Precise Transfer Matrix Method Research Articles

Modeling and Experiment of the Vibro-Acoustic Response of Cylindrical Shells With Internal Substructures

Abstract This study investigates the theoretical and experimental aspects of the vibro-acoustic characteristics of cylindrical shells with internal substructures. On the theoretical side, a hybrid calculation method is proposed, which combines the condensed transfer function method with the direct stiffness method and the precise transfer matrix method. The cylindrical shell with internal substructures is decoupled, and the governing equations for the cylindrical shell substructure and the internal substructure are separately established. Furthermore, the coupling forces between the cylindrical shell substructure and the plate substructure are solved based on the condensed transfer function method. These coupling forces are then incorporated into the overall transfer equation of the cylindrical shell to obtain the vibro-acoustic response of the coupled structure. Compared with the finite element calculation results, the validity of the calculation method in this paper is verified. In terms of experiments, the natural frequency, mode, and vibration acoustic response of the model were tested and compared with the theoretical results, which was in good agreement. The study demonstrates that the proposed hybrid calculation method based on the condensed transfer function is effective in predicting the vibro-acoustic characteristics of cylindrical shells with internal substructures.

Bellows stiffness characteristics of cord-reinforced air spring with winding formation under preload conditions

The bellows structure in an air spring can be constantly reinforced to cope with the complicated work environment, but it exerts a stronger and stronger effect on the stiffness characteristics of the air spring. However, there is not any effective way for the parameterized solution of the bellows stiffness of the air spring. With the precise transfer matrix method, the bellows stiffness characteristics of a cord-reinforced air spring with winding formation under preload conditions were analyzed in this paper. The thin-shell theory was used to solve the bellows pre-stress of the air spring under preload conditions. The pre-stress was introduced into the equilibrium equation for the bellows. Based on the geometrical and physical equations for the bellows with the complex cord winding characteristics, the precise integration method was borrowed to construct a transfer matrix for the bellows of the air spring under preload conditions. The state vector of the bellows in the air spring was solved through boundary conditions. The iteration method was adopted to develop the expression for the bellows stiffness characteristics, and combined with the theoretical model of pneumatic stiffness to solve the stiffness characteristics of the air spring. The comparison with the prototype test results verified the validity and correctness of the theoretical model. On this basis, we explored the influence of preload conditions, geometrical structure, and material characteristics on the stiffness characteristics of the air spring. The research findings will provide significant guidance for the structural design and material selection of cord-reinforced air springs with winding formation.

Free Vibration of Rubber Matrix Cord-Reinforced Combined Shells of Revolution Under Hydrostatic Pressure

Abstract In this paper, the free vibration of rubber matrix cord-reinforced combined shells of revolution under hydrostatic pressure is investigated by the precise transfer matrix method. Under hydrostatic pressure, deformation and stress are generated in the rubber matrix composite shell. Based on the deformation characteristics of the rope structure, the deformation of the shell under hydrostatic pressure is analyzed. The stress of the shell under hydrostatic pressure is included in the shell differential equation of motion in the form of pre-stress. Then considering the fluid-solid coupling boundary condition, the field transfer matrix of the fluid-filled spherical shell is obtained. By the continuous condition of the state vector of the shell and the transformation relationship of the coordinate system, the transfer matrices at the position of the ring-stiffener and the connection position of the cylindrical shell and spherical shell are derived, and then the whole free vibration equation of the fluid-filled combined shells of revolution is assembled, and the natural frequencies are obtained by the boundary conditions. Eventually, the accuracy and reliability of the proposed method are verified by the results of literature and simulation results. Effects of the structural parameters of the spherical shell, the distribution of the ring-stiffeners, and the hydrostatic pressure on the natural frequencies of the fluid-filled combined shells of revolution are also discussed. Results of this paper can provide reference data for future studies in the related field.

An Experimental and Modeling Study on Vibro-Acoustic Response of Double-Walled Steel Cylindrical Shells

Based on precise transfer matrix method (PTMM), the analytical model of the double-walled steel cylindrical shell was setup by taking into account of the annular plate and interlayer water. Under the linear sweep frequency excitation or the fixed frequency excitation, an experimental model of the double-walled steel cylindrical shell has been designed, which is performed to gain the natural frequencies, forced vibration in air and water, underwater acoustic radiation. The analytical model was established to calculate natural frequencies, vibration acceleration level and sound pressure level and compare with the relevant experimental results. The compared results show that analytical results coincide with the experimental value and prove that the analytical model established by PTMM is reliable and credible. Meanwhile, the forced vibration behaviour of measuring positions at inner and outer shells was investigated both theoretically and experimentally. Effects of different types of external excitations on the vibration and sound radiation of the double-walled cylindrical shell are discussed. As to acoustic radiation, the acoustic excitation plays a leading role in the low-frequency range. The force excitation is a major contributor in middle-high frequency range conversely.

Vibro-acoustic modelling of immersed cylindrical shells with variable thickness

Based on the Precise Transfer Matrix Method (PTMM), the dynamic model is constructed to observe the vibration behaviour of cylindrical shells with variable thickness by solving a set of first-order differential equations. The free vibration of stiffened cylindrical shells with variable thickness can be obtained to compare with the exact solution and FEM results. The reliability of the present method of free vibration is well proved. Furthermore, the effect of thickness on the vibration responses of the cylindrical shell is also discussed. The acoustic response of immersed cylindrical shells is analyzed by a Pluralized Wave Superposition Method (PWSM). The sound pressure coefficient can be gained by collocating points along the meridian line to satisfy the Neumann boundary condition. The mode convergence analysis of the cylindrical shell is carried out to guarantee calculation precision. Also, the reliability of the present method on sound radiation is verified by comparing with experimental results and numerical results.

Vibro-acoustic behavior of double-walled cylindrical shells with general boundary conditions

Vibro-acoustic behaviour of submerged double-walled cylindrical shells with general boundary conditions is analyzed by a precise transfer matrix method (PTMM), which is proposed by combining traditional transfer matrix method with precise integration method. Field transfer matrixes of both inner shell and outer shell are obtained accurately by PTMM respectively. The annular plates are simulated by two methods and exist in the form of point transfer matrixes. The dynamic models of double-walled cylindrical shells are established by assembling whole transfer matrixes. Based on the Helmholtz equation, the interlayer and external fluid loads are described to solve the Neumann boundary. The vibro-acoustic response of the double-walled cylindrical shell can be obtained by determining sound pressure coefficients. The free vibration and sound radiation of analytical models are comparing with numerical results and experimental results to verify the present method. The effects of the general boundary constraint stiffnesses on the free vibration and sound radiation of double-walled cylindrical shells are also discussed.

Experimental studies on the vibro-acoustic behavior of a stiffened submerged conical-cylindrical shell subjected to force and acoustic excitation

An experimental model was made to investigate the influence of force and acoustic excitation on the vibration and underwater sound radiation of the stiffened conical-cylindrical shell. Meanwhile, a coupled precise transfer matrix method and wave superposition method was also proposed to analyze vibro-acoustic responses of combined shells. To test accuracy of the present method, vibration and acoustic results of combined shells are firstly examined. As expected, results of present method are in excellent agreement with the ones in literature and model test. The experimental results show that free vibrations of the experimental test are consistent with the literature data and the present method’s results. Forced vibration and acoustic test results are also well agreed with the numerical results from the coupled precise transfer matrix method/wave superposition method. The comparisons show that the coupled precise transfer matrix method/wave superposition method is reliable and credible to solve the vibro-acoustic response of combined shells. The analysis shows that the acoustic excitation is the key factor for radiated noise in low-frequency range. However, the radiated noise resulted from force excitation is dominant in mid-high frequency band.

Experiment and modeling of vibro-acoustic response of a stiffened submerged cylindrical shell with force and acoustic excitation

Abstract Taken a submerged ring-stiffened cylindrical shell as an experimental model, the experimental studies was investigated to study the effects of force and acoustic excitation on the vibro-acoustic response of the cylindrical shell. A precise transfer matrix method (PTMM) was presented to compare the shell vibration and sound radiation of the submerged stiffened cylindrical shell with the experimental results. The result shows that results from PTMM are in good agreement with the experimental results. It shows that the PTMM is reliable and the result from PTMM is credible. The vibration acceleration response of the water case has less peak numbers and the value is less than that of the air case. The peak value of sound pressure in the force excitation case is relate to structural natural frequency. The peak value of sound pressure in the acoustic excitation case is relate to structural natural frequency and internal cavity natural frequency.

Dynamic modeling and vibration characteristics analysis of submerged stiffened combined shells

A semi-analytical method is present to analysis the vibration response of submerged stiffened combined shells. In general, the submarine hull can be modeled as submerged stiffened combined conical-cylindrical-spherical shells. The precise integration method is imported to develop a precise transfer matrix method (PTMM). The dynamic model is established to solve the dynamic responses of the combined shell in vacuo. The fluid load is described by wave superposition method (WSM). Then the structural responses of a submerged stiffened submarine hull can be obtained by coupled PTMM and WSM method. The effectiveness of the present method has been verified by comparing the frequency parameters of the combined shells and the structural responses of the submerged spherical shell with existing results. Furthermore, the effects of the model truncation, stiffness, damping and fluid load on the structural responses of the combined shells are studied.

Structural and acoustic response of a finite stiffened conical shell

In this paper, a precise transfer matrix method is presented to calculate the structural and acoustic responses of the conical shell. The governing equations of conical shells are written as a coupled set of first order differential equations. The field transfer matrix of the shell and non-homogenous term resulting from the external excitation are obtained by precise integration method. After assembling the field transfer matrixes, the whole matrix describing dynamic behavior of the stiffened conical shell is obtained. Then the structural and acoustic responses of the shell are solved by obtaining unknown sound pressure coefficients. The natural frequencies of the shell are compared with the FEM results to test the validity. Furthermore, the effects of the semi-vertex angle, driving force directions and boundary conditions on the structural and acoustic responses are studied.

The Precise Transfer Matrix Method for Dynamic Characteristic Analysis of Curved Box Beams

The dynamic characteristic as one key feature determines the earthquake response and seismic performance of structures.Curved box beams occur coupling of flexural and torsional modes,which companied with warping.Based on the precise transfer matrix method,precise transfer matrixs for solving the natural frequencies and modes of curved box beam out plane have been derivated.The analysis of vibration characteristics of single-span curved box beam with pinned-pinned ends has been done. Example shows that the precise transfer matrix method is a simple and effective method for dynamic characteristic analysis of curved box beams.

Precise Transfer Matrix Method for Plane-Bucking Analysis of Circular Arch

Arch bridge as well as arch frame of building is òne kind of plane-curved-bar system of bearing pressure.When the load of arch carrying reaches some value, the arch will lost the balance stability. Based on the theory of precise transfer matrix method and differential equation of circular arch in plane, a new method for plane-buckling analysis of circular arch under uniform load is derived, by which the critical load of circular arch with two hinge supports is calculated. Compared with the theoretical solution, they anastomosed each other well, that shows the method is right and effective.

Transfer matrix method for analyzing vibration and damping characteristics of rotational shell with passive constrained layer damping treatment

The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory. Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer. A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology. The numerical results show that present method is accurate and effective.