29 research outputs found
An Analytical Technique for Solving Nonlinear Heat Transfer Equations
In this paper, an analytic technique, namely the New Homotopy Perturbation Method (NHPM) is applied for solving the nonlinear differential equations arising in the field of heat transfer. In this method, the solution is considered as an infinite series expansion where converges rapidly to the exact solution. The nonlinear convective鈥搑adioactive cooling equation and nonlinear equation of conduction heat transfer with the variable physical properties are chosen as illustrative examples and the exact solutions have been found for each case
Nonlinear Vibrations of Multiwalled Carbon Nanotubes under Various Boundary Conditions
The present work deals with applying the homotopy perturbation method to the problem of the nonlinear oscillations of multiwalled carbon nanotubes embedded in an elastic medium under various boundary conditions. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der Waals interlayer forces. The amplitude-frequency curves for large-amplitude vibrations of single-walled, double-walled, and triple-walled carbon nanotubes are obtained. The influences of some commonly used boundary conditions, changes in material constant of the surrounding elastic medium, and variations of the nanotubes geometrical parameters on the vibration characteristics of multiwalled carbon nanotubes are discussed. The comparison of the generated results with those from the open literature illustrates that the solutions obtained are of very high accuracy and clarifies the capability and the simplicity of the present method. It is worthwhile to say that the results generated are new and can be served as a benchmark for future works
Sformu艂owanie metody element贸w sko艅czonych dla drga艅 wielkoamplitudowych w belkach gradientowych
On the basis of Euler-Bernoulli beam theory, the large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The von K谩rm谩n type nonlinear strain-displacement relationship is employed where the ends of the beam are constrained to move axially. The material properties are assumed to be graded in the thickness direction according to the powerlaw and sigmoid distributions. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law index, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible.W oparciu o teori臋 Eulera-Bernouliego przeprowadzono analiz臋 wielkoamplitudowych drga艅 belki gradientowej pos艂uguj膮c si臋 metod膮 element贸w sko艅czonych. Zwi膮zek mi臋dzy odkszta艂ceniem i przemieszczeniem, typu von K谩rm谩na, zastosowano tam, gdzie ko艅ce belki s膮 utwierdzone i mog膮 porusza膰 si臋 osiowo. Zak艂ada si臋, 偶e w艂a艣ciwo艣ci materia艂u zmieniaj膮 si臋 w kierunku poprzecznym (grubo艣ci) zgodnie z funkcj膮 pot臋gow膮 lub sigmoidaln膮. Metoda element贸w sko艅czonych jest zastosowana w celu dyskretyzacji nieliniowych r贸wna艅 steruj膮cych, z kt贸rych po rozwi膮zywaniu metod膮 bezpo艣redniego ca艂kowania numerycznego wyznacza si臋 cz臋stotliwo艣ci drga艅 nieliniowych belki gradientowej dla r贸偶nych warunk贸w brzegowych. Badany jest wp艂yw wyk艂adnika funkcji, amplitudy drga艅, geometrycznych parametr贸w belki i podparcia ko艅c贸w na cz臋stotliwo艣ci drga艅 swobodnych. Wyniki numeryczne, przedstawione w artykule, zgadzaj膮 si臋 dobrze z wynikami podawanymi w dost臋pnej literaturze
Modal localization in vibrations of circular cylindrical shells with geometric imperfections
The present study aims to investigate the effect of geometric imperfections in circular cylindrical shells on the vibration characteristics. Perfect circular shells are characterized by the presence of double shell-like modes, i.e., modes having the same frequency with modal shape shifted of a quarter of wave-length in the circumferential direction. However, in the presence of geometric imperfections, the double natural frequencies split into a pair of distinct frequencies, the splitting is proportional to the level of imperfection. In some cases, the imperfections cause an interesting phenomenon on the modal shapes, which present a strong localization in the circumferential direction. The present study has been carried out by means of a semi-analytical approach. Theoretical formulation were derived based on Sanders鈥揔oiter thin shell theory. The analytical results have been compared with those of standard finite element analyses. The results corresponding to the analysis of modal localization are novel and can be used as a benchmark for further studies
On the buckling load estimation of grid-stiffened composite conical shells using vibration correlation technique
In this paper, the vibration correlation technique (VCT) has been used as a nondestructive method for predicting the buckling load of grid-stiffened composite conical shells. This technique is capable of predicting the buckling load of structures without reaching failure point through modal testing. The grid-stiffened composite conical shell has been fabricated using the filament winding process. To perform the experiment, the fundamental natural frequency of the specimen is measured under stepped axial compression loading. The procedure is followed up without actually reaching the instability point when the structure collapses and is no longer usable. A finite element model has been built using ABAQUS software considering the effect of geometric imperfection in order to determine the correlation between natural frequency and applied compressive load. A comparison of the experimental and numerical approaches indicated that the difference between numerical buckling loads and those obtained via the VCT is negligible. Moreover, the VCT has provided a reliable estimate of the buckling load, especially when the maximum applied load is greater than 67% of the experimental buckling load
Vibration Analysis of a Postbuckled Microscale FG Beam Based on Modified Couple Stress Theory
On the basis of modified couple stress theory, the postbuckling behavior of the Euler-Bernoulli microscale FG beams is investigated by means of an exact solution method. The modified couple stress theory as a nonclassical continuum theory is capable of interpreting the size dependencies which become more significant at micro/nanoscales. The Von-Karman type nonlinear strain-displacement relationships are employed. The thermal effects are also incorporated into formulation. The governing equation of motion and the corresponding boundary conditions are derived using Hamilton鈥檚 principle. The material properties are assumed to be graded in the thickness direction according to the power-law distribution. A closed-form solution is obtained for the postbuckling deformation which is beyond the critical buckling load. To study the vibrations taking place in the vicinity of a buckled equilibrium position, the linear vibration problem is exactly solved around the first three buckled configurations. The natural frequencies of the lowest vibration modes around each of the first three buckled configurations are obtained. The influences of power-law exponent, boundary condition, length scale parameter, and thermal environment changes on the static deflection and free vibration frequencies are studied. A comparison is also made between the present results and those obtained via the classical beam theories
Experimental, numerical and analytical investigation of free vibrational behavior of GFRP-stiffened composite cylindrical shells
The present research aims to investigate the vibration characteristics of stiffened composite cylindrical shells using experimental, numerical and analytical techniques. The specimens are fabricated from continuous glass fiber (GFRP) using a specially-designed filament winding setup. The theoretical formulation is established based on Sanders' thin shell theory. In the analytical approach, a smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of shell in order to obtain the equivalent stiffness parameters of the whole panel. Using the Ritz method, the governing eigenvalue equations are obtained and will then be solved for evaluating the natural frequencies of the GFRP-stiffened composite shells. In order to validate the analytical achievements, experimental modal analysis is conducted on a stiffened cylinder. A 3-D finite element model is built for a further validation. This model takes into account the exact geometric configuration of the stiffeners and the shell. Results confirm the accuracy of the analytical method. Furthermore, the influences of changes in the skin thickness and boundary condition are analyzed
Free Vibration Analysis of Fiber Metal Laminate Annular Plate by State-Space Based Differential Quadrature Method
A three-dimensional elasticity theory by means of a state-space based differential quadrature method is presented for free vibration analysis of fiber metal laminate annular plate. The kinds of composite material and metal layers are considered to be S2-glass and aluminum, respectively. A semianalytical approach which uses state-space in the thickness and differential quadrature in the radial direction is implemented for evaluating the nondimensional natural frequencies of the annular plates. The influences of changes in boundary condition, plate thickness, and lay-up direction on the natural frequencies are studied. A comparison is also made with the numerical results reported by ABAQUS software which shows an excellent agreement