scholarly journals A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic Supports

2021 ◽  
Vol 11 (19) ◽  
pp. 9141
Author(s):  
Yeqing Jin ◽  
Ruiping Yang ◽  
Hengxu Liu ◽  
Haiwei Xu ◽  
Hailong Chen
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Present Method ◽  
Displacement Function ◽  
Vibration Characteristics ◽  
Homogeneous Layer ◽  
Sandwich Beams ◽  
Arbitrary Boundary ◽  
Elastic Supports ◽  
Various Boundary Conditions

Free vibration analyses of lattice sandwich beams with general elastic supports have rarely been discussed in this field’s literature. In this paper, a unified method is proposed to study the free vibration characteristics of lattice sandwich beams under various boundary conditions. The proposed method is to convert the three truss cores of lattice sandwich beams into an equivalent homogeneous layer and introduce two different types of constraint springs to simulate the general elastic support boundary at both ends of lattice sandwich beams. By changing the rigidity of the boundary restraint spring, various boundary conditions can be easily obtained without modifying the solving algorithm and solving process. In order to overcome all the discontinuities or jumps associated with the elastic boundary support conditions, the displacement function of lattice sandwich beams is usually obtained as an improved Fourier cosine series along with four sine terms. On this basis, the unknown series coefficients of the displacement function are treated as the generalized coordinates and solved using the Rayleigh–Ritz method. The correctness of the present method is verified through comparison with existing literature. The calculation results of the present method are highly accurate, indicating that the present method is suitable for analyzing the vibration characteristics of lattice sandwich beams with general elastic supports. In addition, the effects of beam length, panel thickness, core height, radius and truss inclination on the natural frequencies of lattice sandwich beams with arbitrary boundary conditions have been discussed in this paper.

scholarly journals Wave Based Method for Free Vibration Analysis of Ring Stiffened Cylindrical Shell with Intermediate Large Frame Ribs

2013 ◽  
Vol 20 (3) ◽  
pp. 459-479 ◽  
Author(s):  
Meixia Chen ◽  
Jianhui Wei ◽  
Kun Xie ◽  
Naiqi Deng ◽  
Guoxiang Hou
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Structure Type ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Stiffened Cylindrical Shell

Wave based method which can be recognized as a semi-analytical and semi-numerical method is presented to analyze the free vibration characteristics of ring stiffened cylindrical shell with intermediate large frame ribs for arbitrary boundary conditions. According to the structure type and the positions of discontinuities, the model is divided into different substructures whose vibration field is expanded by wave functions which are exactly analytical solutions to the governing equations of the motions of corresponding structure type. Boundary conditions and continuity equations between different substructures are used to form the final matrix to be solved. Natural frequencies and vibration mode shapes are calculated by wave based method and the results show good agreement with finite element method for clamped-clamped, shear diaphragm – shear diaphragm and free-free boundary conditions. Free vibration characteristics of ring stiffened cylindrical shells with intermediate large frame ribs are compared with those with bulkheads and those with all ordinary ribs. Effects of the size, the number and the distribution of intermediate large frame rib are investigated. The frame rib which is large enough is playing a role as bulkhead, which can be considered imposing simply supported and clamped constraints at one end of the cabin and dividing the cylindrical shell into several cabins vibrating separately at their own natural frequencies.

FREE VIBRATION ANALYSIS OF DISCRETELY STIFFENED SKEW PLATES

2001 ◽  
Vol 01 (01) ◽  
pp. 125-144 ◽  
Author(s):  
HUAN ZENG ◽  
CHARLES W. BERT
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
Skew Angle ◽  
Various Boundary Conditions ◽  
Skew Plate ◽  
Convergence Study

Stiffened skew plates find application in various engineering fields. The free vibration characteristics of such plates have been studied by various methods. An orthogonally stiffened skew plate is a skew plate with stiffeners running orthogonal to two opposite edges. To the best knowledge of the present investigators, no previous work has been done for free vibration characteristics of skew plates of such stiffening geometry. The present work studies the free vibration of such plates. The pb-2 Rayleigh–Ritz method was employed due to its accuracy and computational efficiency. The conventional finite element method was also used as a comparative check. A convergence study was first performed for various boundary conditions. Then the vibration of orthogonally stiffened skew plates with different boundary conditions was studied. Close agreement was found between these two methods. The variations of natural frequencies with different parameters, including skew angle ϕ, edge ratio b/a, and height-thickness ratio f/h, were investigated for three types of boundary conditions.

Free vibration and buckling analysis of laminated composites and sandwich microbeams using a transverse shear-normal deformable beam theory

2019 ◽  
Vol 26 (3-4) ◽  
pp. 214-228 ◽  
Author(s):  
Armagan Karamanli ◽  
Metin Aydogdu
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Transverse Shear ◽  
Couple Stress Theory ◽  
Laminated Composite ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Arbitrary Boundary ◽  
Various Boundary Conditions ◽  
Aspect Ratios

In this paper, the free vibration and buckling responses of laminated composite and sandwich microbeams with arbitrary boundary conditions are investigated. The governing equations based on the modified couple stress theory are derived by using the total potential energy of a microbeam and employing a transverse shear-normal deformable beam theory. Extensive analysis results in terms of dimensionless fundamental frequencies and dimensionless critical buckling loads are introduced for various boundary conditions, aspect ratios, orthotropy ratios, fiber orientation angles, thickness to material length scale parameter ratios, and core thickness to face layer thickness ratios.

scholarly journals Free vibration of spherical cap subjected to various boundary conditions

2019 ◽  
Vol 11 (9) ◽  
pp. 168781401987926
Author(s):  
Yuan Du ◽  
Ruidong Huo ◽  
Fuzhen Pang ◽  
Shuo Li ◽  
Yongming Huang ◽  
...  
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Jacobi Polynomials ◽  
Thickness Distribution ◽  
Current Method ◽  
Vibration Characteristics ◽  
Numerical Verification ◽  
Spherical Cap ◽  
Various Boundary Conditions ◽  
Spherical Caps

In this article, the free vibration characteristics of spherical caps with different thickness distribution subjected to general boundary conditions are investigated using a semi-analytical approach. Based on the theory of thin shell, the theoretical model of spherical cap is established. Spherical caps are partitioned into sections along the meridional orientation. The displacement components of spherical caps along the meridional direction are represented by Jacobi polynomials. Meanwhile, Fourier series are utilized to express displacement components in the circumferential direction. Various boundary conditions can be easily achieved by the penalty method of the spring stiffness technique. The vibration characteristics of spherical caps are derived by means of the Rayleigh–Ritz energy method. Reliability and validity of the current method are verified by convergence studies and numerical verification. The comparison of results between the current method, finite element method, and those published in the literature prove that the current method works well when handling free vibration of spherical caps. More results of spherical caps with different geometric specifications and edge conditions are displayed in the form of table and graphic, which may serve as a reference for future studies.

scholarly journals Free Vibration Analysis of Closed Moderately Thick Cross-Ply Composite Laminated Cylindrical Shell with Arbitrary Boundary Conditions

Materials ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 884 ◽  
Author(s):  
Dongyan Shi ◽  
Dongze He ◽  
Qingshan Wang ◽  
Chunlong Ma ◽  
Haisheng Shu
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Governing Equation ◽  
Present Method ◽  
Composite Shell ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Composite Laminated Cylindrical Shell ◽  
Laminated Cylindrical Shell

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.

scholarly journals Wave-Based Method for Free Vibration Analysis of Orthotropic Cylindrical Shells with Arbitrary Boundary Conditions

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Fuzhen Pang ◽  
Ruidong Huo ◽  
Haichao Li ◽  
Cong Gao ◽  
Xuhong Miao ◽  
...  
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Displacement Vector ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Arbitrary Boundary

The wave-based method (WBM) is a feasible method which investigates the free vibration characteristics of orthotropic cylindrical shells under general boundary conditions. Based on Reissner–Naghid’s shell theory, the governing motion equation is established, and the displacement variables are transformed into wave functions formed to satisfy the governing equations. On the basis of the kinematic relationship between the force resultant and displacement vector, the overall matrix of the shell is established. Comparison studies of this paper with the solutions in the literatures were carried out to validate the accuracy of the present method. Furthermore, by analyzing some numerical examples, the free vibration characteristics of orthogonal anisotropic cylindrical shells under classical boundary conditions, elastic boundary conditions, and their combinations are studied. Also, the effects of the material parameter and geometric constant on the natural frequencies for the orthotropic circular cylindrical shell under general boundary conditions are discussed. The conclusions obtained can be used as data reference for future calculation methods.

scholarly journals Application of Adomian Modified Decomposition Method to Free Vibration Analysis of Rotating Beams

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Qibo Mao
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Decomposition Method ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Rotating Beams ◽  
Arbitrary Boundary ◽  
Various Boundary Conditions ◽  
Governing Differential Equation

The Adomian modified decomposition method (AMDM) is employed in this paper for dynamic analysis of a rotating Euler-Bernoulli beam under various boundary conditions. Based on AMDM, the governing differential equation for the rotating beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The computed results for different boundary conditions as well as different offset length and rotational speeds are presented. The accuracy is assured from the convergence and comparison published results. It is shown that the AMDM offers an accurate and effective method of free vibration analysis of rotating beams with arbitrary boundary conditions.

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