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Search results for: SPECIAL FUNCTIONS
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INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
Journals -
Journal of Inequalities and Special Functions
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Erratum to "Formulas and Theorems for the Special Functions of Mathematical Physics" by W. Magnus, F. Oberhettinger, R. P. Soni
PublicationWe correct a number of misprints in the handbook "Formulas and theorems for the special functions of mathematial physics" (3rd edition) by Magnus, Oberhettinger and Soni.
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Orthogonality relations for the associated Legendre functions of imaginary order
PublicationOrthogonality relations for the associated Legendre functions of imaginary order are derived. They are expressed in terms of the Dirac delta function. The method is based on some known properties of the associated Legendre functions and the Dirac delta distribution. A special case of one of the relations has appeared in some recent applications.
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A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices
PublicationThe orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices is evaluated in a closed form. It is found to be proportional to a sum of two terms, both depending on the second upper indices and containing the Dirac delta distribution.
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An orthogonality relation for the Whittaker functions of the second kind of imaginary order
PublicationPrzeprowadzono dowód ortogonalności funkcji Whittakera drugiego rodzaju rzędu urojonego. Użyto metody analogicznej do tej, którą zaprezentowano we wcześniejszej pracy tych samych autorów [J. Math. Anal. Appl. 365 (2010) 195-197], poświęconej funkcjom Macdonalda rzędu urojonego.
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Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (-1,1)
PublicationZaprezentowano metode obliczenia dwóch całek oznaczonych zawierających wielomiany Gegenbauera. Wynik wykorzystano do znalezienia sum czterech szeregów o wyrazach zawierających wielomiany Gegenbauera oraz funkcje Legendre'a (pierwszego lub drugiego rodzaju) na odcinku (-1,1).
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On the derivatives $\partial^{2}P_{\nu}(z)/\partial\nu^{2}$ and $\partial Q_{\nu}(z)/\partial\nu$ of the Legendre functions with respect to their degrees
PublicationWe provide closed-form expressions for the degree-derivatives $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=n}$ and $[\partial Q_{\nu}(z)/\partial\nu]_{\nu=n}$, with $z\in\mathbb{C}$ and $n\in\mathbb{N}_{0}$, where $P_{\nu}(z)$ and $Q_{\nu}(z)$ are the Legendre functions of the first and the second kind, respectively. For $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=n}$, we find that % \begin{displaymath} \frac{\partial^{2}P_{\nu}(z)}{\partial\nu^{2}}\bigg|_{\nu=n} =-2P_{n}(z)\Li_{2}\frac{1-z}{2}+B_{n}(z)\ln\frac{z+1}{2}+C_{n}(z), \end{displaymath} % where...
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Existence and approximate solutions of Neumann problems
PublicationDyskutowany jest problem Neumanna dla równań różniczkowych drugiego rzędu.Praca dotyczy istnienia rozwiązań i zbieżnosci iteracji monotonicznych któresą przybliżonymi rozwiązaniami omawianych zagadnień. Określone zostały wa-runki zbieżności takich ciągów oraz określono rodzaj tej zbieżnosci.
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Monotone method to Volterra and Fredholm integral equations with deviating arguments
PublicationPraca dotyczy problemów istnienia rozwiązań równań całkowych typu Volterry i Fredholma z odchylonymi argumentami. Podano warunki dostateczne na istnienie rozwiązań w odpowiedniej klasie. Pewne nierówności całkowe typu opóźnionego są również przedmiotem badań.
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Anisotropic Orlicz–Sobolev spaces of vector valued functions and Lagrange equations
PublicationIn this paper we study some properties of anisotropic Orlicz and Orlicz–Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give conditions which ensure that the principal part of variational functional is finitely defined and continuously differentiable on Orlicz–Sobolev space.
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Wavelet filtering of signals without using model functions
PublicationThe effective wavelet filtering of real signals is impossible without determining their shape. The shape of a real signal is related to its wavelet spectrum. For shape analysis, a continuous color wavelet spectrogram of signal level is often used. The disadvantage of continuous wavelet spectrogram is the complexity of analyzing a blurry color image. A real signal with additive noise strongly distorts the spectrogram based on continuous...
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New Approach to Arc Fitting for Railway Track Realignment
PublicationThis article presents a new method of arc fitting for railway track realignment. The theoretical foundations are presented, along with a detailed algorithm of the iterative computational process. This method is based on solving a set of linearized pseudo-observation equations. The formulas of the functional model of the fitting problem were derived, and a special form of objective function is proposed. An iterative method for optimization...
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Transition dipole moment functions of the KRb molecule
Open Research DataElectronic transition dipole moment functions (TDMF) have been calculated for the singlet (s) and triplet (t) Sigma+ (S+), Pi (P), and Delta (D) electronic states of the KRb molecule. TDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. All results of the transition dipole moments...
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Permanent dipole moment functions of the KRb molecule
Open Research DataElectronic permanent dipole moment functions (PDMF) have been calculated for the singlet (s) and triplet (t) Sigma+, Sigma-, Pi, and Delta electronic states of the KRb molecule. PDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. All results of the permanent dipole moments have been...
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Pedestrian on footbridges, vertical loads and response
PublicationThe paper is a synthesis of the experimental and theoretical investigations on dynamics of pedestrian bridges under vertical load The subject is divided into four issues.1) The pedestrian as a vertical dynamic load on footbridges, theoretic load function for walking and crouching.2) Crowd walking on the footbridge - pedestrian flow.3) Vertical lock-in effect.4) Response of the footbridge - numeric and side test results, -...
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Evaluation of high-frequency roughness measurement errors for composite and ceramic surfaces after machining
PublicationPrecise characterisation of surface topography is of the greatest importance since many factors directly affect the accuracy of the whole measurement process. In this paper, the variety of surface topographies from machined composite and ceramic workpieces was studied with a special emphasis on the measurement results. Surfaces were subjected to the ground diamond, honing and milling processes. Measurement results were analysed...
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The structure of the control system for a dynamically positioned ship
PublicationThe article discusses functions and tasks of dynamic positioning (DP) systems for ships. The analysed issues include ship steering, in particular stabilisation of ship position and direction of motion (real course) at low manoeuvring speeds, and commonly used DP ship models. Requirements imposed by classification societies on DP ships are quoted. A multi-layer structure of the DP control system is presented, with special attention...
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Analysis of the objects images on the sea using Dempster-Shafer Theory
PublicationThe paper presents the concept of using aerial and satellite imagery or images coming from the marine radar to identify and track vessels at sea. The acquired data were subjected to a highly advanced image analysis. The development of remote sensing techniques allows to gain a huge amount of data. These data are useful information source however usually we have to use different data mining methods to gain interested information....
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A tool for designing water tanks for measuring hydroacoustic transducers
PublicationSpecial water tanks are commonly used to measure the parameters of underwater acoustic systems. They must meet specific requirements, the fulfilment of which ensures very small but acceptable measurement errors. These requirements define the size of the tank and its shape as well as the strong attenuation of reflected waves. At the design stage, it is necessary to determine the impact of the tank structure on the measurement errors...
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Analytical solution of non-stationary heat conduction problem for two sliding layers with time-dependent friction conditions
PublicationIn this article we conduct an overview of various types of thermal contact conditions at the sliding interface. We formulate a problem of non-stationary heat conduction in two sliding layers with generalized thermal contact conditions allowing for dependence of the heat-generation coefficient and contact heat transfer coefficient on time. We then derive an analytical solution of the problem by constructing a special coordinate...
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POLITECHNIKA GDAŃSKA W LITERATURZE
PublicationW artykule przedstawiono w jaki sposób Politechnika Gdańska funkcjonuje w literaturze pięknej. Politechnika ukazywana jest jako miejsce nauki, ale także miejsce wydarzeń historycznych i kulturalnych, jej istnienie jest zakorzenione w świadomości gdańszczan, a przede jest to miejsce w którym spędziło się najlepiej wspominany okres w życiu – okres studiów i pracy zawodowej. Wymienione zostały publikacje informacyjne, ale przede wszystkim...
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Integrate-and-fire models with an almost periodic input function
PublicationWe investigate leaky integrate-and-fire models (LIF models for short) driven by Stepanov and μ-almost periodic functions. Special attention is paid to the properties of the firing map and its displacement, which give information about the spiking behavior of the considered system. We provide conditions under which such maps are well-defined and are uniformly continuous. We show that the LIF models with Stepanov almost periodic...
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Pure cross-anisotropy for geotechnical elastic potentials
PublicationThe pure cross-anisotropy is understood as a special scaling of strain (or stress). The scaled tensor is used as an argument in the elastic stiffness (or compliance). Such anisotropy can be overlaid on the top of any elastic stiffness, in particular on one obtained from an elastic potential with its own stress-induced anisotropy. This superposition does not violate the Second Law. The method can be also applied to other functions...
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Frequency Response Functions for Sandvik CoroBore 825 XL boring tool, 733 mm
Open Research DataFrequency Response Functions (FRF) obtained for Sandvik CoroBore® 825 XL mounted at WHN 13-15 TOS VARNSDORF CNC machine at the minimum extension of the spindle adaptor. Tool set to bore a hole with a diameter 733mm
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Potential energy curve, rovibrational energies and nuclear wave functions of 2 singlet Pi state in KLi dimer
Open Research DataThis data sets contains potential energy curve, energy levels and nuclear wave functions of rovibrational states of KLi dimer in 2 singlet Pi electronic state. Potential energy curve (PEC) for the electronic state was calculated in the Born-Oppenheimer approximation by the means of effective core potentials and MRCI method. Nuclear wave functions and...
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Raw data for the paper "Mutually polarizable QM/MM model with in situ optimized localized basis functions"
Open Research DataThis dataset contains raw data used to generate plots in the paper Mutually polarizable QM/MM model with in situ optimized localized basis functions. The paper is devoted to a second generation of the TINKTEP model -- an QM/MM approach combining linear-scaling DFT (ONETEP) and a polarizable force field (AMOEBA).
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Electronic transition dipole moment functions of the second triplet Sigma ungerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the second triplet Sigma ungerade plus (2tSu+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the third singlet Sigma gerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the third singlet Sigma gerade plus (3sSg+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the third triplet Sigma ungerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the third triplet Sigma ungerade plus (3tSu+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the fourth triplet Sigma ungerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the fourth triplet Sigma ungerade plus (4tSu+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the fourth singlet Sigma gerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the fourth singlet Sigma gerade plus (4sSg+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the second singlet Sigma gerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the second singlet Sigma gerade plus (2sSg+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the fifth singlet Sigma gerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the fifth singlet Sigma gerade plus (5sSg+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the fifth triplet Sigma ungerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the fifth triplet Sigma ungerade plus (5tSu+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the first singlet Sigma gerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the first singlet Sigma gerade plus (1sSg+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the first triplet Sigma ungerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the first triplet Sigma ungerade plus (1tSu+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Forecasting of railway track tamping based on settlement of sleepers using fuzzy logic
PublicationThe sleepers in a railway track transfer vertical, transverse and longitudinal loads to the track ballast and subgrade. The sleepers allow for keeping the distance between the rails constant. The thickness of ballast should be between 16 and 35 cm depending on the design standard of the track, and it should be densified where the ballast supports the sleeper. The exploitation causes contamination of the ballast, crushing the material...
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Simple adaptive cubic spline interpolation of fluorescence decay functions
PublicationZaproponowano prostą metodę interpolacji funkcji zaniku fluorescencji. W pierwszym kroku interpolowany zanik jest całkowany za pomocą adaptacyjnego algorytmu wykorzystującego kwadratury Newtona-Cotesa. Uzyskiwana w ten spoób siatka wartości czasu jest używana w drugim kroku polegającym na typowej interpolacji za pomocą funkcji sklejanych trzeciego stopnia.
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Assessment of hearing in coma patients employing auditory brainstem response, electroencephalography, and eye-gaze-tracking
PublicationThe results of the study conducted by Tagliaferri et al. in 12 European countries indicate that the ratio of registered brain injury cases in Europe amounts to 150-300 per 100 000 people, with the European mean value of 235 cases per 100 000 people. The project presented in the paper assumes development of a combined metric of patients’ state remaining in coma by intelligent fusion of GCS (subjective Glasgow Coma Scale or its derivatives)...
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Electronic transition dipole moment functions of the first singlet Delta gerade and first triplet Delta ungerade states of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the first singlet Delta gerade (1sDg) and first triplet Delta ungerade (1tDu) states have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the four ETDMFs have been obtained...
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Electronic transition dipole moment functions of the first singlet Pi gerade and first triplet Pi gerade states of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the first singlet Pi gerade (1sPg) and first triplet Pi gerade (1tPg) states have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the four ETDMFs have been obtained...
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Electronic transition dipole moment functions of the second singlet Pi gerade and second triplet Pi gerade states of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the second singlet Pi gerade (2sPg) and second triplet Pi gerade (2tPg) states have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the four ETDMFs have been obtained...
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The Weibull model of the multipath fading channel
Open Research DataThe dataset contains the results of simulations that are part of the research on modelling the multipath fading in the communication channel. The Weibull fading envelope is generated using the Monte-Carlo simulation (MCS) in the LabVIEW programming environment.
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Simulation of unsteady flow over floodplain using the diffusive wave equation and the modified finite element method
PublicationWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference...
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Interdisciplinary research as a form of monument protection and preparation for the investment process on the example of the former Gdańsk Shipyard complex
PublicationThe multi-layered heritage of many industrial plants operating until the end of the 20th century creates a particular challenge for conservators, designers and investors. In the process of protecting its values, displaying qualities and managing the property, it is necessary to recognize a wider transformation of technology of the entire plant and the individual functions of its buildings, as well as the context of intangible...
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Electronic transition dipole moment functions of the second singlet Sigma ungerade plus and second triplet Sigma gerade plus states of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the second singlet Sigma ungerade plus (2sSu+) and second triplet Sigma gerade plus (2tSg+) states have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the four ETDMFs...
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Electronic transition dipole moment functions of the first singlet Sigma ungerade plus and first triplet Sigma gerade plus states of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the first singlet Sigma ungerade plus (1sSu+) and first triplet Sigma gerade plus (1tSg+) states have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the four ETDMFs...
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Electronic transition dipole moment functions of the third singlet Sigma ungerade plus and third triplet Sigma gerade plus states of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the third singlet Sigma ungerade plus (3sSu+) and third triplet Sigma gerade plus (3tSg+) states have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the four ETDMFs...
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Implementation of Hermite-Ritz method and Navier’s Technique for Vibration of Functionally Graded Porous Nanobeam Embedded in Winkler-Pasternak Elastic Foundation Using bi-Helmholtz type of nonlocal elasticity
PublicationPresent study is devoted to investigating the vibration characteristics of Functionally Graded (FG) porous nanobeam embedded in an elastic substrate of Winkler-Pasternak type. Classical beam theory (CBT) or Euler-Bernoulli beam theory (EBT) has been incorporated to address the displacement of the FG nanobeam. Bi-Helmholtz type of nonlocal elasticity is being used to capture the small scale effect of the FG nanobeam. Further, the...