جستجوی مقالات مرتبط با کلیدواژه « روش تبدیل دیفرانسیلی » در نشریات گروه « مکانیک »

Up to now, several analytical and numerical methods are proposed for free vibration analysis of fluid-structure interaction systems. Concrete gravity or arch dam-reservoir systems and the fluid containers in various shapes, such as rectangular, cylindrical or spherical shapes are the most well-known instances of these “coupled” systems. It should be emphasized that the governing equations of both fluid and structural parts of these coupled systems should be solved simultaneously. In the present article, two classical fluid-structure interaction (FSI) problems, including one-dimensional compressible fluid domain and one or two single degree of freedom (SDOF) system(s) as structural part, are solved in free vibration situation by using differential transform method (DTM). To this end, the solution process is thoroughly described and the numerical results, involving natural frequencies and mode shapes of both systems are obtained in detail. Moreover, to verify the DTM results, the closed-form solution is comprehensively derived for both systems.

In this paper, the free vibration and divergence instability of single-walled carbon nanotubes conveying fluid with considering the effects of non-uniformity of laminar and turbulent flow velocity distribution are investigated based on nonlocal elasticity theory. The non-uniform flow velocity distribution occurs due to the viscosity of the fluids. Based on the Euler-Bernoulli beam theory, the governing equations of motion and boundary conditions are derived by using the Hamilton's principle. The centrifugal force term in the equation of motion of the nonotubes is modified for laminar and turbulent flow profiles. The differential transformation method (DTM) is used to solve the governing differential equations of motion. In vibrational analysis the effects of nonlocal parameter and non-uniform flow velocity on the vibrational properties of the carbon nanotubes with different boundary conditions are investigated. Results show that the effects of nonlocal elasticity may increase the natural frequency and critical divergence flow velocity of systems, while the non-uniform flow velocity decreases the critical divergence flow velocity and natural frequency of nanotube, compared to the uniform case. The validity of the present analysis is confirmed by comparing the results with those obtained in literature.

The present paper studies the effect of nanofluids on natural convection in an assumed Non-Darcy, porous medium on vertical wall embedded with MHD field. The wall temperature and free stream temperature are assumed constant. The base fluid is water that contains 〖Al〗_2 O_(3 )¡CuO_and Cu as nanoparticles. We assumed that the flow is laminar and in no slip and thermal equilibrium condition. Partial differential equations are transformed to ordinary differential equations that are solved by Differential Transform Method (DTM). The current semi-analytic solution is compared with 4th order Runge-Kutta results and a good agreement is achieved. The obtained results show that adding nanoparticles to water, increases the heat transfer amount that is also increased with nanoparticle concentration. On the other hand, increasing the magnetic field decreases the nondimensional heat transfer coefficient.

In this study, the free vibration analysis of a functionally graded rotating double tapered beam is performed. The analysis is based on Euler-Bernoulli beam theory. The Material properties of the beam vary continuously in the thickness direction according to the power-law function. The governing differential equation of motion is derived using the Hamilton’s principle. Natural frequencies are obtained using differential transformation (DTM) technique. The effects of the taper ratios, nondimensional rotational speed, nondimensional hub radius and material volume fraction index on the natural frequencies are discussed. Numerical results are tabulated in several tables and figures. To verify the present analysis, the results of this study are compared with the available results from the existing literature. It is shown that the natural frequencies of a functionally graded rotating double tapered Euler-Bernoulli beam can be obtained with high accuracy by using DTM. It was observed that nondimensional rotational speed, height taper ratio and power-law exponent significantly affect the natural frequency. The effects of hub radius and breadth taper ratio on the natural frequencies are negligible.

In this paper، an analytical method is presented to study thermo-elastic behavior of nanoscale spherical shell subjected to thermal shock based on nonlocal elasticity theory. The shell is considered as elastic، homogeneous and isotropic solid. The nonlocal differential equation of motion is derived in terms of radial displacement. The analytical solution of equation of motion is obtained by Laplace transform and differential transform method (DTM). Mechanical boundary conditions are used to obtain unknown parameters that get in recurrence equation in Laplace domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform method (FLIT). Accuracy of obtained results is evaluated by well-known similar articles. The results have a good agreement in comparison with published data in pervious literatures. Also، the effects of nonlocal parameter and wall thickness of shell on the dynamic characteristics of nanoscale spherical shell are studied in various points across the thickness of shell under thermal shock. The present analytical method provides an appropriate field for analysis of times histories of radial and hoop stresses in a nanoscale shells subjected to various time dependent thermo-mechanical loads.

In this paper، differential transform method (DTM) has been used to determine natural frequencies of free vibration of variable width Euler- Bernoulli isotropic beam. The width of beam varies exponentially with arbitrary non-uniformity parameter. After extracting and nondimensionalization، the governing partial differential equation discretized to two ordinary differential equations in terms of both spatial coordinate and time based on the separation of variables method. Then، for different non-uniformity parameters and boundary conditions، natural frequencies of system have been obtained by using analytical methods and DTM. Boundary conditions are considered as: simple- simple (SS)، clamped- clamped (CC)، clamped- Simple (CS)، free- free (FF)، clamped- free (CF) and simple- free (SF). Comparison of natural frequencies obtained from DTM with analytical solution shows that DTM has a good accuracy in determination of natural frequencies، especially in the lower modes. Since that this method is based on Taylor’s series expansion، more accurate natural frequencies and also natural frequencies of higher modes can be obtain by increasing series size. Results show that for a constant series size، difference between the natural frequencies obtained from DTM with the exact solution increase totally by increasing of mode number.