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A vibration characteristic analysis model of a laminated composite double cylindrical shell system (LCDCSS) coupled with several annular plates under general boundary conditions is established. Artificial springs are used to simulate the coupling relationship between substructures to ensure the continuity of displacement both at ends of the shells and coupling boundaries. The variable number of annular plates can be distributed unevenly and coupled elastically. Displacement functions of LCDCSS are expressed with improved Fourier series. Based on the principle of energy, obtain the unknown coefficients of the displacement components by using the Rayleigh–Ritz method. The convergence and effectiveness of the proposed method are verified by comparing with the results with literature and FEM, and then carried out parametric investigation to study the free and steady-state response vibration characteristics of LCDCSS. Rapid prediction of free vibration and response vibration of a double-layer cylindrical shell system with various structures and scales is realized by exploiting the model, and some new results of double-layer cylindrical shell system are explored, which can provide reference for further research. [ABSTRACT FROM AUTHOR]

The target of this article is to present an analysis model of a laminated composite double beam system (LCDBS) for the first time, and study its free vibration behavior by using an exact solution based on the improved Fourier series method. The motion of the system is described by a homogeneous set of six partial differential equations, which is solved by using the first-order shear deformation theory. The improved Fourier series is used to represent the displacement tolerance function of the LCDBS. Compared with the traditional Fourier series, the improved Fourier series introduce the auxiliary functions to eliminate the jumping phenomenon and improve the potential non-smooth continuity at the boundary, making it applicable to general boundary conditions. On this basis, by introducing the improved Fourier series into the equations of motion and boundary conditions, a set of standard linear algebraic equations is formed. Thus, the partial differential solution of complex systems is transformed into a simple set of linear algebraic equations. By solving the linear algebraic equations directly, the natural frequency and modal shape of the LCDBS can be easily obtained. Through the discussion of numerical examples, it is verified that the proposed model has good convergence and accuracy. Then, the free vibration characteristics of the LCDBS are studied, including boundary elastic parameters, geometric parameters, material parameters, and connection elastic parameters. The research work of this article is innovative, and the research results can be used as reference data for future researches in this field. [ABSTRACT FROM AUTHOR]

An analytical model of laminated composite double-plate system (LCDPS) is established, which efficiently analyzes the common 3D plate structure in engineering applications. The proposed model combines the first-order shear deformation theory (FSDT) and the classical delamination theory, and then the LCDPS's vibration characteristics are investigated. In the process of analysis, the improved Fourier series method (IFSM) is used to describe the displacement admissible function of the LCDPS, which can remove the potential discontinuities at the boundaries. Five sets of artificial springs are introduced to simulate the elastic boundary constraints, and the restraints of the Winkler elastic layer can be adjustable. The improved Fourier series is substituted into the governing equations and boundary conditions; then, applying the Rayleigh–Ritz method, we take all the series expansion coefficients as the generalized coordinates. After that, a set of standard linear algebraic equations was obtained. On this basis, the natural frequency and mode shapes of the LCDPS can be obtained by solving the standard eigenvalue problem. By the discussion of numerical examples and the comparison with those of the reports in the literature, the convergence and the reliability of the present approach are validated. Finally, the parametric investigations of the free vibration with complex boundary conditions are carried out, including the influence of boundary conditions, lamination scheme, plate geometric parameters, and elastic coefficient between two plates. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the wave based method (WBM) is presented to analyze the free vibration of composite laminated cylindrical shells with general classical and elastic restrained boundaries. The Reissner-Naghid's theory is adopted to establish the equations of the motion force and moments, the displacement functions of composite laminated cylindrical shells are extended to wave functions which can accurately satisfy the equations of motion and boundary conditions. According to the kinetic relationship of the composite laminated cylindrical shell, the final equation of the composite shell will be obtained to calculate the free vibration results. To validate its accuracy, the vibration results of composite laminated cylindrical shells subject to various boundary conditions including the classical cases, elastic restraints and their combinations by WBM are compared with those published in the literature. The numerical values of the errors are used to prove the high precision and wide application of WBM. Furthermore, the effects of several important parameters, including boundary conditions, length to radius ratio, and elastic modulus on natural frequencies are discussed. Compared with other existing numerical methods, the present solution has the characteristics of complete matrix assembly and high calculation accuracy. When the boundary conditions change, only the initial parameters of the matrix need modifying to adapt. [ABSTRACT FROM AUTHOR]

Abstract This paper applied the modified Fourier series method to investigate the sound-vibration characteristics by establishing a composite laminated thin sector plate-cavity coupled model for the first time based on the classical plate theory (CPT) and Rayleigh-Ritz energy technique. The coupled system consists of an annular sector or circular sector plate backed by an acoustic cavity filled with air or water. Ignoring the influence of boundary conditions, displacements admissible functions of laminated sector plate and sound pressure admissible functions of cavity can be set up as a Fourier series superposition, whose composition are the superposition of Fourier cosine series and supplementary functions. The addition of these supplementary polynomials can effectively eliminate the discontinuity or jump phenomenon on the boundary. The correctness of the established analytical model has been validated by being compared with the results achieved by the finite element method (FEM). On this basis, the coupling mechanism of the weakly coupled system and the strongly coupled system are discussed in detail. In addition, some new results and discussions are given, including the cavity depth, plate thickness, anisotropic degree, varying boundary conditions and so on, which could provide reference for future research. [ABSTRACT FROM AUTHOR]

This paper presents a simple first-order shear deformation theory (SFSDT), which is used for the first time to analyze the vibro-acoustic characteristics of the laminated rectangular plate-cavity coupling system filled with air or water. The proposed theory contains only four unknowns and has greater application scope and higher computation accuracy compared with the classical plate theory (CPT). The admissible functions of displacements and sound pressure of the fluid-structure coupling system are expressed as superposition of the periodic functions based on the Fourier series method. Combined with the artificial virtual spring technology, the proposed theory could be used to analyze the composite coupling system under various combinations of classical boundary conditions or arbitrary elastic boundary conditions. Based on the free vibration analysis of the laminated rectangular plate in-vacuo, both the natural characteristics analysis and the forced response analysis under the excitation of a unit point force or a unit point sound source are carried out. The differences between the weak coupling system with air as medium and the strong coupling system with water as medium are discussed in detail and some new results and new conclusions have been given, which could be the benchmark for the future research. [ABSTRACT FROM AUTHOR]

This paper investigates the vibro-acoustic characteristics of the moderately thick laminated rectangular plate-cavity coupling system by using a modified Fourier series method. In the established model, two boundary conditions of moderately thick laminated rectangular plate are set as uniform elastic supports and non-uniform elastic supports including multi-points elastic supports or partial elastic supports. Besides, the three-dimensional rectangular cavity with rigid walls or impedance walls is discussed in the studied model. The admissible function of the displacements and sound pressure of the coupling system is set as the superposition function combined with Fourier cosine series and Fourier sin series. The Lagrangian energy principle is used to express the coupling system. The vibro-acoustic coupling characteristics can be obtained based on Rayleigh-Ritz technique. It shows good convergence and agreement of the present method by being compared with the finite element method (FEM) and the related literatures. This paper focuses on the study of free and forced vibro-acoustic analysis for the moderately thick laminated rectangular plate-cavity coupling system. Moreover, some results are achieved by discussing the effects of various plate thicknesses, different types of elastic supports, lamination schemes and various impedance boundary conditions on the natural characteristics and responses of the coupling system. [ABSTRACT FROM AUTHOR]

This paper establishes a plate-cavity system to study the vibro-acoustic coupling characteristics based on an improved Fourier series method (IFSM). The established coupling system consists of an acoustic cavity with rigid walls or impendence walls and a single or double thin laminated rectangular plate with various elastic boundary conditions. The energy principle is employed for the modeling of this coupling system. Under the framework, the displacement and sound pressure admissible functions are generally set, no relations to boundary conditions, to the combinations of Fourier cosine series and supplementary functions which can eliminate the discontinuous or jumping phenomenon in the boundaries. All the series expansion coefficients can be obtained through the Rayleigh-Ritz technique. The results obtained by presented method show good convergence and agreement by being compared with those of the literatures or finite element method (FEM). The natural characteristics of the plate-cavity coupling system are studied. The structure vibration response and acoustic pressure response are also investigated by applying structural force to the plate and applying the monopole source into the acoustic cavity. Furthermore, some new results are given, based on the various boundary conditions, anisotropic degrees, lamination schemes and cavity depths, which can be the benchmark for future research. [ABSTRACT FROM AUTHOR]

An improved Fourier series method (IFSM) is applied to study the free and forced vibration characteristics of the moderately thick laminated composite rectangular plates on the elastic Winkler or Pasternak foundations which have elastic uniform supports and multipoints supports. The formulation is based on the first-order shear deformation theory (FSDT) and combined with artificial virtual spring technology and the plate-foundation interaction by establishing the two-parameter foundation model. Under the framework of this paper, the displacement and rotation functions are expressed as a double Fourier cosine series and two supplementary functions which have no relations to boundary conditions. The Rayleigh-Ritz technique is applied to solve all the series expansion coefficients. The accuracy of the results obtained by the present method is validated by being compared with the results of literatures and Finite Element Method (FEM). In this paper, some results are obtained by analyzing the varying parameters, such as different boundary conditions, the number of layers and points, the spring stiffness parameters, and foundation parameters, which can provide a benchmark for the future research. [ABSTRACT FROM AUTHOR]

In this investigation, an improved Fourier series method is presented for the free vibration analysis of the moderately thick laminated composite rectangular plate with non-uniform boundary conditions, a class of problems which are rarely attempted in the literatures. Under the current framework, the displacement and rotation functions are generally sought, regardless of boundary conditions, in spectral form, as a double Fourier cosine series and three supplementary functions. These supplementary functions are introduced to remove the potential discontinuities associated with the original displacement functions along the edges when they are viewed as periodic functions defined within the entire coordinates of laminate plate. The boundary conditions can be readily realized by setting the stiffness of the five types restraining springs. All the series expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of plate vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. The excellent accuracy of the current result is validated by comparing the present results with those Finite Element Method (FEM) data. Numerous new results for free vibration of moderately thick rectangular plates with various multi-points supported and non-uniform partially supported boundary conditions are presented, which may serve as benchmark solution for future researches in the field. [ABSTRACT FROM AUTHOR]

In this article, the authors presented a unified solution for the dynamic analysis of laminated composite annular, circular, and sector plate with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. Regardless of the shapes of the plates and the types of boundary conditions, each displacement and rotation component of the elements is expanded as an improved Fourier series expansion which is composed of a double Fourier cosine series and several auxiliary functions introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries and to accelerate the convergence of series representations. Since the displacement fields are constructed adequately smooth throughout the entire solution domain, an exact solution is obtained based on the Rayleigh-Ritz procedure by the energy functions of the plates. The accuracy, reliability, and versatility of the current solution is fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions. Some new results of free vibration analysis for composite laminated annular sector plate, circular sector plate, annular plate, and circular plate are presented, which may be served as benchmark solution for future computational methods. The effects of the sector angles, layer numbers, and boundary spring stiffness on vibration characteristics of the plates are reported. In addition, the force vibration analysis of the plates is also studied. The influence of the boundary spring stiffness, layer number, orthotropic stiffness ration, and fiber orientation angle on dynamic characteristics of the plates is investigated. [ABSTRACT FROM AUTHOR]

In this paper, a modified Fourier–Ritz approach has been adopted to analyze the free vibration of axially loaded laminated composite beams with arbitrary layup and general boundary conditions, which include classical boundaries, elastic boundaries, and their combination. The influences of Poisson effect, axial deformation, couplings among extensional, bending and torsional deformations, shear deformation, and rotary inertia are incorporated in the formulation. In this present method, regardless of boundary conditions, the displacements and rotation components of the beam are invariantly expressed as a standard Fourier cosine series and several auxiliary closed-form functions. These auxiliary functions are introduced to eliminate any potential discontinuities of the original displacement function and its derivatives, throughout the whole beam including its ends, and to effectively enhance the convergence of the results. Since the displacement field is constructed to be adequately smooth in the whole solution domain, an accurate solution can be obtained by using Ritz procedure based on the energy functions of the beam. Numerical examples are presented for several different boundary conditions, geometric properties, and material parameters. The results show that the present method enables rapid convergence, high reliability, and accuracy. Numerous new free vibration results for axially loaded laminated composite beams with different lamination schemes and elastic restraints are presented. [ABSTRACT FROM AUTHOR]

A universal model of laminated composite coupled double cylindrical shell-annular-rectangular plate system (LDCARS) is established in this paper, including free vibration and steady state response. Firstly, in the framework of FSDT, the modified Fourier series are adopted to express the displacement components of LDCARS. The coupling and boundary conditions are simulated with artificial spring technique. Then the unknown coefficients of the displacement components are solved by means of Rayleigh-Ritz method. By comparing results obtained by the current method to those of the previous literature, the finite element method (FEM) and experiment, the accuracy and correctness of this method is validated. Finally, a series of comprehensive analysis is carried out, and the contribution of main parameters to the vibration characteristics of LDCARS are analyzed. The present work is innovative, and the numerical results can be used as reference data for future researches in this field. [ABSTRACT FROM AUTHOR]

A semi-analytic method is adopted to analyze the free vibration characteristics of the moderately thick composite laminated cylindrical shell with arbitrary classical and elastic boundary conditions. By Hamilton's principle and first-order shear deformation theory, the governing equation of the composite shell can be established. The displacement variables are transformed into the wave function forms to ensure the correctness of the governing equation. Based on the kinetic relationship between the displacement variables and force resultants, the final equation associated with arbitrary boundary conditions is established. The dichotomy method is conducted to calculate the natural frequencies of the composite shell. For verifying the correctness of the present method, the results by the present method are compared with those in the pieces of literatures with various boundary conditions. Furthermore, some numerical examples are calculated to investigate the effect of several parameters on the composite shell, such as length to radius ratios, thickness to radius ratios and elastic restrained constants. [ABSTRACT FROM AUTHOR]

In this paper, a semi-analytical method is adopted to analyze the free vibration characteristics of composite laminated shallow shells under general boundary conditions. Combining two kinds of shell theory, that is, first-order shear deformation shell theory (FSDT) and classical shell theory (CST), to describe the dynamic relationship between the displacement resultants and force vectors, the theoretical formulations are established. According to the presented work, the displacement and transverse rotational variables are transformed into wave function forms to satisfy the theoretical formulation. Related to diverse boundary conditions, the total matrix of the composite shallow shell can be established. Searching the determinant of the total matrix using the dichotomy method, the natural frequency of composite laminated shallow shells is obtained. Through several classical numerical examples, it is proven that the results calculated by the presented method are more accurate and reliable. Furthermore, to discuss the effect of geometric parameters and material constants on the natural frequencies of composite laminated shallow shells, some numerical examples are calculated to analyze. Also, the influence of boundary elastic restrained stiffness is discussed. [ABSTRACT FROM AUTHOR]

The design of structures made of laminated composites greatly depends on the fiber orientation angle and the number of ply layers. In the present study design optimization of composite submerged pressure hull under 3 MPa hydrostatic pressure, which corresponds to 300 m depth, is carried out. The number of layers and orientation angles are optimized for layups [0 m /90 n /0 o , [10 m /-10 n /90 o /-10 p /10 q , [α 1m /α 2n , [α 1m /α 2n /α 3o and [α 1m /α 2n /α 3o /α 4p /α 5q using three unidirectional composite materials, Carbon/Epoxy, Glass/Epoxy, and Boron/Epoxy. The optimization process is carried out in ANSYS Workbench using a Genetic Algorithm. Minimizing the buoyancy factor is used as the objective function of the optimization. The constraints on the optimization process are Tsai-Wu and Tsai-Hill failure criteria and buckling strength factor. Optimization study is also conducted for one selected layup configuration using ABAQUS and ISIGHT. Additionally, a sensitivity analysis is also carried out to study the effect of various design parameters on the optimum design of composite submerged pressure hull. • Design optimization of composite submersible cylinderical pressure hull is conducted using a genetic algorithm and finite element analysis. • The number of layers and orientation angles are optimized for five layup configurations using three unidirectional composite materials. • A sensitivity analysis is also conducted to investigate the effect of design variables on one selected optimum layup configuration. • It is demonstrated that the optimum design not only depends on the ply orientation but also on the number of ply layers. • A maximum improvement ratio of 62.344% in the buoyancy factor over similar steel hull is obtained for Carbon/Epoxy. [ABSTRACT FROM AUTHOR]

• A unified analytical model of a laminated rotary plate-cavity coupled system is established. • A simplified plate theory is applied to study the vibro-acoustic property. • The coupling mechanism is discussed by introducing external force or internal sound source. • The parameterization study on the coupling system is studied. • The experimental analysis of circular plate coupled with cavity is performed. Effective combination of simplified plate theory (SPT) and the improved Fourier-Ritz method, a unified analytical model for the vibro-acoustic property of a laminated rotary plate coupling with an impedance cavity under complex boundary conditions is established in the investigation. The structure-acoustic coupling potential energy generated by the interaction between the flexible laminated plate and the cavity at the interface is added into the energy functional of the structure domain and the acoustic domain, and the energy functional of the plate-cavity coupling system is obtained. The solution equation of the vibro-acoustic coupling property can be gained through Rayleigh-Ritz energy technique. Besides, by introducing external force or internal sound source, the coupling mechanism between the flexible plate and the cavity is explained thoroughly from two aspects. By comparing the results calculated by the classical plate theory (CPT), the finite element method (FEM), the first-order shear deformation theory (FSDT) and Experimental test, the applicability and accuracy of SPT in analyzing the rotary laminated plate-cavity coupling system are verified. Besides, the effects of geometric parameters, material parameters, elastic boundary conditions, acoustic medium on the coupling system are mainly studied, which provides theoretical guidance for the design and noise control of such engineering structures. Image, graphical abstract [ABSTRACT FROM AUTHOR]

A unified analysis model for vibration characteristics of composite laminated annular sector plate, circular sector plate, annular plate and circular plate with various elastic boundary conditions is established based on the simplified plate theory (SPT) and two-dimensional (2D) improved Fourier-Ritz method. It has significant advantages in the study of free and forced vibration of thin-to-moderately thick rotary composite laminated plates. Under the current framework, the displacement admissible functions of the rotary plate are generally expressed as superposition of simple periodic functions, which includes the multiplication of two cosine functions and two complementary polynomials. The introduction of these polynomials can effectively eliminate jumping or discontinuity at the boundaries. The vibration characteristics of the rotary plate can be obtained by Rayleigh-Ritz energy technique. The present method shows fast convergence and good accuracy. The parameterization study on geometric parameters, material parameters and boundary conditions has been carried out to systematically reveal the vibration characteristics of rotary composite laminated plates, which can be the benchmark for the future research. • A unified analytical model of laminated sector, annular and circular plate is established based on simplified plate theory. • The vibration characteristics of composite laminated sector, annular and circular plate are studied. • The effect of structural and material parameters are further discussed. [ABSTRACT FROM AUTHOR]

The anisotropic U-shaped plate are widely applied in aviation, aerospace, ship, machinery and other fields, and the vibration of U-shaped plate will inevitably produce U-shaped plate–cavity​ coupled system in engineering practice. To investigate the vibration characteristics of anisotropic U-shaped plate and the vibro-acoustic characteristics of U-shaped plate–cavity​ coupled system with varying elastic boundary conditions, a modeling method of anisotropic U-shaped plate and U-shaped plate–cavity coupled system is established: Firstly, the modified Fourier series method is effectively applied to establish the analysis models of U-shaped plate and U-shaped plate–cavity coupled system. Secondly, the simulation of complex elastic boundary and coupling boundary is realized by artificial virtual spring technology. Then, the energy equation of the composite laminate plate is established by Rayleigh–Ritz energy technology. Finally, the solution equation is obtained through Hamilton differential principle. The vibration and vibro-acoustic characteristics are obtained. From the analysis of numerical results, the fast and uniform convergence of analysis modeling and the accuracy of the calculated results are verified. The effects of varying boundary conditions, geometric parameters, acoustic wall conditions and anisotropy degree on the vibration characteristics of U-shaped plate and the vibro-acoustic characteristics of U-shaped plate–cavity coupled system are investigated respectively, which can provide a theoretical basis for future research. [Display omitted] • The anisotropic U-shaped plate and U-shaped plate-cavity coupled system model is established. • The improved Fourier–Ritz method is applied to establish the analysis models. • The sound-vibration characteristics of U-shaped plate-cavity coupled system are studied. • The effects of some important parameters on the sound-vibration characteristics are investigated. [ABSTRACT FROM AUTHOR]

Firstly, the Chebyshev-Ritz method is applied to the free in-plane vibration of arbitrary shaped laminated triangular plates with elastic boundary conditions. In order to facilitate the calculation of energy, the arbitrary shaped triangular laminated plate is mapped into a square plate by the coordinate transformation. The constitutive equation of laminated materials is constructed by the equivalent monolayer theory. The displacement functions of the square plate after transformation are generally expressed as two-dimensional Chebyshev polynomials multiplied by coefficients. By means of artificial virtual spring technology, the arbitrary elastic boundary conditions of the plate can be obtained by changing the stiffness values of each spring. The in-plane free vibration characteristics of the triangular laminated plate under different boundary conditions are calculated and the accuracy of this method is verified by comparing with finite element results and experimental results. In this paper, modal experiments of three different triangular plates with free boundary and cantilever support boundary are carried out. The comparison results show that the present method has good convergence, high efficiency and satisfactory actuarial accuracy. Finally, novelty numerical analysis is carried out, the influence of geometrical properties, material parameters and boundary conditions on in-plane modal characteristics of laminated triangular plates are studied in detail. [ABSTRACT FROM AUTHOR]