The present study focuses on the analysis of free vibrations of axisymmetric functionally graded hollow spheres. The material is assumed to be graded in radial di- rection with a simple power law. Matrix Frrbenious me...The present study focuses on the analysis of free vibrations of axisymmetric functionally graded hollow spheres. The material is assumed to be graded in radial di- rection with a simple power law. Matrix Frrbenious method of extended power series is employed to derive the analytical solutions for displacement, temperature, and stresses. The dispersion relations for the existence of various types of pos- sible modes of vibrations in the considered hollow sphere are derived in a compact form. In order to explore the character- istics of vibrations, the secular equations are further solved by using fixed point iteration numerical technique with the help of MATLAB software. The numerical results have been presented graphically for polymethyl methecrylate materials in respect of natural frequencies, frequency shift, inverse quality factor, displacement, temperature change, and radial stress.展开更多
The vibration and sound radiation of a submerged spherical shell are studied in the time-domain by Laplace transform method, where a CW pulse force acts at the apex of the shell. The numerical results for the case of ...The vibration and sound radiation of a submerged spherical shell are studied in the time-domain by Laplace transform method, where a CW pulse force acts at the apex of the shell. The numerical results for the case of long pulse show that the different vibrational modes and the resonant or beat radiated sound are excited for different carrier-frequencies, but litle sound is radiated for some vibrational modes. For the case of short pulse the waveforms of the pulse become widened and deformed, when the pulse propagates between apexes of the shell. Then, the Doubly Asymptotic Approximations (DAA2) and Kirchhoff's Retarded Potential Formulate (KRPF)are used to solve the same problem. It is shown that the results of DAA2 and KRPF method have a good agreement with the results of Laplace transform method.展开更多
The packing densification of binary spherical mixtures under 3D mechanical vibration was studied experimentally. The influences of vibration frequency （ω）, volume fraction of large spheres （XL）, sphere size ratio...The packing densification of binary spherical mixtures under 3D mechanical vibration was studied experimentally. The influences of vibration frequency （ω）, volume fraction of large spheres （XL）, sphere size ratio （r, diameter ratio of small to large spheres）, and container size （D） on the random binary packing density （p） were systematically analyzed. For any given set of conditions, there exist optimal ω and XL to realize the densest random binary packing; too large or small ω and XL is not helpful for densification. The influences of both r and D on p are monotonic; either reducing r or increasing D leads to a high value of p. With all other parameters held constant, the densest random packing occurs when XL is dominant, which is in good agreement with the Furnas relation. Moreover, the highest random binary packing density obtained in our work agrees well with corresponding numerical and analytical results in the literature.展开更多
基金support provided by CSIR New Delhi via project grant No.25 (0184)/10/EMR–II
文摘The present study focuses on the analysis of free vibrations of axisymmetric functionally graded hollow spheres. The material is assumed to be graded in radial di- rection with a simple power law. Matrix Frrbenious method of extended power series is employed to derive the analytical solutions for displacement, temperature, and stresses. The dispersion relations for the existence of various types of pos- sible modes of vibrations in the considered hollow sphere are derived in a compact form. In order to explore the character- istics of vibrations, the secular equations are further solved by using fixed point iteration numerical technique with the help of MATLAB software. The numerical results have been presented graphically for polymethyl methecrylate materials in respect of natural frequencies, frequency shift, inverse quality factor, displacement, temperature change, and radial stress.
文摘The vibration and sound radiation of a submerged spherical shell are studied in the time-domain by Laplace transform method, where a CW pulse force acts at the apex of the shell. The numerical results for the case of long pulse show that the different vibrational modes and the resonant or beat radiated sound are excited for different carrier-frequencies, but litle sound is radiated for some vibrational modes. For the case of short pulse the waveforms of the pulse become widened and deformed, when the pulse propagates between apexes of the shell. Then, the Doubly Asymptotic Approximations (DAA2) and Kirchhoff's Retarded Potential Formulate (KRPF)are used to solve the same problem. It is shown that the results of DAA2 and KRPF method have a good agreement with the results of Laplace transform method.
文摘The packing densification of binary spherical mixtures under 3D mechanical vibration was studied experimentally. The influences of vibration frequency （ω）, volume fraction of large spheres （XL）, sphere size ratio （r, diameter ratio of small to large spheres）, and container size （D） on the random binary packing density （p） were systematically analyzed. For any given set of conditions, there exist optimal ω and XL to realize the densest random binary packing; too large or small ω and XL is not helpful for densification. The influences of both r and D on p are monotonic; either reducing r or increasing D leads to a high value of p. With all other parameters held constant, the densest random packing occurs when XL is dominant, which is in good agreement with the Furnas relation. Moreover, the highest random binary packing density obtained in our work agrees well with corresponding numerical and analytical results in the literature.
