a b s t r a c tLong term dynamics of a class of mechanical systems is investigated in a computationally efficient way. Due to geometric complexity, each structural component is first discretized by applying the finite element method. Frequently, this leads to models with a quite large number of degrees of freedom. In addition, the composite system may also possess nonlinear properties. The method applied overcomes these difficulties by imposing a multi-level substructuring procedure, based on the sparsity pattern of the stiffness matrix. This is necessary, since the number of the resulting equations of motion can be so high that the classical coordinate reduction methods become inefficient to apply. As a result, the original dimension of the complete system is substantially reduced. Subsequently, this allows the application of numerical methods which are efficient for predicting response of small scale systems. In particular, a systematic method is applied next, leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. An appropriate continuation scheme is also applied, leading to evaluation of complete branches of periodic solutions. In addition, the stability properties of the located motions are also determined. Finally, respresentative sets of numerical results are presented for an internal combustion car engine and a complete city bus model. Where possible, the accuracy and validity of the applied methodology is verified by comparison with results obtained for the original models. Moreover, emphasis is placed in comparing results obtained by employing the nonlinear or the corresponding linearized models.

Cancer is a diverse disease characterized by abnormal cell growth and the ability to invade or spread to other parts of the body. Because the yearly cancer rate is increasing, an important area for cancer researchers is to improve the ability to detect and treat cancer early. The current study analyzes the potential of flow cytometry to be used to detect circulating tumor cells (CTCs) in patients with various cancer types and stages. CTCs are cells that have detached from the primary tumor and entered the blood stream in the process of metastasizing to other organs. To determine the accuracy of flow cytometry in detecting CTCs, a comparative study was performed on healthy donors. In this study, blood samples from patients with breast, prostate, pancreatic, colon and skin cancer were analyzed and compared with healthy donors. The data were collected and analyzed statistically with receiver operating characteristic curve analysis. The results indicate that CTCs can be detected in over 83% of the cancer patients and therefore may be a promising method for diagnosing cancer.

In the first part of this study, the basic steps of a methodology are presented, leading to a long time response of a class of periodically excited mechanical models with contact and dry friction. In particular, the models examined belong to the special class of Filippov-type dynamical systems, which possess continuous displacements and velocities, but exhibit discontinuities in their accelerations. The direct determination of periodic steady state response of this class of models is achieved by combining suitable numerical integration of the equations of motion with an appropriate technique yielding the corresponding monodromy matrix. This matrix, which arises from a linearization of the motion around a located periodic solution, involves saltations (jumps) and is also useful in predicting its stability properties. The analytical part is complemented by a suitable continuation procedure, enabling evaluation of complete branches of periodic motions. In the second part of the study, the effectiveness of the methodology developed is confirmed by presenting representative sets of numerical results obtained for selected examples. The first two of them are single degree of freedom oscillators. Besides investigating some interesting aspects of regular periodic response, some cases involving rich dynamics of the C. Theodosiou · A. Pournaras · S. Natsiavas ( ) class of the system examined are also studied in a systematic way. The last example is a more involved and challenging model, related to the function of an engine valve and characterized by large numerical stiffness.

Fast and accurate simulation of mechanical structures with complex geometry requires application of the finite element method. Τhis leads frequently to models with a relatively large number of degrees of freedom, which may also possess nonlinear properties. Things become more complicated for systems involving unilateral contact and friction. In classical structural dynamics approaches, such constraints are usually modeled by special contact elements. The characteristics of these elements must be selected in a delicate way, but even so the success of these methods can not be guaranteed. This study presents a numerical methodology, which is suitable for determining dynamic response of large scale finite element models of mechanical systems with multiple unilateral constraints. The method developed is based on a proper combination of results from two classes of direct integration methodologies. The first one includes standard methods employed in determining dynamic response of structural models possessing smooth nonlinearities. The second class of methods includes specialized methodologies that simulate response of dynamical systems with unilateral constraints. The validity and effectiveness of the methodology developed is illustrated by numerical results.

Dynamic response related to fatigue prediction of an urban bus is investigated. First, a quite complete model subjected to road excitation is employed in order to extract sufficiently reliable and accurate information in a fast way. The bus model is set up by applying the finite element method, resulting to an excessive number of degrees of freedom. In addition, the bus suspension units involve nonlinear characterstics. A step towards alleviating this difficulty is the application of an appropriate coordinate transformation, causing a drastic reduction in the dimension of the final set of the equations of motion. This allows the application of a systematic numerical methodology leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. Next, typical results were obtained for excitation resulting from selected urban road profiles. These profiles have either a known form or known statistical properties, expressed by an appropriate spatial power spectral density function. In all cases examined, the emphasis was put on investigating ride response. The main attention was focused on identifying areas of the bus suspension and frame subsystems where high stress levels are developed. This information is based on the idea of a nonlinear transfer function and provides the basis for applying suitable criteria in order to perform analyses leading to prediction of fatigue failure.