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Cardiac cine magnetic resonance imaging (CMRI) is the reference standard for assessing cardiac structure as well as function. However, CMRI data presents large variations among different centers, vendors, and patients with various cardiovascular diseases. Since typical deep-learning-based segmentation methods are usually trained using a limited number of ground truth annotations, they may not generalize well to unseen MR images, due to the variations between the training and testing data. In this study, we proposed an approach towards building a generalizable deep-learning-based model for cardiac structure segmentations from multi-vendor,multi-center and multi-diseases CMRI data. We used a novel combination of image augmentation and a consistency loss function to improve model robustness to typical variations in CMRI data. The proposed image augmentation strategy leverages un-labeled data by a) using CycleGAN to generate images in different styles and b) exchanging the low-frequency features of images from different vendors. Our model architecture was based on an attention-gated U-Net model that learns to focus on cardiac structures of varying shapes and sizes while suppressing irrelevant regions. The proposed augmentation and consistency training method demonstrated improved performance on CMRI images from new vendors and centers. When evaluated using CMRI data from 4 vendors and 6 clinical center, our method was generally able to produce accurate segmentations of cardiac structures.