Search Results (22)

Fiber-reinforced and laminated composite materials, widely used in engineering applications, may develop periodic curvature during manufacturing due to technological requirements. Given such curvatures in widely used composites, static and dynamic analyses of plates and shells under loads, along with related stability issues, have been extensively investigated. However, studies focusing specifically on the static analysis of such materials remain limited. Composite materials with structural curvature exhibit complex mechanical behavior, making their analysis particularly challenging. Predicting their mechanical response is crucial in engineering. In response to this need, the present study conducts a static analysis of plates made of periodically curved composite materials using the Navier method. The plate equations were derived based on the Kirchhoff–Love plate theory within the framework of the Continuum Theory proposed by Akbarov and Guz’. Using the Navier method, deflection, stress, and moment distributions were obtained at every point of the plate. Numerical results were computed using MATLAB. After verifying the convergence and accuracy of the developed MATLAB code by comparing it with existing solutions for rectangular homogeneous isotropic and laminated composite plates, results were obtained for periodically curved plates. This study offers valuable insights that may guide future research, as it employs the Navier method to provide an analytical solution framework. This study contributes to the limited literature with a novel evaluation of the static analysis of composite plates with periodic curvature. Full article

Nano-structures play a crucial role in advancing technology due to their unique properties and applications in various fields. This study examines the forced vibration behavior of an orthotropic nano-system consisting of an elastically connected nanoplate and a doubly curved shallow nano-shell. Both nano-elements are simply supported and embedded in a Winkler-type elastic medium. Utilizing the Eringen constitutive elastic relation, Kirchhoff–Love plate theory, and Novozhilov’s linear shallow shell theory, we derive a system of four coupled nonhomogeneous partial differential equations (PDEs) describing the forced transverse vibrations of the system. We perform forced vibration analysis using modal analysis. The developed model is a novel approach that has not been extensively researched by other authors. Therefore, we provide insights into the nano-system of an elastically connected nanoplate and a doubly curved shallow nano-shell, offering a detailed analytical and numerical analysis of the PDEs describing transverse oscillations. This includes a clear insight into natural frequency analysis and the effects of the nonlocal parameter. Additionally, damping proportional coefficients and external excitation significantly influence the transverse displacements of both the nanoplate and nano-shell. The proposed mathematical model of the ECSNPS aids in developing new nano-sensors that respond to transverse vibrations based on the geometry of the nano-shell element. These sensors are often used to adapt to curved surfaces in medical practice and gas sensing. Full article

Flywheels have been largely used in rotating machine engines to save inertial energy and to limit speed fluctuations. A stress distribution problem is created due to the centrifugal forces that are formed when the flywheel is spinning around, which leads to different levels of pressure and decompression inside its structure. Lack of balance leads to high energy losses through various mechanisms, which deteriorate both the flywheel’s expectancy and their ability to rotate at high speeds. Deviation in the design of flywheels from their optimum performance can cause instability issues and even a catastrophic failure during operation. This paper aims to analytically examine the stress distribution of radial and tangential directions along the flywheel structure within a linear elastic range. The eigenvalues and eigenvectors, which are representative of free vibrational features, were extracted by applying finite element analysis (FEA). Natural frequencies and their corresponding vibrating mode shapes and mass participation factors were identified. Furthermore, Kirchhoff–Love plate theory was employed to model the transverse vibration of the system. A general solution for the radial component of the equation of flywheel motion was derived with the help of the Bessel function. The results show certain modes of vibration identified as particularly influential in specific directions. Advanced time-frequency analysis techniques, including but not limited to continuous wavelet transform (CWT) and Hilbert–Huang transform (HHT), were applied to extract transverse vibration features of the flywheel system. It was also found that using CWT, low-frequency vibrations contribute to the majority of the energy in the extracted signal spectrum, while HHT exposes the high-frequency components of vibration that may cause significant structural damage if not addressed in time. Full article

In this study, the resonant characteristics of the off-center-driven Chladni plates were systematically investigated for the square and equilateral triangle shapes. Experimental results reveal that the number of the resonant modes is considerably increased for the plates under the off-center-driving in comparison to the on-center-driving. The Green’s functions derived from the nonhomogeneous Helmholtz equation are exploited to numerically analyze the information entropy distribution and the resonant nodal-line patterns. The experimental resonant modes are clearly confirmed to be in good agreement with the maximum entropy states in the Green’s functions. Furthermore, the information entropy distribution of the Green’s functions can be used to reveal that more eigenmodes can be triggered in the plate under the off-center-driving than the on-center-driving. By using the multiplication of the resonant modes in the off-center-driving, the dispersion relation between the experimental frequency and the theoretical wave number can be deduced with more accuracy. It is found that the deduced dispersion relations agree quite well with the Kirchhoff–Love plate theory. Full article

In recent years, vibration control utilizing smart materials has garnered considerable attention. In this paper, we aim to achieve vibration suppression of a plate structure with a tail-fin shape by employing piezoelectric actuators—one of the smart materials. The plate structure is rigorously modeled based on the Kirchhoff–Love plate theory, while the piezoelectric actuators are formulated in accordance with the Prandtl–Ishlinskii model. This research proposed a control system that addresses the interference effects arising during vibration control by dividing multiple piezoelectric elements into two groups and implementing MIMO control. The efficacy of the proposed control method was validated through simulations and experiments. Full article

The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young’s modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson’s ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated. Full article

The present work’s main objective is to investigate the natural vibrations of the thin (Kirchhoff–Love) plate resting on time-fractional viscoelastic supports in terms of the Stochastic Finite Element Method (SFEM). The behavior of the supports is described by the fractional order derivatives of the Riemann–Liouville type. The subspace iteration method, in conjunction with the continuation method, is used as a tool to solve the non-linear eigenproblem. A deterministic core for solving structural eigenvibrations is the Finite Element Method. The probabilistic analysis includes the Monte-Carlo simulation and the semi-analytical approach, as well as the iterative generalized stochastic perturbation method. Probabilistic structural response in the form of up to the second-order characteristics is investigated numerically in addition to the input uncertainty level. Finally, the probabilistic relative entropy and the safety measure are estimated. The presented investigations can be applied to the dynamics of foundation plates resting on viscoelastic soil. Full article

The main objective of this work is to investigate the natural vibrations of a system of two thin (Kirchhoff–Love) plates surrounded by liquid in terms of the coupled Stochastic Boundary Element Method (SBEM), Stochastic Finite Element Method (SFEM), and Stochastic Finite Difference Method (SFDM) implemented using three different probabilistic approaches. The BEM, FEM, and FDM were used equally to describe plate deformation, and the BEM was applied to describe the dynamic interaction of water on a plate surface. The plate’s inertial forces were expressed using a diagonal or consistent mass matrix. The inertial forces of water were described using the mass matrix, which was fully populated and derived using the theory of double-layer potential. The main aspect of this work is the simultaneous application of the BEM, FEM, and FDM to describe and model the problem of natural vibrations in a coupled problem in solid–liquid mechanics. The second very important novelty of this work is the application of the Bhattacharyya relative entropy apparatus to test the safety of such a system in terms of potential resonance. The presented concept is part of a solution to engineering problems in the field of structure and fluid dynamics and can also be successfully applied to the analysis of the dynamics of the control surfaces of ships or aircraft. Full article

The paper is concerned with equilibrium problems for two elastic plates connected by a crossing elastic bridge. It is assumed that an inequality-type condition is imposed, providing a mutual non-penetration between the plates and the bridge. The existence of solutions is proved, and passages to limits are justified as the rigidity parameter of the bridge tends to infinity and to zero. Limit models are analyzed. The inverse problem is investigated when both the displacement field and the elasticity tensor of the plate are unknown. In this case, additional information concerning a displacement of a given point of the plate is assumed be given. A solution existence of the inverse problem is proved. Full article

This study analyzes the composite laminated T-beams using the composite beam and laminated composite plate theories. The theoretical formula was derived assuming that the composite T-beam has one- and two-dimensional (1D and 2D) structures. The 1D analysis was performed according to the Kirchhoff-Love hypothesis, thereby considering only the axial strain to derive a relationship between the strain and displacement. The 2D analysis was performed considering the T-beam as a combination of two composite sheets. The effective stiffness of the beam was derived from the stress-strain and moment-curvature relationships. Furthermore, the deflection of the beam and the stress of each laminate were calculated. A simple support beam, made of AS4/3501-6 carbon/epoxy, was used as a composite laminated T-beam. MSC/NASTRAN finite element software was used for analysis. The accuracy of the theoretical formula and limitations of its use was verified using the finite element analysis. Higher accuracy of the theoretical formula was obtained at a composite beam aspect ratio greater than 15. The formula derived in this study is suitable for thin and long beams. Full article

The main motivation of this work was to present a semi-analytical extension of the correspondence principle in stochastic dynamics. It is demonstrated for the stochastic structural free vibrations of Kirchhoff–Love elastic, isotropic and rectangular plates supported by viscoelastic generalized Maxwell dampers. The ambient temperature of the plate affects the dampers only and is included in a mathematical model using the frequency–temperature correspondence principle. The free vibration problem of the plate–viscoelastic damper system is solved using the continuation method and also the Finite Element Method (FEM). The stochastic approach begins with an initial deterministic sensitivity analysis to detect the most influential parameters and numerical FEM recovery of the polynomial representation for lower eigenfrequencies versus these parameters. A final symbolic integration leads to the first four basic probabilistic characteristics, all delivered as functions of the input uncertainties. Full article

The main subject of this study is to determine the optimal position of a fixed number of viscoelastic dampers on the surface of a thin (Kirchhoff-Love) plate. It is assumed that the dampers are described according to the generalized Maxwell model. In order to determine the optimal position of the dampers, a metaheuristic optimization method is used, called the particle swarm optimization method. The non-dimensional damping ratio of the first mode of the plate vibrations is assumed as an objective function in the task. The dynamic characteristics of the plate with dampers are determined by solving the non-linear eigenproblem using the continuation method. The finite element method is used to determine the stiffness matrix and the mass matrix occurring in the considered eigenproblem. The results of exemplary numerical calculations are also presented, where the final optimal arrangement of dampers on the surface of sample plates with different boundary conditions is shown graphically. Full article

The research object of this work is an orthotropic viscoelastic plate with an arbitrarily varying thickness. The plate was subjected to dynamic periodic load. Within the Kirchhoff–Love hypothesis framework, a mathematical model was built in a geometrically nonlinear formulation, taking into account the tangential forces of inertia. The Bubnov–Galerkin method, based on a polynomial approximation of the deflection and displacement, was used. The problem was reduced to solving systems of nonlinear integrodifferential equations. The solution of the system was obtained for an arbitrarily varying thickness of the plate. With a weakly singular Koltunov–Rzhanitsyn kernel with variable coefficients, the resulting system was solved by a numerical method based on quadrature formulas. The computational algorithm was developed and implemented in the Delphi algorithmic language. The plate’s dynamic stability was investigated depending on the plate’s geometric parameters and viscoelastic and inhomogeneous material properties. It was found that the results of the viscoelastic problem obtained using the exponential relaxation kernel almost coincide with the results of the elastic problem. Using the Koltunov–Rzhanitsyn kernel, the differences between elastic and viscoelastic problems are significant and amount to more than 40%. The proposed method can be used for various viscoelastic thin-walled structures such as plates, panels, and shells of variable thickness. Full article

Reconstruction of buildings and structures is becoming one of the main directions in the field of construction, and the design and production of works during reconstruction are significantly different from the ones of new buildings and structures. After carrying out a number of studies on the inspection of the technical condition of buildings in order to determine the effect of defects on the bearing capacity, the criteria for assessing the state of floor slab structures were identified. Conclusions on the state and further work of elements of reinforced concrete structures are considered. The authors achieve the aim of reinforcing flexural elements of reinforced concrete structures with fiber-reinforced mortar, which is especially important for floor elements with increased operational requirements. A technique for constructing a reinforcement layer using fiber-reinforced mortar from coarse basalt fiber has been developed. The parameters of basalt fiber in the reinforcement layer are substantiated. A method for solving problems of the operation of multilayer coatings under the influence of operational loads is used, in which the model prerequisites for describing the operation of layers are simplified, where the bearing layers are represented by classical Kirchhoff-Love plates. When solving problems, the maximum possible number of design features of flexural members is taken into account, in combination with appropriate experimental studies, the method allows us to consider all the variety of structures for reinforcing coatings and meet the needs of their practical application. Full article

The main objective of this study is to conveniently and rapidly develop a new dimensionless number to characterize and predict the deflection of square plates subjected to fully confined blast loading. Firstly, based on the Kirchhoff–Love theory and dimension analysis, a set of dimensionless parameters was obtained from the governing equation representing the response of a thin plate subjected to impact load. A new dimensionless number with a definite physical meaning was then proposed based on dimensional analysis, in which the influence of bending, torsion moment and membrane forces on the dynamic response of the blast-loaded plate were considered along with the related parameters of the blast' energy, the yield strength of the material, the plate thickness and dimensions of the confined space. By analyzing the experimental data of plates subjected to confined blast loading, an approximately linear relationship between the midpoint deflection–thickness ratio of the target plate and the new dimensionless number was derived. On this basis, an empirical formula to predict the deflection of square plates subjected to fully confined blast loading was subsequently regressed, and its calculated results agree well with the experimental data. Furthermore, numerical simulations of square plates subjected to blast loading in a cuboid chamber with different lengths were performed. The numerical results were compared with the calculated data to verify the applicability of the present empirical formula in different scenarios of blast loading from explosions in a cuboid space. It is indicated that the new dimensionless number and corresponding empirical formula presented in this paper have good applicability and reliability for the deflection prediction of plates subjected to fully confined explosions in a cuboid chamber with different lengths, especially when the plates experience a large deflection–thickness ratio. Full article