Free Vibration Analysis of a Rectangular Duct with Different Axial Boundary Conditions

3This paper describes the free vibration analysis of a rectangular duct by using the Rayleigh-Ritz method. Static beam functions are used as admissible functions in the Rayleigh-Ritz method. These basis functions are the static solutions of a point-supported beam under a series of sinusoidal loads. The unique advantage of using this method is that it allows for the consideration of different axial boundary conditions of a duct. Computational results are validated with existing literature data for a simply supported rectangular duct and the finite element method (FEM) for other axial boundary conditions. A validated analytical model is used for generating natural frequency data for different dimensions of rectangular ducts. Further curve fitting has been done for the generated data, and an empirical relation has been presented to calculate the first fundamental natural frequency for different material properties of ducts and different axial boundary conditions, which can be used for any dimensions of the duct within the specified range

Free vibrational analysis of rectangular ducts with different joint conditions

Rectangular ducts are fabricated using thin sheets of a metal with different joint conditions. Due to the presence of these joints, ducts deviate from their assumptive ideal shapes. The objective of the present work is to study the effect of different joint conditions and wall thickness on dynamic characteristics of the ducts. Experimental Modal Analysis (EMA) is performed on three rectangular ducts of different joint types. Numerical Modal Analysis (NMA) is also performed by considering that the ducts are of ideal rectangular shape (without joint condition). Correlation analysis is performed between EMA and NMA in terms of Modal Assurance Criteria (MAC), Relative Frequency Difference (RFD) plots and auto-MAC. It is observed that natural frequencies are in good agreement but there is a discrepancy in mode shapes

Structural-acoustic coupling of circular membrane backed by cylinder cavity using mode coupling approach

Circular membrane backed by cylinder cavity configuration has encountered in various acoustical applications such as musical instruments, automotive horns, sensors and loud speaker design. Vibration Characteristics of membrane are important in understanding sound radiation behavior. Natural frequencies of membrane are influenced by the presence of acoustic cavity, and this interaction is named as structural-acoustic coupling. The coupled natural frequencies of the membrane are predicted using Mode Coupling approach. In this approach, the coupled system behaviour is expressed in terms of the finite number of uncoupled sub-system modes. Acoustic impedances of cavity and structural mobility of membrane are arranged in a matrix form. The matrix representation helps to do efficient computations. It also helps to find modes participation in coupling. The predicted results are corroborated with numerical results

Free vibration analysis of circular membrane backed by cylinder cavity using mode coupling approach

Circular membrane backed by cylinder cavity configuration has come across in various acoustic applications such as musical instruments, sensors and loudspeaker design. The Vibration Characteristics of membrane are influenced by the presence of acoustic cavity, and this interaction is named as structural- acoustic coupling. The coupled natural frequencies of the membrane are predicted using Mode Coupling approach. In this approach, the coupled system behaviour is expressed in terms of the finite number of uncoupled sub-system modes. Acoustic impedances of cavity and structural mobility of membrane are arranged in a matrix form. The matrix representation helps to do efficient computations. It also helps to find modes participation in coupling. The predicted results are corroborated with numerical result

New sesquiterpenes from the marine sponge <i>Dysidea fragilis</i>^†

393-395Three new sesquiterpenes (+)-furodysinin lactone 1, (+)-O-methylfurodysinin lactone 2 and spirofragilide 3 have been isolated from the sponge Dysidea fragilis and characterized based on spectral data and optical rotations