... response of time-periodic system differs distinctly from that of the time-invariant system. Utilizing Sylvester’s theorem and Fourier series expansion method, commonly used in the spectral decomposition for matrix, the frequency response functions (FRFs) of a single-degree-of-freedom (SDOF) parametrically...

... of the supporting springs tend to infinity. In the current solution, each of the in-plane displacement components is expressed as a 2D Fourier series plus four auxiliary functions in the form of the product of a polynomial times a Fourier cosine series. These auxiliary functions are introduced to ensure and improve...

... function method is employed, which possesses good expandability and has significant implications for further vibro-acoustic investigations. The simply supported boundary condition is accounted for by using the method of modal function and the double Fourier series solutions are obtained to characterize...

... by applying the Fourier series expansion to a macrocell spanning two (or more) irreducible unit cells of the periodic medium. This multicell approach allows the simultaneous approximation of low frequency and high frequency dynamic behavior and provides the capability of analyzing the structural response...

... frequency makes this device an effective mechanical Fourier series generator. The proposed topology makes use of symmetry to assign poles and zeros at optimal frequencies. The system zeros play the role of suppressing the energy at certain frequencies while the poles amplify the input at their respective...

... the dynamometer card curve. The parametric equation of the dynamometer card curve is transformed into Fourier series whose coefficients can be computed according to the curve’s chain codes. By means of these coefficients, shape characteristics of the curve are extracted. The Euclidean distance is introduced...

.... In the 2D exact solution, the coupled governing equations for the vibration mode are derived using Fourier series. Using transfer matrix approach and the boundary conditions, homogeneous equations are set up for the variables at the bottom. The determinant of their coefficient matrix is set to zero...

... into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear...

...James McNames, Assistant Professor, Synchronous averaging is difficult to use with epicyclic gear systems because the dominant frequencies are slightly skewed and asymmetrical. This Tech Brief uses Fourier series analysis to add new insight to this phenomenon. The results are illustrated...

... of the equation of motion with a Fourier series analysis suitable to situations where the parametric frequency is a multiple of the forcing frequency. Studies of the behavior for excitation frequencies close to, and far from, the natural frequency lead to a general guideline for selecting the parametric...

.... In this method, the inverse Laplace transform of the controller transfer function is expressed in terms of a Fourier series. This expression leads to an online computation algorithm that allows us to update the values of base functions of the control force at each digital sampling time. The effectiveness...