Vietnam Journal of Mechanics

Trong nghiên cứu này, phân tích dao động tự do của các vi mô Timoshenko làm từ Vật liệu Phân lớp Chức năng (FGM) trên nền móng đàn hồi Winkler-Pasternak được thực hiện dựa trên Lý thuyết Căng thẳng Kết hợp Đã Điều chỉnh (MCST). Đặc tính vật liệu của vi mô thay đổi xuyên suốt độ dày theo phân phối công suất và được ước lượng thông qua các kỹ thuật đồng hóa Mori–Tanaka, Hashin-Shtrikman và Voigt. Mô hình vi mô Timoshenko xem xét tham số độ dài được áp dụng. Các phương trình vi phân dao động tự do của các vi mô FGM được thiết lập dựa trên Phương pháp Phần tử Hữu hạn (FEM) và các hàm hình dạng của Kosmatka. Ảnh hưởng của hiệu ứng kích thước, nền móng, vật liệu và các tham số hình học đến tần số dao động sau đó được phân tích. Kết quả cho thấy rằng nghiên cứu này có thể áp dụng cho các FGM khác cũng như các cấu trúc vi mô phức tạp hơn.

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The first natural frequency directly affects the operational conditions of compliant mechanisms in precision engineering systems. To address this challenge, a computational method based on the surface response method is proposed to optimize the frequency of a new one degree of freedom (DOF) compliant mechanism. Initially, a 1-DOF 3D model of a compliant mechanism is built. The dynamic equation and the frequency response are formulated via equivalent stiffness and the Lagrange method. Subsequently, a series of numerical simulations are conducted to find the fundamental frequency of the mechanism. The initial dimensions of the flexible joints are determined, and the initial frequency is analyzed by using finite element analysis. Next, the flexible joints in the designed mechanism are optimized by a variant of the genetic algorithm. The optimized dimensions of the mechanism are found with the thickness of the circular joint of 1.10 mm, the thickness of the leaf joint of 1.19 mm, and the length of the leaf joint of 54.50 mm. The optimized result showed that there is a significant improvement in the frequency of the mechanism, increasing from an initial design of 53.218 Hz to an optimal design of 75.927 Hz with an improvement of 42.6%. This study provides important reference materials for future research on compliant mechanisms.

The interaction between nonlinear oscillations is an interesting problem which has attracted many researches. The interaction between forced and parametric excitations and between two parametric excitations of first and second degrees and first and third degrees, is informed in [1]. In the present paper, we study interaction between two parametric excitations of the second and third degrees. The asymptotic method of nonlinear mechanics in combination with a computer is used.

In [2], a modified Poincare method has been presented and applied to evaluate the period (frequency) of free oscillation in an undamped Duffing oscillator with large cubic restoring nonlinearity. There, the system examined is supposed to be near certain linear one with unknown (to be evaluated) frequency.

This paper presents the use of a commercial Navier-Stokes turbulent flow code (FLUENT) as a mean to evaluate the behavior of a Francis turbine runner for the design and off-design conditions. The flow in the runner is analyzed numerically at different operating points. The numerical results permit to observe physical phenomena in the runner that are important in the process of hydraulic turbo machinery design. Values of different velocity components in the flow, blade pressure distribution ... given by the model are compared with experimental data at nominal and off-design flow conditions. Computer resource involves in the flow analysis should be compatible with the need of design process of a runner. Therefore 12 hours of CPU time can be considered as acceptable for calculating at each operating point on a computer workstation of medium size power.

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Dynamic modeling and analysis of flexible manipulators play an essential role in optimizing mechanical design parameters and control law of real robot systems. In this paper, a nonlinear dynamic model of a manipulator is formulated based on the Finite Element Method. To analyze the dynamic behavior effectively, a numerical simulation scheme is proposed by taking full advantages of MATLAB and SIMULINK toolboxes. In this manner, the effect of varying payload and link length ratio of the manipulator to its elastic displacement is dynamically taken into account. The simulation results show that the payload and length link ratio have significant influences on the elastic displacements of the system. In particular, a proper spectrum of the link length ratio, in which the flexural displacement of the end point of the manipulator is smallest, is demonstrated. To this end, the proposed methodology could be used further to select optimal geometric parameters for the links of new robot designs.

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In [3, 4, 5] the form of equations of motion in holonomic coordinates has constructed. The equations obtained give an effective tool for investigating complicated systems. In the present paper the form of equations of motion is written in quasi-coordinates. These equations are solved with respect to quasi-accelerations, which allow to define the motion of a holonomic and nonholonomic systems by a closed set of algebraic – differential equations. The reaction forces of constraints imposed on the system under consideration are calculated by means of a simple algorithm. For illustrating the effectiveness of this form of equations an example is considered.