Journal of Solid Mechanics
Volume:15 Issue: 3, Summer 2023

In this study, free vibration of stepped beam which is parallel to a uniform beam with same length and elastically connected to it, is considered. Euler-Bernoulli beam theory has been applied to drive equations of motion, abrupt change in height of beam considered as step and Winkler-type elastic layer model serve as connection between beams. The differential transform method (DTM) is applied to determine dimensionless frequencies and mode shapes. In the case of two uniform parallel beams accuracy of solution is verified by comparing with results reported by other methods. It is assumed all supports have one type and fully clamped and fully hinged supports considered for boundary conditions. The effects of different parameters such as: step location and ratio, connecting layer coefficient and boundary conditions on dimensionless frequencies and mode shapes investigated and discussed. This problem handled for first time in present study and results are completely new.

The current article investigates the free vibrations of a three-layer beam. The middle layer of this structure is selected from porous material. For modeling the porous layer, linear pro-elasticity relationships are applied, while Young's modulus and its density vary along the thickness. The upper and lower layers of the structure are reinforced with graphene nanoplates and can take different configurations as Parabolic, linear, and uniform. In this study, with the help of Halpin-Tsai modified theory, equivalent composite coefficients will be extracted. The equations of motion in three layers are derived with the help of third order shear theory, energy method and Hamilton's Principle. Among the significant results of this article, we can mention the effect of amplifiers in improving the vibration behavior of the beam, the effect of pore pressure and volume fraction of reinforcement on the frequency of vibrations. The results of this research can be applied in marine, aerospace, and civil industries.

Using appropriate shape functions and distribution of nodal points in local domains and sub-domains and choosing an approximation or interpolation method has an effective role in the application of meshless methods for the analysis of computational fracture mechanics problems, especially problems with geometric discontinuity and cracks. In this research, computational geometry technique based on Voronoi diagram and Delaunay triangulation is used to distribute nodal points in the sub-domain of analysis. Therefore, with this technique, the nodal points used in the MLS approximation to apply the MLPG method with enriched polynomial base functions are optimally increased in different steps. By doing this process, the problems caused by too closeness of nodal points in computationally sensitive areas that exist in general methods of nodal point distribution are also solved. Comparing the effect of the number of sentences of basic functions and their order in the definition of shape functions, performing the Mono-objective PSO algorithm to find the penalty factor the coefficient, convergence, arrangement of nodal points during the three stages of Voronoi diagram implementation and the accuracy of the answers found indicates, the efficiency of V-E-MLPG method with Ns=7 andto estimation of 3D-SIFs in computational fracture mechanics.

The dimensionless equations of motion are derived based on the Timoshenko beam theory to study the transverse vibration of beams without further usage of any approximate method. The exact closed form characteristic equations are given within the validity of the Timoshenko beam theory for beams having various boundary conditions. Accurate Eigen frequency parameters are presented for a different length to height ratio for each case. The exact closed form mode shapes related to deflection, slope due to bending and stress resultants are also presented and illustrated for some cases. The modal tests are performed for beams with clamped-Free and Free-Free boundary conditions. Finally, the effect of boundary conditions, length to height ratio on the eigenvalues parameters and vibratory behavior of each distinct case are studied. Validity of the derived closed form characteristic equations are checked through comparison of numerical solutions with the available results. It is believed that in the present work, the exact closed form characteristic equations and their associated Eigen functions, except for the beams with simply supported ends, for the rest of considered cases are obtained for the first time.

This work deals with the thermal, mechanical and dynamic properties of hybrid composites reinforced with carbon fibers and aramid fibers, whose matrix is ​​epoxy resin. In this study a series of hybrid fiber composite are prepared with carbon and aramid fibers as reinforcement. Thermal properties are obtained by thermal gravimetric analysis (TGA), Thermo-mechanical analysis (TMA) and hot plate analysis. Also mechanical properties are obtained by tensile and modal analysis tests. The experimental results are compared with the similar theoretical ones. Besides the effect of stacking sequence and hybrid ratio (adding the number of layers of carbon fibers), on the thermal and mechanical properties are investigated. The results show that by increasing the hybrid ratio although the weight of the sample is more, the thermal conductivity of the carbon fibers used is higher than that of the aramid fibers and this increase in thermal conductivity causes the heat to be transferred to the sample much faster and the temperature of the glass increases with the increase of the hybrid ratio. Due to the high stiffness of carbon fibers, adding it to the composite causes, the tensile modulus of the samples increases. By combining carbon fibers with aramid fibers, the toughness of carbon fibers can be increased and at the same time the brittle property of carbon fibers is removed due to the malleability of aramid fibers. It is concluded that aramid fiber has an effective role in improving failure strain due to its high toughness and malleability, while carbon fiber is very fragile. The lowest tensile strength occurs at the hybrid ratio of 29% with a value of 677.66 MPa. which is very close to the theoretical critical hybrid ratio. The results also show when the carbon fibers and aramid fibers are on the outer and the middle layers of the beam respectively, the frequency has a larger value because the aramid fibers have a very high impact resistance.

In this paper, dynamic behaviour of composite tube equipped with piezoelectric actuator ring and conveying fluid flow is studied. The effects of incompressible Newtonian internal fluid flow with constant velocity are considered. The stiffened composite shell with different boundary conditions is exposed to electro- mechanical loading. The governing equations of motion are obtained based on the classical shell theory and using Hamilton’s principle. Then, these equations are discretized by using differential quadrature (DQ) method in longitudinal direction and harmonic differential quadrature (HDQ) method in circumferential direction. Solving these equations results in eigenvalues and mode shapes of the smart pipe conveying fluid. After comparing results with those existing in the literature, the detailed parametric study is conducted, by concentrating on the effects of fluid flow properties, geometry, material and boundary conditions of composite pipe, temperature, and piezo-actuator ring (size and position) on the vibration behavior of the coupled system, as well as dimensionless critical fluid velocity. It is expected that stability of the coupled system strongly depends on the imposed electric load. The present study can be applied for optimum design of sensors and actuators in active control systems, MEMS and biomechanical applications.

In this paper, the creep analysis in a thick-walled cylinder subjected to internal pressure and heat flux at the inner and outer surfaces has been investigated. The displacement field is obtained based on the first-order shear deformation theory and the thermal field is assumed two-dimensional through the thickness and along cylinder whose in radial direction the thermal field is considered linear. The equilibrium equations of the mechanical and thermal fields were derived using the energy method and the principle of virtual work for mechanical loading and heat flux. The creep behavior is described by Bailey-Norton’s time-dependent creep law. Analytical solutions with iteration methods have been used to obtain the stresses, strains, and displacement. The relationship between the temperature and the creep deformation was investigated by examining changes in the radial displacement by increasing the temperature by two to three times at a specific point. The effects of parameters such as pressure, heat flux and radial displacement at different temperatures on stress distribution were discussed. It was shown the circumferential stress accounts for the most changes caused by creep behavior. The presented method provides a semi-analytical solution to investigate the creep behavior of the thick-walled cylinders, which can be used for purposes such as designing and their optimization and parametric study under real temperature loading conditions.

Nowadays, engine components are subjected to higher loads at elevated temperatures due to the increasing requirements regarding weight, performance, and exhaust gas emission. Thus, fatigue due to simultaneous thermal and mechanical loading became a determinant among the damage forms. The effect of a thermal barrier coating (TBC) on the thermal stress and fatigue life in a gasoline engine piston with considering stress gradient was studied. For this purpose, coupled thermo-mechanical analysis of a gasoline engine piston was performed. Then fatigue life of the component was predicted using a standard stress-life analysis and results were compared to the original piston. The results of finite element analysis (FEA) indicated that the stress and number of cycles to failure have the most critical values at the upper portion of piston pin and piston compression grooves. The obtained thermo-mechanical analysis results proved that the TBC system reduces the stress distribution in the piston by about 2.4 MPa and 8.5 MPa at engine speeds of 1000 rpm and 5000 rpm, respectively. The fatigue life results showed that the number of cycles of failure for the coated piston is approximately 12% and 31% higher than the original piston at engine speeds of 1000 rpm and 5000 rpm, respectively. To evaluate properly of results, stress analysis and fatigue life results is compared with experimental damaged piston and it has been shown that critical identified areas, match well with areas of failure in the experimental sample.