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Resonance and anti-resonance frequencies are important parameters that determine the dynamic behavior of mechanical systems. The change of these parameters, which depend on the physical properties of the system such as mass and stiffness, also changes the dynamic behavior of the system. Finding the necessary structural changes to adjust the resonance and anti-resonance frequencies of a system to the desired values is the subject of the inverse structural modification workspace. In this study, a method is presented for calculating the masses required to shift these frequencies to the desired values. The presented method uses the frequency response functions (FRFs) of the original system. For one modification an exact solution can be obtained and for two or more modifications some nonlinear equations have to be solved. For the solution of these nonlinear equations in this study, a meta-heuristic optimization technique grey wolf optimizer is used. The validity of the method was shown on a system of six degrees of freedom consisting of masses and springs and successful results were obtained. Also, it can be said it is very convenient for practical applications as the presented method uses the FRFs of the system directly.

In this study, an analytical solution for dynamic analysis of uniform and nonuniform cross-section cantilever sandwich beam is presented. The sandwich beam was assumed to be an Euler-Bernoulli beam and formed with a thin core and two thin skin layers. So the shear deformations and rotational effects were neglected. The equivalent flexural rigidity was obtained for the entire sandwich structure. Some implementations for the solution method are given and the results are compared with numerical solutions. The usability of the Euler-Bernoulli Beam Theory for thin layered uniform or non-uniform sandwich beams is investigated. The solutions obtained from analytical and numerical solutions are in good agreement.

In many mechanical systems, it is very common to bring together different structural elements or subsystems produced by different producers and create a whole coupled system. It is often not possible to manufacture an entire mechanical system in one place. Although the dynamic properties of each of the subsystems produced by different manufacturers are known, it is a matter that should be known and studied how the dynamic behavior of the new system will be after the creation of a new system by combining these subsystems. In this study, a method for structural coupling of mechanical systems is presented in order to contribute to the solution of structural dynamic problems. It is based on Sherman–Morrison formula known for solving mathematical inverse problems of modified matrices. The method is very useful and practical for real mechanical engineering applications due to only the frequency response functions belong to the coupling coordinates of the subsystems are used. The main highlight of the presented method is there is no need a matrix inversion for calculations.