scholarly journals Vibration-based, nondestructive methodology for detecting multiple cracks in bending-torsion coupled laminated composite beams

2021 ◽  
Author(s):  
Stephen R. Borneman ◽  
Seyed M. Hashemi
Keyword(s):  
Composite Structures ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Multiple Cracks ◽  
Frequency Data ◽  
Shape Functions ◽  
Impact Fatigue ◽  
Safe Operation ◽  
Cantilevered Beams ◽  
Laminated Composite Beams

Damage to composite structures occurs from impact, fatigue, or over stress and can be critical in the safe operation of wings or any structural member. This paper presents a method for detection of multiple cracks present in laminated composite bending-torsion coupled cantilevered beams using natural frequency data, a type of Nondestructive testing (NDT). This methodology relies on both experimentally collected natural frequencies and frequencies calculated using a mathematical model. Precise natural frequencies are calculated using a new dynamic finite cracked element (DFCE) formulated within and based on dynamic trigonometric shape functions. An algorithm is devised based on the Adam–Cawley criterion and extended to laminated composites with multiple cracks. This method has shown exceptional convergence on the size and location of cracks using a number of modes of free vibration with and without error in measured frequencies.

scholarly journals Vibration-based, nondestructive methodology for detecting multiple cracks in bending-torsion coupled laminated composite beams

2021 ◽  
Author(s):  
Stephen R. Borneman ◽  
Seyed M. Hashemi
Keyword(s):  
Composite Structures ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Multiple Cracks ◽  
Frequency Data ◽  
Shape Functions ◽  
Impact Fatigue ◽  
Safe Operation ◽  
Cantilevered Beams ◽  
Laminated Composite Beams

Damage to composite structures occurs from impact, fatigue, or over stress and can be critical in the safe operation of wings or any structural member. This paper presents a method for detection of multiple cracks present in laminated composite bending-torsion coupled cantilevered beams using natural frequency data, a type of Nondestructive testing (NDT). This methodology relies on both experimentally collected natural frequencies and frequencies calculated using a mathematical model. Precise natural frequencies are calculated using a new dynamic finite cracked element (DFCE) formulated within and based on dynamic trigonometric shape functions. An algorithm is devised based on the Adam–Cawley criterion and extended to laminated composites with multiple cracks. This method has shown exceptional convergence on the size and location of cracks using a number of modes of free vibration with and without error in measured frequencies.

scholarly journals Vibration-Based, Nondestructive Methodology for Detecting Multiple Cracks in Bending-Torsion Coupled Laminated Composite Beams

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Stephen R. Borneman ◽  
Seyed M. Hashemi
Keyword(s):  
Composite Structures ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Multiple Cracks ◽  
Frequency Data ◽  
Shape Functions ◽  
Impact Fatigue ◽  
Safe Operation ◽  
Cantilevered Beams ◽  
Laminated Composite Beams

Damage to composite structures occurs from impact, fatigue, or over stress and can be critical in the safe operation of wings or any structural member. This paper presents a method for detection of multiple cracks present in laminated composite bending-torsion coupled cantilevered beams using natural frequency data, a type of Nondestructive testing (NDT). This methodology relies on both experimentally collected natural frequencies and frequencies calculated using a mathematical model. Precise natural frequencies are calculated using a new dynamic finite cracked element (DFCE) formulated within and based on dynamic trigonometric shape functions. An algorithm is devised based on the Adam–Cawley criterion and extended to laminated composites with multiple cracks. This method has shown exceptional convergence on the size and location of cracks using a number of modes of free vibration with and without error in measured frequencies.

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

Analytical Solution for Vibration of a Rotating Delaminated Composite Beam with End Mass

2016 ◽  
Vol 16 (06) ◽  
pp. 1550013 ◽  
Author(s):  
Ramazan-Ali Jafari-Talookolaei
Keyword(s):  
Analytical Solution ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Material Anisotropy ◽  
Rotating Speed ◽  
Multipliers Method ◽  
Free Mode ◽  
The Difference ◽  
Laminated Composite Beams

In this paper, the free vibration of rotating laminated composite beams (LCBs) with general lay-ups and single through-the-width delamination is analytically investigated. The Hamilton’s principle is used to derive the coupled governing differential equations and boundary conditions for the rotating delaminated beam, considering the effects of shear deformation, rotary inertia, material couplings (bending–tension, bending–twist and tension–twist couplings), and Poisson’s effect. Both the free mode and constrained mode assumptions are adopted. Analytical solution for the natural frequencies and mode shapes are presented by incorporating the constraint conditions using the Lagrange multipliers method. The accuracy is assured by the convergence of the natural frequencies, as well as by comparison with published results. The effects of various factors such as delamination parameter, fiber angle, hub radius, material anisotropy, end mass and rotating speed are studied in detail. The difference between the results based on the free mode and constrained mode assumptions is also investigated.

scholarly journals Effects of transverse normal strain on bending of laminated composite beams

2018 ◽  
Vol 40 (3) ◽  
pp. 217-232 ◽  
Author(s):  
Trung-Kien Nguyen ◽  
Ngoc-Duong Nguyen
Keyword(s):  
Ritz Method ◽  
Laminated Composite ◽  
Beam Theory ◽  
Composite Beams ◽  
Normal Strain ◽  
Shape Functions ◽  
Height Ratio ◽  
Order Variation ◽  
Transverse Normal Strain ◽  
Laminated Composite Beams

Effect of transverse normal strain on bending of laminated composite beams is proposed in this paper. A Quasi-3D beam theory which accounts for a higher-order variation of both axial and transverse displacements is used to consider the effects of both transverse shear and normal strains on bending behaviours of laminated composite beams. Ritz method is used to solve characteristic equations in which trigonometric shape functions are proposed. Numerical results for different boundary conditions are presented to compare with those from earlier works, and to investigate the effects of thickness stretching, fibre angles, span-to-height ratio and material anisotropy on the displacement and stresses of laminated composite beams.

Modal Analysis of Laminated Composite Beams Based on Elastic Wave Theory

2012 ◽  
Vol 151 ◽  
pp. 275-280 ◽  
Author(s):  
Xue Jing Shen ◽  
Jiao Xia Lan ◽  
Xiao Rong Yang ◽  
Fang Ji
Keyword(s):  
Natural Frequencies ◽  
Vibration Mode ◽  
Laminated Composite ◽  
Wave Theory ◽  
Coefficient Matrix ◽  
Governing Equations ◽  
Laminated Beam ◽  
Unit Impulse ◽  
Impulse Load ◽  
Laminated Composite Beams

The reverberation ray matrix method (MRRM) for analyzing dynamic response of elastic trusses is extended and used to solve the natural frequency and vibration mode of laminated beams. In this study, the MRRM is employed to obtain the frequency response function (FRF) of displacement of a laminated beam under the action of a unit impulse load. The natural frequencies are determined from the peak of the curve of FRF when a resonant frequency is approached. And the mode is retrieved from the ad joint matrix of the coefficient matrix of the governing equations of MRRM. The accuracy of result of MRRM is verified by a simply supported symmetrically laminated beam compared with the analytical solution of classical theory, which is also proved by finite element method (FEM).

Ritz-Based Analytical Solutions for Bending, Buckling and Vibration Behavior of Laminated Composite Beams

2018 ◽  
Vol 18 (11) ◽  
pp. 1850130 ◽  
Author(s):  
Ngoc-Duong Nguyen ◽  
Trung-Kien Nguyen ◽  
Thuc P. Vo ◽  
Huu-Tai Thai
Keyword(s):  
Natural Frequencies ◽  
Laminated Composite ◽  
Composite Beams ◽  
Material Anisotropy ◽  
Height Ratio ◽  
Buckling Loads ◽  
Various Boundary Conditions ◽  
Fiber Angle ◽  
Order Variation ◽  
Laminated Composite Beams

In this paper, the Ritz-based solutions are developed for the bending, buckling and vibration behaviors of laminated composite beams with arbitrary lay-ups. A quasi-3D theory, which accounts for a higher-order variation of both the axial and transverse displacements, is used to capture the effects of both shear and normal deformations on the behaviors of composite beams. Numerical results for various boundary conditions are presented and compared with existing ones available in the literature. Besides, the effects of fiber angle, span-to-height ratio, material anisotropy and Poisson’s ratio on the displacements, stresses, natural frequencies and buckling loads of the composite beams are investigated.

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