics model was set up.The subsidence model before roof collapse was solved by Navier double trigonometric series and the deflection surface expression of rock deformation was put forword. At last, the reliability and practicality of the models was verified by engineering examples.

scholarly journals LISMA_HDS language for modeling heterogeneous dynamic systems

2021 ◽  
pp. 103-122
Author(s):  
Evgeny Popov ◽  
◽  
Yury Shornikov ◽  
Keyword(s):  
Dynamic Systems ◽  
Initial Value Problems ◽  
Method Of Lines ◽  
System Of Equations ◽  
Modeling Languages ◽  
Cauchy Problems ◽  
Systems Of Equations ◽  
Initial Value ◽  
Algebraic Systems ◽  
Different Types

Heterogeneous dynamic systems (HDS) simultaneously describe processes of different physical nature. Systems of this kind are typical for numerous applications. HDSs are characterized by the following features. They are often multimode or hybrid systems. In general, their modes are defined as initial value problems (Cauchy problems) for implicit differential-algebraic systems of equations. Due to the presence of heterogeneous dynamic components or processes evolving in both time and space, the dimension of the complete system of equations may be pretty high. In some cases, the system of equations has an internal structure, for instance, the differential-algebraic system of equations approximating a partial differential equation by the method of lines. An original huge system of equations can then be algorithmically rewritten in a compact form. Moreover, heterogeneous hybrid dynamical systems can generate events of qualitatively different types. Therefore one has to use different numerical event detection algorithms. Nowadays, HDSs are modeled and simulated in computer environments. The modeling languages widely used by engineers do not allow them to fully specify all the properties of the systems of this class. For instance, they do not include event typing constructs. That is why a declarative general-purpose modeling language named LISMA_HDS has been developed for the computer-aided modeling and ISMA simulation environment. The language takes into account all of the characteristic features of HDSs. It includes constructs for plain or algorithmic declaration of model constants, initial value problems for explicit differential-algebraic systems of equations, and initial guesses for variables. It also allows researchers to define explicit time events, modes and transitions between them upon the occurrence of events of different types, to use macros and implement event control. LISMA_HDS is defined by a generative grammar in an extended Backus-Naur form and semantic constraints. It is proved that the grammar belongs to the LL(2) subclass of context-free grammars.

Normal Loading on a Wedge-Shaped Plate

1955 ◽  
Vol 6 (3) ◽  
pp. 196-204 ◽  
Author(s):  
D. E. R. Godfrey
Keyword(s):  
Thin Plate ◽  
Mellin Transform ◽  
Plate Theory ◽  
Normal Loading ◽  
Thin Plate Theory

SummaryThe equations of thin plate theory are expressed in polar co-ordinates and transformed using the Mellin transform. Problems involving discontinuous and isolated normal loadings may then be solved in the case of the built-in or freely supported wedge-shaped boundary.

scholarly journals Parametric structural modelling of fish bone active camber morphing aerofoils

2018 ◽  
Vol 29 (9) ◽  
pp. 2008-2026 ◽  
Author(s):  
Andres E Rivero ◽  
Paul M Weaver ◽  
Jonathan E Cooper ◽  
Benjamin KS Woods
Keyword(s):  
Analytical Model ◽  
Composite Laminates ◽  
Plate Theory ◽  
Ritz Method ◽  
Linear Equations ◽  
Variable Stiffness ◽  
Automated Analysis ◽  
Fish Bone ◽  
Two Dimensional ◽  
Wide Range

Camber morphing aerofoils have the potential to significantly improve the efficiency of fixed and rotary wing aircraft by providing significant lift control authority to a wing, at a lower drag penalty than traditional plain flaps. A rapid, mesh-independent and two-dimensional analytical model of the fish bone active camber concept is presented. Existing structural models of this concept are one-dimensional and isotropic and therefore unable to capture either material anisotropy or spanwise variations in loading/deformation. The proposed model addresses these shortcomings by being able to analyse composite laminates and solve for static two-dimensional displacement fields. Kirchhoff–Love plate theory, along with the Rayleigh–Ritz method, are used to capture the complex and variable stiffness nature of the fish bone active camber concept in a single system of linear equations. Results show errors between 0.5% and 8% for static deflections under representative uniform pressure loadings and applied actuation moments (except when transverse shear exists), compared to finite element method. The robustness, mesh-independence and analytical nature of this model, combined with a modular, parameter-driven geometry definition, facilitate a fast and automated analysis of a wide range of fish bone active camber concept configurations. This analytical model is therefore a powerful tool for use in trade studies, fluid–structure interaction and design optimisation.

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