• Advances in nano research
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• v.17 no.3
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• pp.221-234
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• 2024

In this paper, dynamic response of annular nanoplates in improving sports equipment with surface effect embedded by visco Pasternak fractional foundation is studied. Size effects are evaluated by modified couple stress theory (MCST) and the surface effects are considered by the Gurtin-Murdoch theory. The structural damping effect is considered in this research using Kelvin-Voigt model. Sinusoidal shear deformation theory (SSDT) is applied for mathematical modelling of the nanostructure system. The numerical procedure of differential quadrature (DQ) is presented to determine the dynamic deflection as well as dynamic response of the annular nanoplates. The numerical results dynamic deflection of the nanostructure is considering, including material length scale parameter, spring and damper constants of visco-pasternak fractional foundation, geometrical parameters of annular nanoplates, surface stress effects.

• Steel and Composite Structures
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• v.48 no.3
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• pp.335-351
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• 2023

This research studies the primary resonance and nonlinear vibratory responses of multilayer functionally graded shallow (MFGS) shells under external excitations. The shells considered with functionally graded porous (FGP) core and resting on two types of nonlinear viscoelastic foundations (NVEF) governed by either a linear model with two parameters of Winkler and Pasternak foundations or a nonlinear model of hardening/softening cubic stiffness augmented by a Kelvin-Voigt viscoelastic model. The shells considered have three layers, sandwiched by functionally graded (FG), FGP, and FG materials. To investigate the influence of various porosity distributions, two types of FGP middle layer cores are considered. With the first-order shear deformation theory (FSDT), Hooke's law, and von-Kármán equation, the stress-strain relations for the MFGS shells with FGP core are developed. The governing equations of the shells are consequently derived. For the sake of higher accuracy and reliability, the P-T method is implemented in numerically analyzing the vibration, and the method of multiple scales (MMS) as one of the perturbation methods is used to investigate the primary resonance. The results of the present research are verified with the results available in the literature. The analytical results are compared with the P-T method. The influences of material, geometry, and nonlinear viscoelastic foundation parameters on the responses of the shells are illustrated.

• Advances in nano research
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• v.13 no.4
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• pp.369-378
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• 2022

Dynamic study of concrete plates under impact load is presented in this article. The main objective of this work is presenting a mathematical model for the concrete plates under the impact load. The concrete plate is reinforced by carbon nanoparticles which the effective material proprieties are obtained by mixture's rule. Impacts are assumed to occur normally over the top layer of the plate and the interaction between the impactor and the structure is simulated using a new equivalent three-degree-of-freedom (TDOF) spring-mass-damper (SMD) model. The structure is assumed viscoelastic based on Kelvin-Voigt model. Based on the classical plate theory (CPT), energy method and Hamilton's principle, the motion equations are derived. Applying DQM, the dynamic deflection and contact force of the structure are calculated numerically so that the effects of mass, velocity and height of the impactor, volume percent of nanoparticles, structural damping and geometrical parameters of structure are shown on the dynamic deflection and contact force. Results show that considering structural damping leads to lower dynamic deflection and contact force. In addition, increasing the volume percent of nanoparticles yields to decreases in the deflection.

• Structural Engineering and Mechanics
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• v.46 no.3
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• pp.417-431
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• 2013

This paper presents responses of the free end of a cantilever micro beam under the effect of an impact force based on the modified couple stress theory. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the classical beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the classical beam theory based on the modified couple stress theory must be used instead of the classical theory for small values of beam height.

• Steel and Composite Structures
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• v.37 no.1
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• pp.51-73
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• 2020

The present paper investigates the simultaneous resonance behavior of spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells with internal and external functionally graded stiffeners under the two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The cylindrical shell has three layers consist of ceramic, FGM, and metal. The exterior layer of the cylindrical shell is rich ceramic while the interior layer is rich metal and the functionally graded material layer is located between these layers. With regard to classical shells theory, von-Kármán equation, and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The simultaneous resonance is obtained using the multiple scales method. Finally, the influences of different material and geometrical parameters on the system resonances are investigated comprehensively.

• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.489-505
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• 2016

Sinusoidal shear deformation theory (SSDT) is developed here for dynamic buckling of functionally graded (FG) nano-plates. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. In order to present a realistic model, the structural damping of nano-structure is considered using Kelvin-Voigt model. The surrounding elastic medium is modeled with a novel foundation namely as orthotropic visco-Pasternak medium. Size effects are incorporated based on Eringen'n nonlocal theory. Equations of motion are derived from the Hamilton's principle. The differential quadrature method (DQM) in conjunction with Bolotin method is applied for obtaining the dynamic instability region (DIR). The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, orthotropic visco-Pasternak foundation, power index of FG plate, structural damping and boundary conditions on the dynamic instability of system. The results are compared with those of first order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the dynamic buckling responses of system.

• Structural Engineering and Mechanics
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• v.73 no.5
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• pp.555-563
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• 2020

The objective of present paper is assessment of dynamic buckling behavior of an embedded sandwich microplates in thermal environment in which the layers are reinforced through functionally graded carbon nanotubes (FG-CNTs). Therefore, mixture rule is taken into consideration for obtaining effective material characteristics. In order to model this structure much more realistic, Kelvin-Voigt model is presumed and the sandwich structure is rested on visco-Pasternak medium. Exponential shear deformation theory (ESDT) in addition to Eringen's nonlocal theory are utilized to obtain motion equations. Further, differential cubature method (DCM) as well as Bolotin's procedure are used to solve governing equations and achieve dynamic instability region (DIR) related to sandwich structure. Different parameters focusing on volume percent of CNTs, dispersion kinds of CNTs, thermal environment, small scale effect and structural damping and their influences upon the dynamic behavior of sandwich structure are investigated. So as to indicate the accuracy of applied theories as well as methods, the results are collated with another paper. According to results, presence of CNTs and their dispersion kind can alter system's dynamic response as well.

• Structural Engineering and Mechanics
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• v.80 no.6
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• pp.727-736
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• 2021

In this work, mathematical modeling of the passive vibration controls of a three-layered sandwich beam under hard excitation is developed. Kelvin-Voigt Viscoelastic model is considered in the core. The formulation is based on the higher-order zig-zag theories where the normal and shear deformations are taken into account only in the viscoelastic core. The dynamic behaviour of the beam is represented by a complex highly nonlinear ordinary differential equation. The method of multiple scales is adopted to solve the analytical frequency-amplitude relationships in the super-harmonic resonance case. Parametric studies are carried out by using HSDT and first-order deformation theory by considering different geometric and material parameters.

• Steel and Composite Structures
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• v.50 no.4
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• pp.403-418
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• 2024

In this paper, vibration and energy absorption characteristics of a nanostructure which is composed of two embedded porous annular/circular nanoplates coupled by a viscoelastic substrate are investigated. The modified couple stress theory (MCST) and the Gurtin-Murdoch theory are applied to take into account the size and the surface effects, respectively. Furthermore, the structural damping effect is probed by the Kelvin-Voigt model and the mathematical model of the problem is developed by a new hyperbolic higher order shear deformation theory. The differential quadrature method (DQM) is employed to obtain the out-of-phase and in-phase frequencies of the structure in order to predict the dynamic response of it. The acquired results reveal that the vibration and energy absorption of the system depends on some factors such as porosity, surface stress effects, material length scale parameter, damping and spring constants of the viscoelastic foundation as well as geometrical parameters of annular/circular nanoplates. A bird's-eye view of the findings in the research paper offers a comprehensive understanding of the vibrational behavior and energy absorption capabilities of annular/circular porous nanoplates. The multidisciplinary approach and the inclusion of porosity make this study valuable for the development of innovative materials and applications in the field of nanoscience and engineering.

• Steel and Composite Structures
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• v.52 no.6
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• pp.621-626
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• 2024

The work researched the application of artificial intelligence to the design and analysis of advanced nanoplates, with a particular emphasis on size and surface effects. Employing an integrated theoretical framework, this study developed a more accurate model of complex nanoplate behavior. The following analysis considers nanoplates embedded in a Pasternak viscoelastic fractional foundation and represents the important step in understanding how nanoscale structures may respond under dynamic loads. Surface effects, significant for nanoscale, are included through the Gurtin-Murdoch theory in order to better describe the influence of surface stresses on the overall behavior of nanoplates. In the present analysis, the modified couple stress theory is utilized to capture the size-dependent behavior of nanoplates, while the Kelvin-Voigt model has been incorporated to realistically simulate the structural damping and energy dissipation. This paper will take a holistic approach in using sinusoidal shear deformation theory for the accurate replication of complex interactions within the nano-structure system. Addressing different aspectsof the dynamic behavior by considering the length scale parameter of the material, this work aims at establishing which one of the factors imposes the most influence on the nanostructure response. Besides, the surface stresses that become increasingly critical in nanoscale dimensions are considered in depth. AI algorithms subsequently improve the prediction of the mechanical response by incorporating other phenomena, including surface energy, material inhomogeneity, and size-dependent properties. In these AI- enhanced solutions, the improvement of precision becomes considerable compared to the classical solution methods and hence offers new insights into the mechanical performance of nanoplates when applied in nanotechnology and materials science.