Displacement Solution for a Static Vertical Rigid Movement of an Interior Circular Disc in a Transversely Isotropic Tri-Material Full-Space

This article is concerned with the determination of the static interaction of a vertically loaded rigid circular disc embedded at the interface of a horizontal layer sandwiched in between two different transversely isotropic half-spaces called as tri-material full-space. The axes of symmetry of different regions are assumed to be normal to the horizontal interfaces and parallel to the movement direction. With the use of a potential function method, and by implementing Hankel integral transforms in the radial direction, the government partial differential equation for the solely scalar potential function is transformed to an ordinary 4th order differential equation, and the mixed boundary conditions are transformed into a pair of integral equations called dual integral equations, which can be reduced to a Fredholm integral equation of the second kind, which is solved analytically. Then, the displacements and stresses are given in the form of improper line integrals, which is due to inverse Hankel integral transforms. It is shown that the present solutions are in exact agreement with the existing solutions for a homogeneous full-space with transversely isotropic material. To confirm the accuracy of the numerical evaluation of the integrals involved, the numerical results are compared with the solutions exists for the homogeneous full-space. Then, some different cases with different degrees of material anisotropy are compared to portray the effect of degree of anisotropy

Development of an Acoustic Metamaterials for Aero Acoustic Noise Control

This paper aims at proposing a novel type tunable acoustic metamaterials with complete band gap composed of piezoelectric rods (Lithium Niobate) with square array as inclusion embedded polyimide aerogel background. The plane wave expansion method and the principles of Bloch-Floquet method used to get a band frequency and study the pass band for noise control. The results of this paper provide the required guidance for designing tunable wave filters or wave guide which might be useful in high-precision mechanical systems operated in certain frequency ranges, and switches made of piezoelectric; they also propose a novel type of tunable mechanical meta composite, where is independent of wave direction and has an equal sensitivity in all directions in which reacts omnidirectional and improves the aero acoustic noise control (e.g. bladeless fans) as well as general performance of vibrating structures (e.g. wind turbine)

A pattern recognition methodology for analyzing residential customers load data and targeting demand response applications

© 2019 Elsevier B.V. The availability of smart meter data allows defining innovative applications such as demand response (DR) programs for households. However, the dimensionality of data imposes challenges for the data mining of load patterns. In addition, the inherent variability of residential consumption patterns is a major problem for deciding on the characteristic consumption patterns and implementing proper DR settlements. In this regard, this paper utilizes a data size reduction and clustering methodology to analyze residential consumption behavior. Firstly, the distinctive time periods of household activity during the day are identified. Then, using these time periods, a modified symbolic aggregate approximation (SAX) technique is utilized to transform the load patterns into symbolic representations. In the next step, by applying a clustering method, the major consumption patterns are extracted and analyzed. Finally, the customers are ranked based on their stability over time. The proposed approach is applied on a large dataset of residential customers’ smart meter data and can achieve three main goals: 1) it reduces the dimensionality of data by utilizing the data size reduction, 2) it alleviates the problems associated with the clustering of residential customers, 3) its results are in accordance with the needs of systems operators or demand response aggregators and can be used for demand response targeting. The paper also provides a thorough analysis of different aspects of residential electricity consumption and various approaches to the clustering of households which can inform industry and research activity to optimize smart meter operational use

Investigation of Piezoelectric Coupling and Anisotropy Effect on Acoustic Wave Propagation at LithiumNiobate Crystalloacoustic

The acoustic wave velocity depends on elasticity and density at most materials, but because of anisotropy and especially piezoelectric coupling effect, the acoustic wave propagation at piezoelectric based crystalloacoustic materials, is an applied and challenging problem. In this paper, using modified Christoffel's equation based on group velocity concept, the effect of anisotropy and piezoelectric coupling at different wafers of lithium niobate crystalloacoustic (strong anisotropy) on acoustic wave velocity (semi-longitudinal, semi-vertical transverse wave and semi-horizontal transverse wave) is investigated, and validated by experimental data. Then, the acoustic wave velocity ranges that can be supported are determined. The result of this study can be essential at acoustic metamaterials design, Phononic crystal and piezoelectric based wave-guides

Development of the Multiquadric mesh-less method for analyzing the dynamic interaction of dam-reservoir-foundation problems

The Multiquadric Radial Basis Function (MQ-RBF) method, despite its advantages, has not yet been developed to be used for Dam-Reservoir-Foundation Interaction (DRFI) problems. In this study, this mesh-less method was developed for solving the DRFI systems in the frequency domain. A new domain decomposition technique was also used for analyzing dynamic interaction problems for the first time in MQ-RBF. In this regard, the computational domain is divided into dam, reservoir, and foundation subdomains. Then, the MQ-RBF method is separately applied to each subdomain. For applying the dynamic interaction between two adjacent subdomains, two Multiquadric shape functions must be considered for each computational center on their interaction boundary. Besides, each shape function is also defined using the computational centers in the subdomain. One of the important challenging issues in RBFs is the determination of the Optimal Shape Parameter (OSP). Thereafter, some new relations in terms of the earthquake frequencies are proposed for the OSPs in different cases of the interaction systems. In this regard, a few frequency magnitudes were considered and, consequently, different relations were presented for all frequencies using the obtained OSPs. It is found that, the OSP does not depend on the shear modulus of neither the dam nor the foundation. Moreover, the OSP value are not sensitive to the fluid compressibility and do not depend on the number of subdomains. Apparently, these properties reduce the computational costs and facilitate the MQ-RBF application. In order to validate the capabilities of the approach, nine numerical examples are solved in which the Roots Mean Square Error (RMSE) criterion has been evaluated for comparing the results with those of the exact and FD methods. Results show that the proposed method is of acceptable accuracy, i.e. more accurate than FD even with much more FD computational nodes. Also, it is shown that the errors increase by increasing the earthquake frequency value while the FD errors seem to be unacceptable in frequency values close to the resonance frequency, unlike those of the MQ-RBF

Analytical Solution for a Two-Layer Transversely Isotropic Half-Space Affected by an Arbitrary Shape Dynamic Surface Load

The dynamic response of a transversely isotropic, linearly elastic layer bonded to the surface of a half-space of a different transversely isotropic material under arbitrary shape surface loads is considered. With the help of displacements and stresses Green’s functions, an analytical formulation is presented for the determination of the displacements and stresses at any point in both surface layer and the underneath half-space in frequency domain. Special results are prepared for circular, ellipsoidal, square and recangular patch load. It is shown that the displacements and stresses due to circular patch load are colapesd on the existing solution in the literature. Some new illustrations are prepared to show the effect of the shape of the patch on the responses of the domain specially near the load

Displacement potential functions for elastodynamic problems in transversely isotropic media based on nonlocal strain gradient theory

Today nanotechnology has become important in many fields, including industry, medicine, engineering, aerospace, national security and electronics. As the dimensions of the structures decrease, the effects of size play a crucial role in properties of the media. Mechanical properties, electrical conductivity, thermal properties and other known chemical and physical properties are some examples that differ on nanoscales. Classical continuum mechanics are impotent to cover the effects of dimensions of the constituents of the media on nanoscales. Hence, several non-classical continuum theories, including non-local elasticity theory, strain gradient theory, and non-local strain gradient theory, have been developed by researchers to explain size-dependent mechanical behavior on a nanoscale. In this research, governing equations in terms of displacement potential functions based on nonlocal strain gradient theory are introduced for elastodynamic problems in homogeneous Transversely isotropic media. To this end, the three-dimensional equations of motion of the homogeneous Transversely isotropic media are first calculated using the nonlocal strain gradient theory. Then, using a systematic method, a set of complete displacement potential functions will be presented to solve elastodynamic problems in these media. By use of potential functions, the governing equations of motion will be decoupled. The proposed potentials include two scalar functions. One of them satisfies an 8th-order partial differential equation and 4th-order PDE is governed on the other. These potential functions are obtained in the form of a combination of wave operators, non-local parameter, and characteristic length, which are functionally and physically meaningful. These potential functions are obtained in the form of a combination of wave operators, non-local parameter, and characteristic length, which are functionally and physically meaningful. In addition, potential functions for limiting cases namely strain gradient theory and Eringen nonlocal elasticity theory are presented, separately. Also, by neglecting non-local parameters and characteristic length, the solution is degenerated to the Eskandari-Ghadi solution for classical theory of elasticity. Moreover, a new set of potential functions is presented to solve the elastodynamics of nonlocal strain gradient theory for the simpler case of isotropic materials

Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems

Different methods for the numerical evaluations of the inverse Laplace and inverse of joint Laplace–Hankel integral transforms are applied to solve a wide range of initial-boundary value problems often arising in engineering and applied mathematics. The aim of the paper is to present a performance comparison among different numerical methods when they are applied to transformed functions related to actual engineering problems found in the literature. Most of our selected test functions have been found in the solution of boundary value problems of applied mechanics such as those related to transient responses of isotropic and transversely isotropic half-space to concentrated impulse or those related to viscoelastic wave motion in layered media. These classes of test functions are frequently encountered in similar problems such as those in boundary element or boundary integral equations, theoretical seismology, soil–structure-interaction in time domain and so on. Therefore, their behavior with different numerical inversion algorithms could make a useful guide to a precise choice of more suitable inversion method to be used in similar problems. Some different methods are also investigated in detail and compared for the inversion of the joint Hankel–Laplace transforms, where more sophisticated integrand functions are encountered. It is shown that Durbin, Crump, D’Amore, Fixed-Talbot, Gaver–Whyn–Rho (GWR), and Direct Integration methods have excellent performance and produce good results when applied to the same problems. On the contrary, Gaver–Stehfest and Piessens methods furnish results not very reliable for almost all classes of transformed functions and they seem good only for “simple” transformed functions. Particularly the performance of GWR algorithm is very good even for transformed functions with infinite number of singularities, where the other methods fail. In addition, in case of double integral transforms, only the Fixed-Talbot, Durbin and Weeks methods are recommended

A comparative study of clustering techniques for electrical load pattern segmentation

Smart meters have been widely deployed in power networks since the last decade. This trend has resulted in an enormous volume of data being collected from the electricity customers. To gain benefits for various stakeholders in power systems, proper data mining techniques, such as clustering, need to be employed to extract the underlying patterns from energy consumptions. In this paper, a comparative study of different techniques for load pattern clustering is carried out. Different parameters of the methods that affect the clustering results are evaluated and the clustering algorithms are compared for two data sets. In addition, the two suitable and commonly used data size reduction techniques and feature definition/extraction methods for load pattern clustering are analysed. Furthermore, the existing studies on clustering of electricity customers are reviewed and the main results are highlighted. Finally, the future trends and major applications of clustering consumption patterns are outlined to inform industry practitioners and academic researchers to optimize smart meter operational use and effectiveness