Dynamic properties of hybrid machine tool body – Theoretical and experimental investigation

The article presents theoretical and experimental investigation in order to obtain dynamic properties of hybrid machine tool body in comparison with cast iron body. For this purpose, the theoretical and experimental modal analyses were carried out. The influence of the mineral cast material for filling voids on the dynamic properties of the machine tool body was discussed. During the analysis, the modes and frequencies of free vibrations, the amplitude values and the damping ratios were compared. Despite lowering the free vibration frequency of the hybrid construction, compared to the cast iron body, in some cases, the dynamic properties were affected. This could be determined on the basis of decreasing the amplitude value of the transfer function (from 12.16% to 58.66%) and the increasing the vibration damping coefficient ratio (from 12.22% to 75.24%) in the case of a hybrid body as compared to a cast iron body. The final conclusions were drawn about the application of mineral casts in the construction of machine tools and its impact on the dynamic properties of the structure.

Free Vibration Analysis of a Graphene-Reinforced Porous Composite Plate with Different Boundary Conditions

Plates are commonly used in many engineering disciplines, including aerospace. With the continuous improvement in the capacity of high value-added airplanes, large transport aircrafts, and fighter planes that have high strength, high toughness, and corrosion resistance have gradually become the development direction of airplane plate structure production and research. The strength and stability of metal plate structures can be improved by adding reinforced materials. This paper studies graphene platelets (GPLs) reinforced with a free vibration porous composite plate. The porous plate is constructed with a multi-layer model in a metal matrix containing uniform or non-uniformly distributed open-cell internal pores. Considering the random and directional arrangement of graphene platelets in the matrix, the elastic modulus of graphene composites was estimated using the Halpin–Tsai micromechanical model, and the vibration frequencies of graphene composite were calculated using the differential quadrature method. The effects of the total number of layers, GPL distribution pattern, porosity coefficient, GPL weight fraction, and boundary conditions on the free vibration frequency of GPLs reinforced porous composite plates are studied, and the accuracy of the conclusions are verified by the finite element software.

Dynamic response analysis of fluid-saturated porous rectangular plates

Based on Biot’s model for saturated porous media, the governing equation of fluid-saturated porous rectangular plates is presented, in which the compressibility of solid particles and fluid and the viscosity of pore fluid is taken into account. A series solution is given for simply-supported fluid-saturated porous plates. The accuracy of the solution is validated by degenerating the fluid-saturated porous rectangular plates into single-phase solid rectangular plates. As a numerical example, the free vibration characteristic and the dynamic response under harmonic loads are analysed. The influence of surface infiltration conditions, porosity, pore fluid permeability coefficient and loading frequency on the free vibration frequency is discussed.

Free Vibration Frequency of Thick FGM Spherical Shells Based on a Third-order Shear Deformation Theory

In this paper, we consider free vibration problems of functionally graded thick spherical shells. The analysis performs by collecting the radial basis functions, according to the Third Order Shear Deformation Theory that accounts for through the thickness deformation using the principle of virtual work. Numerical results include spherical shell panels with all edges clamped or simply supported to demonstrate the accuracy of the present approach.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

Experimental Validation of Role of Cut-Out Parameters on Modal Responses of Laminated Composite — A Coupled FE Approach

The free vibration frequency responses of the laminated composite structure with a cut-out of variable shapes (square/circular/elliptical), position (center/eccentric) and orientation (parallel/inclined) are investigated for the first time in this research including geometrical shapes. The eigenvalues are obtained computationally for the cut-out borne structure via a linear isoparametric finite element model of the composite structure in association with cubic-order of displacement kinematics. Also, a coupled code is prepared in MATLAB environment by joining the higher-order formulation and the simulation model (ABAQUS) to achieve the generic form to investigate the influential cut-out parameter (shape, size and position) on their eigenvalues. Further, a series of experimentations are carried out using the cut-out borne composite panel and compared with the computational frequency, including the experimental properties. Finally, the key behavior is surveyed through different kinds of numerical examples for various design constraint parameters including the cut-out relevant factors (shape, position and orientation) to show the subsequent inclusiveness of the proposed model.

Free vibration analysis of large deformed curved beam incorporating rotary inertia and shear deformation effects and its experimental validation

The paper theoretically and experimentally analyzes free vibration characteristics of statically loaded moving boundary type curved beam considering rotary inertia and shear deformation effects. Effects of rotary inertia and shear deformation are observed for different thickness to span ratios of curved beam. The subject problem is decoupled into two interrelated problems: determining equilibrium configuration under static load and finding the corresponding free vibration frequency. The static problem is analyzed incrementally in body fitted curvilinear frame as it involves geometric nonlinearity due to generalized curvature, large deformation, and moving boundaries. Variational energy principle is employed to derive governing equation. The nonlinear governing equation associated with complicated boundary conditions is solved through iterative geometry updation. Once static problem is solved for current load step, governing equation for dynamic characteristics is derived using Hamilton’s principle. The governing equation gets linearized by using the static configuration, which finally yields a linear eigenvalue problem. Experiment is performed in a dedicated setup with two master leafs having different thickness to span ratios. The roller supported specimens are excited with an instrumented hammer and response signals are captured by accelerometers. The excitation and response signals are recorded using HBM-MX840B data acquisition system. Frequency response functions of the curved beam systems under different static loads are obtained from postprocessing of the dynamic signals in MATLAB®. First two natural frequencies of the specimens are noted from the experimental results and the corresponding theoretical results are generated. The specimens are also modeled in ABAQUS® CAE and finite element results are computed. Comparison between the theoretical, experimental, and finite element results validates the present model. The study also provides some meaningful observations on effects of rotary inertia and shear deformation. Based on the observations, more results are generated for different thickness to span ratios and findings are reported suitably.

Free Vibration Frequency of Thick FGM Circular Cylindrical Shells with Simply Homogeneous Equation by Using TSDT

The objective of this study is to provide the frequency solutions of free vibration in thick FGM circular cylindrical shells by mainly considering both shear correction coefficient and nonlinear coefficient term. This paper investigates the effects of third-order shear deformation theory (TSDT) and the varied shear correction coefficient on the free vibration of thick functionally graded material (FGM), the circular cylindrical shells with simply homogeneous equation under thermal environment. The approach of derivations are given as follows, the varied value of shear correction coefficient is included in the simple homogeneous equation. The nonlinear term of displacement field of TSDT is also included to derive the simply homogeneous equation, some reasonable simplifications in the elements of homogeneous matrix under free vibration of thick FGM circular cylindrical shells are assumed, thus, the natural frequency can be found. Three parameters effect on the frequency of thick FGM circular cylindrical shells are computed and investigated, they are nonlinear coefficient c1 term, environment temperature and power law index. There are some main conclusions obtained, generally the natural frequency results are in decreasing value with the mode shape numbers for the thicker circular cylindrical shells. The values of natural frequencies are also affected by the nonlinear coefficient term.