Increase In Natural Frequency Research Articles

Influence of fly-ash filler and moisture content on vibrational and acoustic properties of basalt fibre reinforced composites

ABSTRACT Fly ash, a by-product of coal combustion consisting of particulates and flue gases expelled from coal-fired furnaces, has found application as a substitute for organic fillers in the composites industry. In this study, the focus lies on assessing the vibrational and acoustic performance of composites composed of epoxy-based basalt combined with fly ash. Experimental investigations were carried out on specimens containing different weight percentages of fly ash (0%, 10%, 15% and 20% of the epoxy weight) to evaluate free vibration and acoustic impedance. Additionally, the impact of moisture on the vibrational and acoustic properties of Basalt/Fly ash-Epoxy composites was examined by subjecting the specimens to 3 months of ageing in distiled water. The results revealed that increasing the filler content up to 15% led to an increase in natural frequencies (8.5 Hz) and stiffness (3.8 N/mm) of the material, although the damping ratio (0.219) has decreased. Notably, as the specimens aged, the damping ratio is improved by 9%, while the natural frequency and stiffness decline by 9.67% and 12.5%, respectively. The material density emerged as a critical factor influencing the sound absorption capability of the specimens. The inclusion of fly ash in the epoxy matrix has enhanced the acoustic properties of the tested specimens.

A deviatoric couple stress Mindlin plate model and its degeneration

Based on the classical couple stress theory, the deviatoric couple stress theory (DCST), where both couple stress and curvature tensors are traceless, is developed. The deviatoric couple stress Mindlin plate is established based on a new hypothesis of the vanishing curvature of the transverse normal, and the governing equations and associated boundary conditions of the simplified size-dependent Mindlin plate are respectively derived by the principle of virtual work. In the absence of couple stresses, a simplified Mindlin plate model between the classical Kirchhoff plate model and classical Mindlin plate model is derived. To illustrate the simplified DCST-based Mindlin plate model, the static bending and free vibration of rectangular plates are studied. The dependence of the length scale parameter and curvature ratio on the deflection, rotation and natural frequency is analyzed. The numerical results show that the consideration of couple stresses and curvatures hardens the stiffness of the microstructure, resulting in a decrease in its deflection and rotation compared with that of the macroscopic structure under the same conditions, while the natural frequency increases, which is consistent with the size effect observed in experiments.

Dynamic properties of natural fiber-reinforced polymer composite plates and tubes

Thirty-six flax fibre-reinforced epoxy (FFRE) plates with two, three, and four fabric layers and lengths ranging from 160 mm to 270 mm and nine FFRE tubes with a diameter of 60 mm, a length of six times the tube diameter plus an overly of 50 mm with two, three, and four fabric layers were manufactured. One-hundred-eighty impulse excitation tests were conducted on FFRE plates to determine the dynamic properties of the plates in the bending mode, and 91 impulse excitation tests were conducted on the FFRE tubes to determine the dynamic properties of the tubes in the transverse, torsional, and longitudinal directions. FFRE plates showed up to six times larger specific energy capacities compared to counterpart glass fibre-reinforced polymer plates, showing significant potential for FFRE plates to replace the use of GFRP plates where considerable damping of energy is required. The results showed that the damping ratio of the FFRE plates decreased with the increase in layers and natural frequency. For the FFRE tubes, the highest damping ratio belonged to the transverse vibration mode, followed by the torsional or longitudinal vibration modes.

Experimental free vibration and tensile test results of a five-layer sandwich plate by comparing various carbon nanostructure reinforcements with SMA

Considering to need for the sensitive and destructive industries for high stiffness and low weight, an experimental free vibration and tensile test results of a five-layer sandwich plate by comparing various carbon nano structures reinforcements with SMA is discussed. The effect of various reinforcements, including carbon nanostructures (carbon nanotubes (CNT), carbon nanorods (CNRs), Graphene platelets (GPLs)) and nitinol shape memory alloy (SMA) wire on the vibration behavior of a five-layer sandwich plate with a foam core is investigated. The purpose and novelty of this work are to compare the effect of different reinforcements on the vibrations of a five-layer plate so that by using this comparison, one can choose the best reinforcements according to the needs of the desired industry and more suitable economic conditions. Considering a 1 % weight fraction of epoxy resin, GPLs, CNTs, and CNRs increase Young's modulus of face sheets by 30 %, 25 %, and 5.8 %, respectively. In this work, a five-layer sandwich structure model can be suggested, and numerically analyzed. The special advantage novelty of this research compared to previous research is the construction of this five-layer model. This is a simple modeling structure for the construction and preliminary examination of structures with five layers experimentally. Also, the composite structure is made by the vacuum pump method, which does not have the disadvantages of the manual method, and the method is completely optimal. At first, the Young's and shear moduli of unidirectional glass fiber (UGF) are calculated by performing a tensile test. To examine all aspects of the construction of five-layer structures during construction, in this article first, the face sheets are made separately using resin, UGF, and various reinforcements, and then the layers of face sheets and the cores are connected using glue. In the following, the equations of motion for the sandwich plate are derived using refined first-order shear deformation theory (RFSDT) by employing Hamilton's principle. Using the Halpin-Tsai equation and the extended rule of mixture, the mechanical properties of the reinforced composite face sheets are obtained. According to the Brinson model, the constitutive equations of the SMA are presented. The influence of various parameters such as side ratio, thickness ratio, weight fraction of CNRs, CNTs, GPLs and SMA wire, fiber angle, and temperature changes on dimensionless fundamental frequency is also represented. Also, the natural frequency of orthotropic plates by considering reinforcements is higher than that without considering reinforcements. By increasing the aspect ratio (a/h), the dimensionless natural frequency increases, while the natural frequency decreases. For two-layer square angular asymmetric laminated sheets (-θ/θ), the minimum dimensionless natural frequency occurred at the fiber placement angle approximately equal to 26 and 64°. The highest frequency is related to the sandwich plate in that its face sheets have higher strength and stiffness because it is placed further from the middle plane. Also, the highest frequency is related to the sandwich plate, whose face sheets are reinforced with GPLs.

Multi-objective optimization design for the table of a CNC machine tool based on bionic structures

To improve the static and dynamic performance of CNC machine tool tables, a multi-objective optimization design method based on bionic structures is proposed, which involves bionic design and size optimization design. Based on the bionics, four types of bionic structure tables for the original XK5032 machine tool were designed, namely bamboo cross-section bionic structure table, spider web bionic structure table, honeycomb bionic structure table, and prairie rushes bionic structure table. Static and modal analysis of the original and four types of bionic tables were conducted using finite element simulation methods validated through modal experiments. The results show that the overall mechanics of the four bionic tables have been improved compared to the original table. Using the entropy weight TOPSIS method, the prairie rushes bionic structure table was selected from four types of bionic tables. Conducting multi-objective optimization design on the prairie rushes bionic structure table, three optimization candidate schemes were obtained. The entropy-weighted TOPSIS method was used again to select the optimal solution from these three schemes, resulting in a 0.8% reduction in mass, an increase in first-order natural frequency by 2.8%, a decrease in maximum displacement by 3.2%, and a significant 21.6% reduction in maximum equivalent stress compared to the original table.

Nonlinear vibrations of cracked microbeams based on modified couple stress theory

In this study, nonlinear vibrations of cracked microbeams have been investigated. The micro size characteristics of the beam have been involved in the model by utilizing the modified couple stress theory. Longitudinal elongation of the microbeam during transverse vibrations have been considered to capture the nonlinear behavior. To model the crack, a torsional spring has been introduced at the crack location and the spring constant corresponds to the severity of the crack. Approximate solutions have been obtained by using the method of multiple scales, a perturbation technique. The results have been validated by comparing them with existing literature and have been presented in terms of both crack severity and micro scale properties. The effects of the crack have been examined on various aspects, including natural frequency, nonlinear frequency-response curves and nonlinear frequency responses. These effects have been investigated with respect to parameters such as crack severity, crack location, amplitude of excitation, slenderness of the beam, all under differing boundary conditions. The predicted results reveal that as the crack severity increases, both natural frequency and nonlinear frequency decrease. Furthermore, the modified couple stress theory predicts an increase in natural frequencies as the size scale of the microbeams reduces. The frequency-response curves with varying crack severity and crack locations have indicated the significant effects of the presence of the crack in microbeams.

Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model for Vibrational Analysis of Single-Walled Carbon Nanotubes

In this study, a new anisotropic elastic shell model with a nonlocal strain gradient is developed to investigate the vibrations of simply supported single-walled carbon nanotubes (SWCNTs). The Sanders–Koiter shell theory is used to obtain strain–displacement relationships. Eringen’s nonlocal elasticity and Mindlin’s strain gradient theories are adopted to derive the constitutive equations, where the anisotropic elasticity constants are expressed via Chang’s molecular mechanics model. An analytical method is used to solve the equations of motion and to obtain the natural frequencies of SWCNTs. First, the anisotropic elastic shell model without size effects is validated through comparison with the results of molecular dynamics simulations reported in the literature. Then, the effects of the nonlocal and material parameters on the natural frequencies of SWCNTs with different geometries and wavenumbers are analyzed. From the numerical simulations, it is confirmed that the natural frequencies decrease as the nonlocal parameter increases, while they increase as the material parameter increases. As new results, the reduction in natural frequencies with increasing SWCNT radius and the increase in natural frequencies with increasing wavenumber are both amplified as the material parameter increases, while they are both attenuated as the nonlocal parameter increases.

Analysis of the vortex-induced vibration response characteristics of riser under the soft suspension evacuation condition

This paper establishes a nonlinear dynamic model for a suspended riser under the condition of considering realistic configurations, based on the principles of virtual work and Hamilton's variational principle. The nonlinearity of the model is manifested by considering vortex-induced vibration in the cross flow (CF) and in-line (IL) directions, as well as large deformations, taking into account the variable diameter of the riser in the compliant riser system. The model is discretized using the finite element method and solved using the Newmark-β method. Experimental validation is conducted to verify the effectiveness of the model. Utilizing the parameters of a riser in a well in the South China Sea, the paper explores the influence of different environmental and structural parameters on the VIV response characteristics of a compliant riser. Results show that the vibration frequency is controlled by both the bare tube and buoyant block when the buoyant block coverage rate is 25%, which can significantly inhibit VIV. With the increase of flow velocity, the VIV energy jumps from low order to high order, and the riser mode also transitions from low order to high order. The increase in suspension length transfers the vibration energy from high to low frequency, thus realizing energy transition and mode shape transformation. With the increase in LMRP weight, the vibration and natural frequencies of the riser increase synchronously, the vibration amplitude decreases, and the mode shape remains unchanged.

Free vibration analysis of functionally graded carbon nanotubes reinforced double plates

The specific objective of this study is to analyze the dynamics of functionally graded carbon nanotubes (FGCNT) reinforced double plates. Connected via an elastic layer, the plates have simply supported boundary conditions. In the current study, three carbon nanotubes functionally graded patterns, varying in the thickness direction are considered, including uniformly distributed, functionally graded O-pattern, and functionally graded X-pattern. Following the development of the coupled equations of motion using the Hamilton principle while considering the influences of the elastic layer, the equations are subsequently solved utilizing a two-spatial-variable modal decomposition method. For verification purposes, the equations developed are compared to simplified configurations provided in the existing studies. The solution methodology is verified through comparing against numerical results of simplified configurations of plates obtained from the development of the finite element method and existing studies. Both verifications have shown very good agreement. Influences of plates’ dimensions, carbon nanotubes reinforcement, and the stiffness of elastic layer are analyzed and provided in this study. The transverse-motion natural frequencies of the double plates are also identified, and they follow a decreasing trend as the aspect ratio increases for all the cases. The fundamental lateral-motion and axial-motion natural frequency also follows a similar trend as the aspect ratio increases. The reinforcement effect of carbon nanotubes on the transverse-motion natural frequencies is less obvious for thinner plates. An increase in the elastic layer stiffness increases the second series transverse-motion natural frequencies of the double-plate system. Among the considered functionally graded patterns, the functionally graded X-pattern reinforcement provides the largest increase in the transverse-motion natural frequencies.

Employing finite element analysis for assessing the condition monitoring of sandwich beams

In engineering and transportation, beams are frequently utilized as structural elements for both static and dynamic loads. This paper focuses on a smart structure method that incorporates ANSYS software for modeling and simulation. Piezoelectric transducers are employed for actuation and sensing throughout the structure. The governing equation of a finite element that converts the mechanical energy of the structure into the electric energy of the piezoelectric material is derived using Hamilton's principle. Debonding of piezoelectric sensors/actuators is caused by structural alterations in sandwich beams, and this leads to a notable fluctuation in both static and dynamic responses. It has been shown that Finite Element Modeling with ANSYS software yields accurate numerical solutions over a broad range of related parameters. The results are displayed and vibration modes are animated by utilizing the graphical post processing capabilities. It has been observed that the material and structural alterations are what cause the increase in natural frequencies. With an input of 1 V, the load is adjusted between 0 and 5000 Hz for every material configuration.

Theoretical and Simulation Finite Element Modal Analysis of Rotating Cantilever Beam

The finite element method is used to carry out modal analysis of rotating cantilever beam. The virtual work method is then used to derive the stiffness matrix of a rotating beam element. The stiffness matrix of a rotating beam element is simply seen to be sum of the stiffness matrix of the non-rotating beam and an incremental stiffness matrix induced by rotation. This work presents a novel generalized incremental stiffness matrix that takes care of any element at any distance from the rotation axis. The established rotational stiffness matrix is then used together with consistent mass matrix (not affected by rotation) to carry out modal analysis of rotating cantilever beam. Theoretical computations were validated by simulations from ANSYS. It is seen that the contribution to modal frequencies and shapes of the blade of rotation via incremental stiffness matrix is very marginal at low rotational speeds. For exampleit is seen for a numerical case study that five-element model computes slight increase in fundamental natural frequency due to rotation relative to that of the non-rotating blade as 0.000195% for rotational speed of 300rpm. It is also seen that ten times increase in speed leads to about hundred times increase in rotational contribution meaning that it becomes more imperative to model rotation as speed of the blade increases. Points are also made regarding application to avoiding resonance of rotating cantilever beam.

Buckling Stability and Vibration Characteristics of Functionally Graded Graphene Platelet-Reinforced Composites Multi-Arc Concave Honeycomb Sandwich Panels Under Thermal Loading

The utilization of functionally graded graphene platelet-reinforced composites (FG-GPLRC) and honeycomb sandwich constructions is prevalent in the field of engineering. Therefore, it is crucial to investigate the buckling and vibration properties of these materials under heat circumstances. This paper specifically focuses on the vibration and thermal buckling characteristics of a novel multi-arc concave honeycomb sandwich plate (MACHSP) equipped with an adjustable positive-negative Poisson’s ratio. The governing equations of motion for the system are derived based on the first-order shear deformation theory in conjunction with Hamilton’s principle. The formulation of the system’s characteristic equation involves the establishment of displacement functions that satisfy distinct boundary conditions. Using computational programming, natural frequencies, mode shapes, and critical buckling temperatures of MACHSP with three different FG-GPLRC distributions under thermal influences are determined. Subsequently, these results are compared with outcomes from finite element simulations and findings from previously published literature. Additionally, the amplitude-frequency response characteristics of the structure under harmonic excitation are analyzed, followed by a discussion of the impact of structural parameters on its buckling and vibration characteristics. The results indicate that the established theoretical model for predicting the buckling and vibration characteristics of MACHSP with FG-GPLRC distribution aligns well with simulation models and prior research. In contrast to solid plates, MACHSP not only achieves a substantial reduction in weight but also demonstrates a significant increase in natural frequency. Furthermore, graphene platelets have the potential to enhance the structure’s natural frequency values and critical buckling temperatures. Lastly, various structural parameters exert a notable influence on the structure’s performance.

Thermal Oscillations of Nanobubbles.

Nanobubble cavitation is advancing technologies in enhanced wastewater treatment, cancer therapy and diagnosis, and microfluidic cleaning. Current macroscale models predict that nanobubble oscillations should be isothermal, yet recent studies suggest that they are adiabatic with an associated increase in natural frequency, which becomes challenging when characterizing nanobubble sizes using ultrasound in experiments. We derive a new theoretical model that considers the nonideal nature of the nanobubble's internal gas phase and nonequilibrium effects, by employing the van der Waals (vdW) equation of state and implementing a temperature jump term at the liquid-gas interface, respectively, finding excellent agreement with molecular dynamics (MD) simulations. Our results reveal how adiabatic behavior could be erroneously interpreted when analyzing the thermal response of the gas using the commonly employed polytropic process and explain instead how nanobubble oscillations are physically closer to their isothermal limit.

Viscoelastic and vibrational studies of nano hybrid fibre metal laminates

Employment of distinct fibres (glass/carbon etc.) in Fibre Metal Laminates (FMLs) is one way of enhancing the durable life of an FML and its performance under dynamic loads. In the present work, carbon fibre is employed in GLARE (Glass/Aluminium laminated epoxy) to enhance the vibration (natural frequency) and viscoelastic (storage modulus ( E′), loss modulus ( E″) and Tan δ) properties. Similarly, the influence of 1 wt% of Al2O3 (alumina), ZrO2 (zirconium oxide) and TiO2 (titanium oxide) nano particles are also studied in hybrid (carbon/glass) FML. The mean particle size of Al2O3 (5.1 nm), ZrO2 (25.3 nm) and TiO2 (63.2 nm) were estimated using the Scherer equation with the aid of X-ray diffractometer analysis. Hybridisation resulted in a 22%, 10% and 2% increase of natural frequencies from mode 1 to mode 3 and 36.3%, 15% and 13.2% of E′, E″ and Tanδ, respectively, when compared to GLARE (glass fibre reinforced aluminium laminated epoxy). TiO2-reinforced hybrid FML shows the highest natural frequencies among all nanohybrid FMLs. The results summarise that natural frequencies and viscoelastic properties of nanohybrid FMLs are sensitive to the type of fibre, nano particle reinforcement and its size. A stereo microscope and a scanning electron microscope (SEM) were used to analyse the defects at the interface and the nanoparticle dispersion in the matrix, respectively. Further, a numerical model was developed to perform free vibration analysis, and it was noticed that the results were similar to experimental values.

Pengaruh Pengerolan Alur Pelat Heksagonal Terhadap Frekuensi Pribadinya Dalam Kondisi Bebas-Bebas

Public interest in pick-up cars as a means of transportation for transporting goods has continued to increase lately because they are considered more flexible for transporting raw materials, workshop products and agricultural products and are capable of being operated on urban and rural roads that have different road roughness, as well as in very high traffic conditions. Plate panels that must be used in pick-up vehicles need to be designed as thin as possible but have high stiffness and natural frequency so that they are more efficient in fuel use and able to withstand vibrations that occur during driving. This study aims to determine the natural frequency that occurs in the plate panel profile for vehicle bodies resulting from the cold rolling process. The galvanized steel plates used are 0.6 and 0.8 mm thick. The natural frequency test method is used with free boundary conditions, where the conditioning plate is suspended by a rope. The natural frequency test tool used is the vibroport 80 at an existential pressure of 10 grams, with the hammer hitting the centre of the panel and the sensors being positioned at 0 and 90 degrees. Based on the test results that have been carried out, the panel specimen with a thickness of 0.8 mm obtained the highest natural frequency value of 922.5 Hz, while for a plate thickness of 0.6 mm, the highest value was only 816.25 Hz. However, the two groups of specimens with plate panel thicknesses of 0.6 and 0.8 mm because of rolling experienced an average increase in natural frequency, reaching 2.3 – 2.5 times when compared to the flat plates without the rolling process. The conclusion is that as the natural frequency value increases, the plate panel stiffness also increases.

On the mechanical properties and vibrational characteristics of the nanoparticle-reinforced composite cylindrical panels in the acidic environment: Numerical and experimental investigation

The purpose of this study is to determine the impact of nano-clay and nano-silica particles on the vibrational characteristics of composite cylindrical panels in corrosive environments. In this context, due to the presence of diluted sulfuric acid as the corrosive solution, the coupling effects of material degradation and hygroscopic loading on the natural frequencies are taken into consideration. In order to achieve this, it is first explored through experiment how adding nanoparticles affects the coefficient of hygroscopic expansion of the glass/epoxy specimens. Using this coefficient, the in-plane loading caused by corrosive solution is then applied in the equations. The mechanical properties and hygroscopic expansion coefficients of the composite samples exposed to the corrosive environment are first determined by certain experimental testing. The equations of motion are derived using the first-order shear deformation theory (FSDT), and the vibration problem is solved using the generalized differential quadrature (GDQ) technique. Investigation is conducted into the effects of various nanoparticles, immersion time, geometrical elements, and boundary conditions on the natural frequencies of the cylindrical panels. It is found that adding nanoparticles can significantly improve the mechanical properties, the corrosion resistance, and the natural frequencies of composites in which the nano-clay is more effective. For example, adding nano-clay and nano-silica particles, respectively, results in 32.32% and 26.29% increase in elasticity modulus of reinforced glass/epoxy composite. In addition, 12.71% and 47.32% improvements are observed in the natural frequency of the nano-clay reinforced composite panel before and after 90 days of immersion in sulfuric acid. In comparison, the nano-silica particles are responsible for 7.80% and 23.03% increase in natural frequency before and after immersion time.

Thermoelastic nonlinear vibration and dynamical response of geometrically imperfect carbon nanotube-reinforced composite plates on elastic foundations including tangential edge constraints

The combined influences of initial geometrical imperfection, elasticity of in-plane constraints of edges, elastic foundations and elevated temperature on the nonlinear vibration and dynamical response of carbon nanotube-reinforced composite rectangular plates are investigated in this paper. Carbon nanotubes (CNTs) are reinforced into matrix according to functionally graded distributions. The properties of CNTs and matrix are assumed to be temperature dependent and effective properties of nanocomposite are determined using an extended rule of mixture. Governing equations in terms of deflection and stress function are established within the framework of thin plate theory including von Kármán nonlinearity, geometric imperfection and interactive pressure from elastic foundation. Analytical solutions are assumed for simply supported plates and Galerkin method is applied to result in nonlinear time differential equation. This nonlinear equation is solved using fourth-order Runge–Kutta scheme. Parametric studies are executed to examine numerous influences on the natural frequency, nonlinear to linear frequency ratio and nonlinear dynamical response of CNT-reinforced composite plates. The results reveal that increase in imperfection size results in increase and decrease in natural frequencies and the amplitude of forced vibration, respectively. In contrast, it is found that the elevated temperature reduces the natural frequencies and enhances the amplitude of forced vibration.

Torsional vibration of simply supported nanoplate using nonlocal mathematical model

Present article is promoted to analyze the torsional vibration of simply supported nanoplate using nonlocal elasticity model. The equations motion of the nonlocal nanoplate are evaluated by rewriting the classical Hooke’s law through Eringen‘s model. Then, the numerical calculations are carried out to examine the reactions of the natural frequency of considered nanoplate to change of small-scale‘s coefficient, nanoplate‘s thickness, and torsional stiffness‘s parameter. The results reported that, any increase in the small-scale‘s parameter leads to a decrease in the natural frequency of nonlocal simply-supported nanoplate, while any increase of torsional stiffness‘s parameter leads to an increase of natural frequency. Additionally, the natural frequency of nonlocal nanoplates noticeably decreases as nanoplate thickness increases. Moreover, the torsional vibration analysis of nanoplates is significantly important in modelling real cases such as the nanodevices, which the nanoplates are common structural components in its designs. As a result, the findings of this investigation may be helpful in understanding torsional vibrations in nanostructures and nanodevices.

Structural and Vibro-Acoustics Optimization of a Car Body Rear Part

The perceived vibro-acoustic comfort, inside the passenger compartment, under driving conditions, is strictly related to the car body torsional behavior. The aim of this work was to identify which parts of a car body most influence the first torsional mode, in order to modify them and acquire an increase in such car body natural frequency. It was also intended to exploit the great potential of 3D printing that allows an increase in the complexity of component shapes, with an acceptable compromise with respect to production costs. A design and material (from steel to aluminum) change of a car body rear part, which was identified as the structural part of the car body with the most relevant impact on the frequency of the first torsional mode, was assessed in terms of structural and vibro-acoustic performances. In particular, with the constraint of increasing the structural and vibro-acoustic performances and, at the same time, minimize the weight of the structure itself, geometric, structural (e.g., type of connections), and material changes of the car body rear part were assessed. Working on a car model dating back to 2008, which was already compliant with structural and vibro-acoustic regulatory norms, an increase of 2 Hz on the first torsional mode frequency of the Trimmed Body model was obtained. In parallel, a weight reduction in the optimized components was also gained. It was also requested to lower the cabin sound pressure levels, optimizing the vibro-acoustic transfer functions from the accelerations at engine mounts and suspension attachment points to the cabin inside. It was shown how the combined use of advanced topological and structural optimization tools, with the capabilities of an unconventional manufacturing technology, such as 3D printing in aluminum, could guarantee an increase in the vibro-acoustics and structural car performances, also gaining a weight reduction.

Static and free vibration analysis of functionally graded annular plates using stress-driven nonlocal theory

This study presents analytical and numerical solutions of the bending and the free vibration analysis of a functionally graded annular nanoplate based on the stress-driven nonlocal theory. The nonlocal equation is obtained using the classical plate theory; the power law distribution is assumed to model changes in material properties throughout the thickness. The governing differential equation is analytically solved for different types of edge supports. The explicit analytical solution is obtained in terms of special functions, namely, hypergeometric and Meijer functions. Furthermore, based on the Galerkin technique, a finite element method is introduced to figure out the nanoplate’s flexural deformation and natural frequencies. The analytical and numerical solutions are compared with those available in the literature. The size effects in the nonlocal theory and FGM’s gradient properties have been discussed, considering clamped and simply supported boundary conditions. According to the stress-driven nonlocal model, size-dependent flexural responses of the plate demonstrate stiffening behavior with increasing nonlocal parameters. Which, in general, leads to a decrease in the value of transversal deformation and an increase in natural frequencies when compared to the plate’s local solutions.