Showing papers in "International Applied Mechanics in 2018"
TL;DR: In this article, the stress-strain state of open and closed variable-thickness elliptic cylindrical shells is studied using the Mushtari-Donell-Vlasov model and numerical-analytical approach based on splinecollocation and discrete-orthogonalization methods.
Abstract: The stress–strain state of open and closed variable-thickness elliptic cylindrical shells is studied. To solve the problem, the Mushtari–Donell–Vlasov shell model and numerical-analytical approach based on the spline-collocation and discrete-orthogonalization methods are used. Various types of boundary conditions and variable loadings are considered. The influence of the type of variable loading and thickness on the distribution of displacements and stresses in the shells is analyzed.
21 citations
TL;DR: In this article, a composite elliptical cylindrical shell with a curved hole is considered and the system of governing equations based on Timoshenko's refined theory of non-shallow shells and Hooke's law for orthotropic materials is derived.
Abstract: Static problems for a composite elliptical cylindrical shell with a curved hole are formulated and solved numerically using a developed method. The system of governing equations based on Timoshenko’s refined theory of non-shallow shells and Hooke’s law for orthotropic materials is derived. The method is based on the finite-element method. The influence of the mechanical and geometrical parameters of the shell acted upon by a tensile axial force on the stress, strain, and displacement distributions near a circular hole is studied.
17 citations
TL;DR: In this article, the forced non-axisymmetric vibration of stiffened ellipsoidal shells under nonstationary load is formulated and a numerical algorithm for solving the problem is developed, and the results obtained are analyzed.
Abstract: The problem of the forced non-axisymmetric vibration of stiffened ellipsoidal shells under nonstationary load is formulated. A numerical algorithm for solving the problem is developed, and the results obtained are analyzed.
16 citations
TL;DR: The program adaptation of the controller for the flight control system (FCS) of an unmanned aerial vehicle (UAV) is considered and the use of the Lagrange interpolation between true airspeed sub-ranges provides continuous adaptation.
Abstract: The program adaptation of the controller for the flight control system (FCS) of an unmanned aerial vehicle (UAV) is considered. Linearized flight dynamic models depend mainly on the true airspeed of the UAV, which is measured by the onboard air data system. This enables its use for program adaptation of the FCS over the full range of altitudes and velocities, which define the flight operating range. FCS with program adaptation, based on static feedback (SF), is selected. The SF parameters for every sub-range of the true airspeed are determined using the linear matrix inequality approach in the case of discrete systems for synthesis of a suboptimal robust H∞-controller. The use of the Lagrange interpolation between true airspeed sub-ranges provides continuous adaptation. The efficiency of the proposed approach is shown against an example of the heading stabilization system.
13 citations
TL;DR: In this paper, the equations of non-axisymmetric vibrations of three-layer elliptical cylindrical shells with reinforcement rings under non-stationary loading are derived and the elements of this elastic structure are described using the refined Timoshenko-type model of shells and rods.
Abstract: The equations of non-axisymmetric vibrations of three-layer elliptical cylindrical shells with reinforcement rings under non-stationary loading are derived. The elements of this elastic structure are described using the refined Timoshenko-type model of shells and rods. The numerical method of solving the dynamic equations is based on the integro-interpolation method of constructing the finite-difference schemes for equations with discontinuous coefficients. The problem of the dynamic behavior of a three-layer elliptical cylindrical shell with discrete ribs under distributed non-stationary loading is solved. The numerical results are given in the form of plots and analyzed.
13 citations
TL;DR: In this paper, the dynamic characteristics of a thick-walled cylindrical shell are determined numerically using the finite-element method implemented with licensed FEMAR software, and the natural frequencies and modes are compared with those obtained earlier experimentally by the method of stroboscopic holographic interferometry.
Abstract: The dynamic characteristics of a thick-walled cylindrical shell are determined numerically using the finite-element method implemented with licensed FEMAR software. The natural frequencies and modes are compared with those obtained earlier experimentally by the method of stroboscopic holographic interferometry. Frequency coefficients demonstrating how the natural frequency depends on the physical and mechanical parameters of the material are determined.
12 citations
TL;DR: In this paper, the stress-strain state of a continuously inhomogeneous hollow sphere is analyzed using a spatial problem statement, and the axisymmetric problem is solved using the splinecollocation and finite-element methods.
Abstract: The stress–strain state of a continuously inhomogeneous hollow sphere is analyzed using a spatial problem statement. The axisymmetric problem is solved using the spline-collocation and finite-element methods. The SSS of the sphere is investigated for various materials with elastic modulus varying along the radius. The numerical results obtained with two different methods are analyzed.
10 citations
TL;DR: In this article, a new method for determining the latitude of a fixed base is presented based on the strapdown inertial navigation technology using an inertial measurement unit (IMU) consisting of three accelerometers, three gyroscopes, and a processing board.
Abstract: A new method for determining the latitude of a fixed base is presented. This method is based on the strapdown inertial navigation technology using an inertial measurement unit (IMU) consisting of three accelerometers, three gyroscopes, and a processing board. It is shown that constant inclination of the base does not affect the latitude determination. The experiments conducted validate this method. The experimental equipment consists of an IMU with laser gyroscopes and accelerometers. A mathematical model of the error in the latitude that depends on the errors of gyroscopes and accelerometers is developed. The results that demonstrate the requirements to the latitude determination method are presented.
10 citations
TL;DR: In this paper, the geometric nonlinear vibrations of pretensioned orthotropic membrane with four edges fixed, which is commonly applied in building membrane structure, were studied and the nonlinear partial differential governing equations were derived by von Karman's large deflection theory and D'Alembert's principle.
Abstract: The geometric nonlinear vibrations of pretensioned orthotropic membrane with four edges fixed, which is commonly applied in building membrane structure, are studied. The nonlinear partial differential governing equations are derived by von Karman’s large deflection theory and D’Alembert’s principle. Because of the strong nonlinearity of governing equations, the homotopy perturbation method (HPM) to solve them is applied. The approximate analytical solution of the vibration frequency and displacement function is obtained. In the computational example, the frequency, vibration mode and displacement as well as the time curve of each feature point are analyzed. It is proved that HPM is an effective, simple and high-precision method to solve the geometric nonlinear vibration problem of membrane structures. These results provide some valuable computational basis for the vibration control and dynamic design of building and other analogous membrane structures.
10 citations
TL;DR: It is shown by way of an example that the dynamic characteristics of a closed system with dynamic observers hardly differs from those of a system without dynamic observers.
Abstract: The problem of increasing the reliability of the control system of a quadcopter by introducing a dynamic observer is solved. This problem has been thoroughly analyzed for an algorithm of control of motion along the y-axis. It is obvious that a similar approach can be used to control motion along the x-axis. In such a problem statement, the procedure used to choose of the gains is unconventional. The inverse problem of synthesis of the optimal controller is solved. It is shown by way of an example that the dynamic characteristics of a closed system with dynamic observers hardly differs from those of a system without dynamic observers.
10 citations
TL;DR: In this article, a theory and method of solving nonlinear problems of the magnetoelasticity of shells of revolution taking into account Joule heat in the microsecond range are proposed.
Abstract: A theory and method of solving nonlinear problems of the magnetoelasticity of shells of revolution taking into account Joule heat in the microsecond range are proposed. A numerical example is given.
TL;DR: In this article, the problem of the forced resonant vibrations and dissipative self-heating of a hinged flexible beam with piezoelectric sensors and actuators is formulated taking into account the in-plane shear strain.
Abstract: The problem of the forced resonant vibrations and dissipative self-heating of a hinged flexible beam with piezoelectric sensors and actuators is formulated taking into account the in-plane shear strain. The effect of geometrical nonlinearity, in-plane shear strain, and heat transfer conditions on the beam surfaces on the amplitude- and temperature–frequency characteristics of the beam as well as on the thermal failure of the system is studied. The possibility of active damping of the flexural vibration mode with piezoactuators and sensors is examined.
TL;DR: The problem of time optimal control of the motion of a simple pendulum for the classical and modified constraints is formulated and the optimization problem is reduced to a nonlinear programming problem with constraints.
Abstract: A modification of control constraints in optimal control problems for a simple pendulum with a movable pivot is substantiated The problem of time optimal control of the motion of a simple pendulum for the classical and modified constraints is formulated By analytically integrating the system of equations of motion, the optimization problem is reduced to a nonlinear programming problem with constraints This problem is solved numerically with the particle swarm method The proposed method of solving time optimal control problems is generalized to mathematical models that can be integrated analytically
TL;DR: In this paper, an iterative procedure is suggested for obtaining the higher-order approximate solutions of a conservative system comprising an oscillator with cubic and quintic restoring force function, which is similar to the traditional harmonic balance methods but, unlike them, the errors obtained from the previous step are considered at the current step to increase the accuracy of the solution.
Abstract: An iterative procedure is suggested for obtaining the higher-order approximate solutions of a conservative system comprising an oscillator with cubic and quintic restoring force function. The proposed method is similar to the traditional harmonic balance methods but, unlike them, the errors obtained from the previous step are considered at the current step to increase the accuracy of the solution. A comparison of results with those obtained by exact solution and other approximate analytical techniques confirms the accuracy of the method. It is shown that the achieved approximate solutions are valid for both small and large amplitudes of oscillation and can meet the exact solutions with a high level of accuracy in the lower-order of approximations. Furthermore, using the obtained analytical solutions, the effect of cubic and quintic terms on the frequency is discussed.
TL;DR: In this article, the frequency response of a curved microbeam at the primary resonance is determined using the multiple time scales perturbation method, which may be useful to select the optimum values of design parameters.
Abstract: The nonlinear forced vibrations of a curved micro-beam resting on a nonlinear foundation are examined. The equations of motion are derived using Hamilton’s principle and the modified strain gradient theory which is capable to examine the size effects in microstructures. The nonlinear partial differential equations of motion are reduced to a time-dependent ordinary differential equation containing quadratic and cubic nonlinear terms. The frequency response of the curved microbeam at the primary resonance is determined using the multiple time scales perturbation method. From the application point of view, the frequency response curves may be useful to select the optimum values of design parameters. The effects of geometry parameters and foundation moduli on the vibration behavior of the curved microbeam are illustrated.
TL;DR: In this paper, the forced resonant vibrations and vibrational heating of viscoelastic plates with actuators were modeled considering geometrical nonlinearity and transverse shear.
Abstract: The forced resonant vibrations and vibrational heating of viscoelastic plates with actuators are modeled considering geometrical nonlinearity and transverse shear. An approximate analytical solution of the problem is obtained for a hinged rectangular plate by the Bubnov–Galerkin method. The effect of geometrical nonlinearity and shear deformations on the efficiency of active damping of vibrations with piezoelectric actuators is analyzed.
TL;DR: In this article, the effect of initial stresses and half-space of compressible ideal fluid and the thickness of the elastic layer on the phase velocities of quasi-Lamb modes is analyzed.
Abstract: A problem is formulated for quasi-Lamb waves propagating in a prestrained elastic layer interacting with a half-space of compressible ideal fluid. The results are obtained using the three-dimensional equations of linearized theory of finite deformations for the elastic layer and the three-dimensional linearized Euler equations for the compressible ideal fluid. The problem statement and the approach are based on the general solutions of the linearized equations for elastic solid and fluid. The dispersion equations that describe the propagation of quasi-Lamb waves in hydroelastic systems over a wide frequency range are obtained. The effect of initial stresses and half-space of compressible ideal fluid and the thickness of the elastic layer on the phase velocities of quasi-Lamb modes is analyzed. The approach developed and the results obtained for wave processes allow establishing the limits of applicability of the models based on different versions of the theory of small initial deformations. The numerical results are presented in the form of graphs and are analyzed.
TL;DR: In this paper, the contact interaction of a rigid cylindrical ring punch and half-space with initial (residual) stresses is considered disregarding the friction forces in the case of unequal roots of the characteristic equation.
Abstract: The problem of the contact interaction of a rigid cylindrical ring punch and half-space with initial (residual) stresses is considered disregarding the friction forces in the case of unequal roots of the characteristic equation. The study is performed in common form for the theory of large (finite) initial deformations and two variants of the theory of small initial deformations within the framework of the linearized theory of elasticity for arbitrary elastic potential. The numerical results are presented in the form of graphs for Treloar’s potential.
TL;DR: In this paper, a system of perturbed equations of motion with quadratic nonlinearity is considered and boundedness conditions for some of the variables are established for two coupled systems of equations.
Abstract: A system of perturbed equations of motion with quadratic nonlinearity is considered. New estimates of the Lyapunov function are established and two conclusions are formulated. New motion constraints are presented. For two coupled systems of equations, boundedness conditions for some of the variables are established. Practical motion constraints in given domains of initial and subsequent perturbations are established. A system of quasi-linear equations is considered as an example.
TL;DR: In this paper, the Laplace-Carson integral transform method and numerical inversion of the solutions are used to establish the relationship between hereditary kernels that define the scalar properties of isotropic linear viscoelastic materials in combined stress state.
Abstract: The Laplace–Carson integral transform method and numerical inversion of the solutions are used to establish the relationship between hereditary kernels that define the scalar properties of isotropic linear viscoelastic materials in combined stress state. The hereditary creep kernel characterizing the behavior of the viscoelastic Poisson’s ratio with time is identified. The calculation of shear creep strains and transverse creep under uniaxial loading with allowance for the time-dependent Poisson’s ratio are experimentally validated.
TL;DR: In this article, a method for numerical analysis of the elastoplastic axisymmetric stress-strain state of thin shells undergoing nonisothermal deformation along paths of small curvature with allowance for secondary plastic strains and the third invariant of stress deviator is elaborated.
Abstract: A method for numerical analysis of the elastoplastic axisymmetric stress–strain state of thin shells undergoing nonisothermal deformation along paths of small curvature with allowance for secondary plastic strains and the third invariant of stress deviator is elaborated. The stress–strain state of a shell during heating and cooling is analyzed numerically.
TL;DR: In this paper, the problem of propagation of quasi-Lamb wave in a prestrained elastic layer interacting with a half-space of compressible viscous fluid is considered.
Abstract: The problem of propagation quasi-Lamb waves in a prestrained elastic layer interacting with a half-space of compressible viscous fluid is considered. The problem is solved using the three-dimensional linearized equations of theory of finite deformations for the elastic layer and the three-dimensional linearized Navier–Stokes equations for the compressible viscous fluid. A problem statement and approach based on the general solutions of linearized equations for the elastic body and fluid are used. The dispersion equations describing the propagation of quasi-Lamb waves in hydroelastic systems over wide range of frequencies are derived. The effect of the initial stresses and the thickness of the elastic layer and compressible viscous liquid half-space on the phase velocities and damping factors of quasi-Lamb modes are analyzed. The approach developed and the results obtained make it possible to establish the limits of applicability of the models for wave processes, based on different versions of the theory of small initial deformations, the classical theory of elasticity, and the model of ideal fluid. The numerical results are presented in the form of graphs and analyzed.
TL;DR: In this paper, the stress problem for layered hollow inhomogeneous cylinders with concave semi-corrugations is solved in spatial statement, and their stress state is studied depending on the stiffness of the core layer.
Abstract: The stress problem for layered hollow inhomogeneous cylinders with concave semi-corrugations is solved in spatial statement, and their stress state is studied depending on the stiffness of the core layer. To solve the problem, the analytical methods of variable separation, approximation of functions by discrete Fourier series, and the numerical discrete-orthogonalization method are used. Numerical results are analyzed.
TL;DR: In this article, the propagation of a pressure wave in a fluid bounded by two parallel plane boundaries generated by an infinitely long cylindrical electroelastic shell submerged into the fluid is considered.
Abstract: The propagation of a pressure wave in a fluid bounded by two parallel plane boundaries generated by an infinitely long cylindrical electroelastic shell submerged into the fluid is considered To describe the motion of the shell and the processes in the fluid, the equations of the linear theory of shells generalized to the case of electromechanics and the acoustic approximation are used The problem-solving method is based on application of the image source method, the method of separation of variables, and Laplace integral transform The method is used to reduce the problem to an infinite system of Volterra equations with delay arguments, which is numerically solved using the reduction method and regularizing procedures The hydrodynamic pressure is calculated for the case where either step-wise or sinusoidal electric pulse load is applied to the continuous electrodes of the shell
TL;DR: It is shown that an increase in the length and depth of the cavity in the tooth crown leads to an increased in the stress intensity in the crown layers.
Abstract: Using the finite-element method, the stress–strain state of a tooth crown with a caries cavity acted upon by a vertical force is simulated. The tooth crown is modeled by a two-layer cylinder with outer enamel layer and inner dentinal layer. The effect of the location and geometry of the caries cavity and the mechanical properties of the enamel and dentin on the load-bearing capacity of the tooth crown is analyzed. It is shown that an increase in the length and depth of the cavity in the tooth crown leads to an increase in the stress intensity in the crown layers. The stress intensity peaks in the enamel layer near the walls of the caries cavities located near the tooth neck.
TL;DR: In this article, the forced vibrations of a mechanical vibration isolation system consisting of a ball vibration absorber (BVA) with linear viscous resistance and a movable carrier body under an external harmonic load are considered.
Abstract: The forced vibrations of a mechanical vibration isolation system consisting of a ball vibration absorber (BVA) with linear viscous resistance and a movable carrier body under an external harmonic load are considered. Appell’s formalism is used to formulate and numerically solve the equations of combined motion of the heavy ball without sliding in the spherical cavity of the carrier body. The frequency response of the system and curves of the maximum amplitude of vibrations of the carrier body versus the radius of the spherical cavity and the coefficient of viscous resistance of the BVA are plotted. The conditions and constraints on the rolling of the heavy ball in the spherical cavity without sliding are established.
TL;DR: In this article, the authors studied the action of the acoustic radiation force on a rigid spherical particle near the free liquid surface on which a plane sound wave is normally incident and found that the radiation force causes particles to group at the antinodes in the sound field.
Abstract: The action of the acoustic radiation force on a rigid spherical particle near the free liquid surface on which a plane sound wave is normally incident is studied. A standing sound pressure wave with displacement node at the free surface results from the interference between the incident and scattered waves. The dependence of the radiation force on the frequency, the radius of the particle, and the distance between it and the liquid surface is established. It is found out that the nodes and antinodes of the standing sound wave are the equilibrium positions of the particle. The antinodes are stable equilibrium positions, while the nodes are unstable equilibrium positions. It is confirmed that the radiation force causes particles to group at the antinodes in the sound field.
TL;DR: In this article, a technique of describing the damage of deformable inelastic isotropic and elastic orthotropic materials in studying the thermoelastoplastic stress-strain state of compound bodies of revolution under nonaxisymmetrical loading and heating is proposed.
Abstract: A technique of describing the damage of deformable inelastic isotropic and elastic orthotropic materials in studying the thermoelastoplastic stress–strain state of compound bodies of revolution under nonaxisymmetrical loading and heating is proposed. The numerical results are plotted and analyzed.
TL;DR: In this article, the problem of the stress-strain state of quadrangular complex-shaped plates is solved by using spline-collocation, and the two-dimensional boundary-value problem for the system of partial differential equations is reduced to one-dimensional one.
Abstract: The problem of the stress–strain state of quadrangular complex-shaped plates is solved. The solutions of the boundary-value problem obtained with two numerical approaches are compared. One approach is based on discrete-continuous methods. In this approach, the system of governing equations is represented in new coordinates based on variations taking into account the plate geometry. Using spline-collocation, the two-dimensional boundary-value problem for the system of partial differential equations is reduced to one-dimensional one, which is solved by the numerical discrete-orthogonalization method. The other (discrete) approach is based on the finite-element method. The results for trapezoidal plates designed with both approaches are compared. The values of the displacements determined agree with high accuracy.
TL;DR: In this article, two versions of the semi-analytical finite-element method are developed within the framework of the three-dimensional theory of elasticity, and the distributions of the unknown functions over the thickness are obtained by analytically solving the appropriate system of differential equations.
Abstract: Two versions of the semi-analytical finite-element method are developed within the framework of the three-dimensional theory of elasticity. In the first version, the unknown functions are subject to a polynomial finite-element approximation in the planar coordinate X, expanded into Fourier series in the coordinate Y, and are approximated by known polynomials in coordinate Z (thickness). In the second version, linear polynomials are used for the approximation in the coordinate X and the Fourier series are applied in the coordinate Y. The distributions of the unknown functions over the thickness are obtained by analytically solving the appropriate system of differential equations. The reason of developing the two versions of the method is their approximation and arithmetic errors. The stress–strain state of a layered composite slab under local normal and tangential loading is calculated. The site of load application is square with side length equal to the slab thickness. Three types of boundary conditions on a slab bottom surface (free, clamped and resting on an elastic foundation) are considered.