# Vibration and Reliability Analysis of Non-Uniform Composite Beam under Random Load
###### Abstract  
Non-uniform structures and composite materials have advantages in engineering applications, such as light weight design, multi-functionality, and better buckling /flutter load capacity. For composite structures under dynamic loading conditions, reliability is a key problem to be analyzed during practical operations. However, there is little research work on non-uniform composite structural reliability analysis under random load. The forced vibration response of non-uniform composite beam under random load is firstly solved by the Adomian Decomposition Method (ADM) and iterative process for reliability analysis. Different variation laws of the cross-section rigidity and mass distribution along the length of the non-uniform composite beam structures are analyzed. Various angular frequency and amplitude of random base motion acceleration following Gaussian distribution are considered. Influences of different random excitations  
composite beams [11]. The natural frequencies of longitudinal and transverse vibration modes have been obtained by using the method of power series [12]. Except for the free vibration analysis, [PERSON], [PERSON] and [PERSON] developed a control scheme based on the linear quadratic regulator/independent modal space control (LQR/IMSC) method and used this to do the active vibration control of composite sandwich beams [13]. [PERSON], [PERSON] and [PERSON] used finite element method for damage detection [14]. [PERSON] et al. proved the feasibility of the ultrasonic non-destructive testing with the combination of a strain measurement for fatigue crack details detection of headed shear studs in composite beams [15]. [PERSON] et al. obtained the fitting formula for calculating the equivalent flexural stiffness of composite beams through extensive parameter analysis, and they studied and analyzed the equivalent flexural stiffness of composite frame beams to evaluate their vertical deflection [16]. [PERSON] et al. studied the free and forced vibration of cracked laminated composite beam through the Jacobi-Ritz method and the first-order shear deformation theory (FSDT) [17; 18]. In addition to research and understanding of the uniform composite beam, some researchers have also used various methods to solve and analyze vibration responses of the non-uniform beams. For the geometrically non-uniform beams, the vibration responses of non-uniform beams were solved and analyzed by the amatrix transfer method in [19; 20; 21; 22]. In addition, [PERSON] investigated the free vibration characteristics of a non-uniform cantilever beam carrying multiple two degree-of-freedom spring-damper-mass systems by means of two finite element methods, FEM1 and FEM2 [23]. [PERSON] and [PERSON] used Timoshenko beam theory, Hamilton principle and differential transformation method (DTM) to study the vibration of axially loaded non-uniform spinning twisted Timoshenko beam [24]. [PERSON] et al. gave the semi-analytic solution of moving load problem, which is used to analyze the stress of multi-span uniform beam and non-uniform beam under a moving load [25]. [PERSON] and [PERSON] studied the bending vibration of non-uniform Rayleigh beams with single-edge and double-edge cracks [26]. [PERSON] et al. presented the design, test and analysis of a non-uniform thickness piezoelectric beam for impact vibration energy harvesting. [27]. [PERSON] et al. determined the frequency response curve of a non-uniform beam under nonlinear vibration by the multiple time scale method analytically [28]. Based on the nonlocal elastic theory, [PERSON] and [PERSON] studied the free vibration of non-uniform Euler-Bernoulli nanobeams by using the Rayleigh-Ritz method [29]. [PERSON] studied the free vibration of non-uniform Euler-Bernoulli beams under different support conditions through the Chebyshev wavelet collocation method [30]. For beam structures with anisotropic material properties (FGM), the finite element method was used to solve and analysis the free vibration of FGM beam in references [31; 32; 33].