In this paper, an identification method is presented for calculating impulsive loads from the propagating mechanical wave which are produced in beam-like structures. This method uses a spectral finite element method (SFEM) model of a segment of the structure to calculate force information from the measured response. The SFEM model is prepared from the Euler-Bernoulli beam equation in the frequency domain. The method is studied using simulated response data and then applied to data collected from an experimental system. Excellent performance is observed for nominal conditions and a parametric study is performed to determine how different factors affect accuracy. Factors studied include structure size, loading location, and loading duration. When limited to only acceleration data, the use of finite differencing methods to obtain the required slope response information is determined to provide the most significant source of error in the identified force information.Keywords SFEM • Structural finite element method • Impact force identification IntroductionDirect measurement of the impact force applied to a mechanical structure is not always possible due to the nature of the impact or the complexity of the structure. Research efforts have focused on developing indirect methods to identify the applied impact force. Inverse methods are a common technique for calculating the impact force from a measured response and an accurate model of the system. Impact force identification has been studied for applications in various fields such as gas pipes [1], composite structures [2], and health monitoring [3].Numerous methods have been developed using inverse methods for impact force identification. Some common techniques for force identification are the deconvolution method [4], state variable formulation [5], the sum of weighted accelerations [6] and the spectral element method [7]. The popular method is the deconvolution technique which uses an assumption of linear behavior of the response to allow for the application of the convolution integral in order to determine the system response. When using this method, the applied force is obtained by extracting the impact force from the relationship between the response and the convolution integral of the impact force and the system's impulse response. This technique has been applied in both the time domain (e.g. [4]) and the spectral domain (e.g. [8]).In the work of Doyle [4], a time domain deconvolution technique was developed in order to experimentally obtain dynamic contact laws. Response behavior was monitored by using strain gauges mounted onto a beam-like structure and the impulsive load was applied by using a pendulous ball. Chang and Sun [9] calculated the applied impact force by using an experimental Green's function and the time domain signal deconvolution. The reconstructed force was found independent of the location of the sensor on a composite beam-like structure.

In this paper, two new methods are proposed to study wave propagation in materials with constitutive law that have nonlinear terms. In the first method, the gauge transformation is used to derive the dynamic shape function. A perturbation method is then applied in order to derive an equation for the wavenumber. The influence of the nonlinearity takes the form of a dependence of the wavenumber on the magnitude of the corresponding frequency component. Under the small amplitude and weak nonlinearity assumptions of the perturbation method, the wavenumber is incorporated into the spectral finite element method (SFEM). The second approach is a numerical method based on alternating frequency-time (AFT) iterations. The nonlinear term represented as a residual nonlinear force term is reduced through the alternating iterations between the time-domain and the frequency-domain. Finally, response behaviors under impact loading predicted with these methods are studied and compared to equivalent linear response behavior.

Identifying the force information and location of an impact event is important for predicting and/or monitoring potential damage to the structures. Directly measuring the impact event and/or locating the impact force is not always possible due to the nature of the impact or the structure. In this work, a new force and location identification method is introduced which utilizes a spectral finite element method (SFEM) model of the structure. The identification technique is demonstrated and studied through its application to beam structures in order to identify impulsive loads. Wave propagation data collected with accelerometers placed on the structure are used in order to determine the impact information.When the impact force is applied between the accelerometers, the calculated force is distributed over the two accelerometer positions on either side of the impact location. The location identification process uses the distribution of the identified force information in order to locate the impact position. This method is performed by matching simulated data to the identified force data by tuning the impact location within the numerical model. When a sufficient level of agreement is achieved, the impact location is determined. In order to validate the results of the numerical studies, identified impact forces and locations are calculated for experimental data and good agreement is observed with the * Corresponding author

In this study, a two-component autoparametric resonator utilizing piezoelectric actuation is proposed. The resonator consists of a plate component which serves as the exciter and a beam component which serves as the oscillator. When an electric signal is applied, the plate component experiences in-plane oscillations which serve to provide axial excitation to the beam component. The system is designed to operate in autoparametric resonance with a plate to beam principal frequency ratio of 1:2. Due to the oscillations of the beam component, a dynamic force and a moment are applied to the plate and can cause out-of-plane oscillations of the plate component. The possibility of internal-resonance between the beam oscillations and the out-of-plane vibrations of the plate component are also considered. A model is derived in order to describe these three motions and the coupling between them. By assuming single mode behavior for each motion, the model is discretized and represented with a three degree-of-freedom model. The model is solved analytically by using the method of multiple scales and results are verified with the numerical simulations. Also, the influence of system parameters on response behavior is studied and the ideal operational conditions and parameter values for nominal performance are obtained.

In this paper a semi-analytical method is developed to analyze functionally graded cylindrical panels. In this method, the radial domain is divided into some finite sub-domains and the material properties are assumed to be constant in each subdomain. Imposing the continuity conditions at the interface of the adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are derived. Solving the linear algebraic equations, the elastic response for the thick-walled FG cylindrical panel is obtained. The method can be used for all material properties variations but in present study, material properties are assumed vary with Mori-Tanaka estimation. Results are compared with the first order shear deformation theory and third order shear deformation theory of Reddy and accuracy of these theories in assessed for FG cylindrical panels with different aspect ratios.